Effect of accounting for crash severity on the relationship between mass reduction and crash frequency and risk per crash
Tom Wenzel, Lawrence Berkeley National Laboratory
Draft report: March 30, 2015
  
The 2012 LBNL Phase 2 study, which analyzed the effect of mass reduction on crash frequency and casualty risk per crash, as well as the DRI and LBNL simultaneous two-stage regression models, which analyzed the effect on crash frequency and US fatality risk per crash, found that mass reduction was associated with increases in crash frequency but no effect on, or even decreases in, risk per crash, for all types of vehicles (Wenzel 2012, Wenzel 2013).  These results were unexpected: one would expect that lighter vehicles, with better maneuverability and shorter braking distances, would have lower crash frequency than heavier vehicles; and that heavier vehicles would have lower risk once a crash has occurred than lighter vehicles.  LBNL examined the sensitivity of the results on crash frequency to adding several additional explanatory variables to the baseline NHTSA regression model; none of these variables, either independently or combined, changed the relationship between mass reduction and increased crash frequency (Wenzel 2014).

In his 2012 report Kahane suggested two possible explanations for these unexpected results: that the analysis did not account for the severity of the crash, and possible bias in the crashes reported to police in different states, with less severe crashes being under-reported for certain vehicle types (Kahane 2012).  The full text from Kahane 2012 is included in the Appendix.  (In his preliminary 2011 report Kahane speculated that owners of heavier vehicles such as SUVs and pickups would be less likely to report minor crashes than owners of lighter passenger cars, because the heavier vehicles would sustain less damage in a two-vehicle crash; however this suggestion was removed from the final report.  It would seem just as likely that owners of vehicles that are un- or under-insured would refrain from reporting a minor crash; their vehicles are likely to be inexpensive passenger cars rather than heavier and more expensive pickups or SUVs.)

This report analyzes the first of Kahane's explanations for the unexpected result of mass reduction being associated with decreased risk per crash: that the regression models do not account for the severity of the crash.  Of the 13 states whose police-reported crash data were used, seven report the severity of the damage sustained by the subject vehicle, two report whether the vehicle had to be towed from the crash scene, and three report both. Because Washington does not report either of these measures of crash severity, it had to be excluded from the analysis. For the seven states that report crash damage severity, vehicles that were described as "disabled" were included, while vehicles with functional, none, or unknown damage were excluded.  95% of crashes involving a casualty occurred in states other than Washington; of these crashes, 46% were severe crashes.  98% of casualties occurred in states other than Washington; of these casualties, 90% occurred in severe crashes.  

Table 1 compares the estimates for selected variables for the crash frequency and casualty risk per crash regression models, under two regression models: the "Base" estimates are from the NHTSA baseline model, while the "Ex WA" are from a model which excludes all crashes that occurred in Washington. Values in red are statistically significant at the 95% level, while the estimates shaded green are in the expected direction, and those shaded yellow are in the opposite direction.  Table 1 indicates that excluding the Washington crashes has only a small effect on the estimated coefficients for crash frequency and casualty risk per crash.  (Estimated coefficients for all variables included in the model are shown in Appendix A.)

Table 1. Estimated effect on crash frequency (crashes per mile traveled, Cr/M) and casualty risk per crash (C/Cr), NHTSA baseline model and excluding crashes in Washington
Variable
                       Crash frequency (crashes per VMT)
                             Casualties per crash

                                     Cars
                                 Light Trucks
                                 CUVs/minivans
                                     Cars
                                 Light Trucks
                                 CUVs/minivans

                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Base
                                     Ex WA
                                     Base
UNDRWT00
                                     1.97%
                                     2.02%
                                     1.43%
                                     1.46%
                                       -- 
                                       -- 
                                     0.17%
                                     0.22%
                                    -0.12%
                                    -0.15%
                                       -- 
                                       -- 
OVERWT00
                                     1.34%
                                     1.37%
                                     0.93%
                                     0.86%
                                       -- 
                                       -- 
                                    -1.01%
                                    -1.03%
                                    -0.71%
                                    -0.73%
                                       -- 
                                       -- 
LBS100
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.93%
                                     0.85%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                    -0.26%
                                    -0.22%
FOOTPRNT
                                     0.85%
                                     0.86%
                                     1.09%
                                     1.12%
                                    -0.53%
                                    -0.40%
                                     0.42%
                                     0.36%
                                    -0.17%
                                    -0.14%
                                     0.79%
                                     0.87%
TWODOOR
                                     4.98%
                                     5.48%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     1.29%
                                     1.24%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
SUV
                                       -- 
                                       -- 
                                    -0.80%
                                    -0.47%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     1.85%
                                     1.50%
                                       -- 
                                       -- 
HDPU
                                       -- 
                                       -- 
                                    -3.40%
                                    -3.72%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                    -0.28%
                                    -0.94%
                                       -- 
                                       -- 
BLOCKER1
                                       -- 
                                       -- 
                                    -0.21%
                                    -1.09%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.60%
                                     0.67%
                                       -- 
                                       -- 
BLOCKER2
                                       -- 
                                       -- 
                                    -0.69%
                                    -0.28%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                    -4.82%
                                    -4.75%
                                       -- 
                                       -- 
MINIVAN
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     2.68%
                                     1.96%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     13.0%
                                    14.36%
ROLLCURT
                                    -1.93%
                                    -1.88%
                                       -- 
                                       -- 
                                    -0.89%
                                    -0.81%
                                    -3.97%
                                    -3.91%
                                       -- 
                                       -- 
                                    -1.85%
                                    -1.81%
CURTAIN
                                    -0.10%
                                     0.00%
                                       -- 
                                       -- 
                                    -3.40%
                                    -2.94%
                                    -3.02%
                                    -2.94%
                                       -- 
                                       -- 
                                    -3.63%
                                    -3.03%
COMBO
                                     2.36%
                                     2.55%
                                       -- 
                                       -- 
                                    -0.37%
                                    -0.79%
                                    -1.58%
                                    -1.66%
                                       -- 
                                       -- 
                                     5.13%
                                     5.49%
TORSO
                                    -5.43%
                                    -5.07%
                                       -- 
                                       -- 
                                    -4.81%
                                    -4.59%
                                    -10.4%
                                    -10.4%
                                       -- 
                                       -- 
                                    -2.80%
                                    -2.91%
ABS
                                    -6.14%
                                    -5.73%
                                       -- 
                                       -- 
                                    -19.6%
                                    -19.0%
                                    -1.82%
                                    -1.98%
                                       -- 
                                       -- 
                                    -9.11%
                                    -9.08%
ESC
                                    -16.8%
                                    -16.7%
                                    -15.7%
                                    -15.1%
                                    -1.20%
                                    -1.28%
                                    -12.0%
                                    -12.4%
                                    -18.2%
                                    -18.3%
                                    -10.1%
                                    -10.2%
AWD
                                       -- 
                                       -- 
                                     44.9%
                                     39.4%
                                     10.7%
                                     8.84%
                                       -- 
                                       -- 
                                     0.96%
                                     1.07%
                                    -4.86%
                                    -4.14%
DRVMALE
                                     6.43%
                                     6.66%
                                    -0.95%
                                    -1.12%
                                     1.90%
                                     2.02%
                                    -0.28%
                                    -0.01%
                                    -0.14%
                                    -0.06%
                                     7.94%
                                     8.09%
M14_30
                                     4.41%
                                     4.36%
                                     3.83%
                                     3.76%
                                     5.11%
                                     5.03%
                                     1.05%
                                     1.02%
                                     0.64%
                                     0.63%
                                     0.58%
                                     0.52%
M30_50
                                     0.35%
                                     0.33%
                                     0.39%
                                     0.40%
                                     0.18%
                                     0.18%
                                     0.02%
                                     0.02%
                                    -0.16%
                                    -0.17%
                                    -0.15%
                                    -0.15%
M50_70
                                     0.16%
                                     0.16%
                                     0.33%
                                     0.31%
                                     0.61%
                                     0.63%
                                     1.30%
                                     1.27%
                                     1.12%
                                     1.11%
                                     1.26%
                                     1.28%
M70_96
                                     3.98%
                                     3.93%
                                     4.42%
                                     4.42%
                                     3.40%
                                     3.27%
                                     2.37%
                                     2.36%
                                     1.87%
                                     1.87%
                                     1.87%
                                     1.95%
F14_30
                                     3.49%
                                     3.46%
                                     3.57%
                                     3.53%
                                     3.62%
                                     3.61%
                                     0.73%
                                     0.75%
                                     0.60%
                                     0.62%
                                     1.25%
                                     1.24%
F30_50
                                    -0.04%
                                    -0.05%
                                     0.01%
                                     0.03%
                                    -0.01%
                                     0.00%
                                    -0.45%
                                    -0.43%
                                    -0.14%
                                    -0.12%
                                    -0.25%
                                    -0.18%
F50_70
                                     0.71%
                                     0.70%
                                     0.93%
                                     0.91%
                                     1.10%
                                     1.09%
                                     1.09%
                                     1.08%
                                     1.34%
                                     1.32%
                                     2.06%
                                     2.08%
F70_96
                                     4.37%
                                     4.33%
                                     3.37%
                                     3.31%
                                     3.43%
                                     3.36%
                                     1.84%
                                     1.86%
                                    -0.37%
                                    -0.16%
                                     0.65%
                                     0.58%
NITE
                                     32.4%
                                     32.4%
                                     37.8%
                                     37.2%
                                     25.2%
                                     25.2%
                                     44.2%
                                     43.1%
                                     42.2%
                                     40.9%
                                     32.1%
                                     32.0%
RURAL
                                     21.3%
                                     20.9%
                                     20.3%
                                     19.3%
                                     15.6%
                                     15.2%
                                     48.5%
                                     48.4%
                                     42.2%
                                     41.4%
                                     43.7%
                                     43.3%
SPDLIM55
                                     62.1%
                                     60.4%
                                     41.9%
                                     41.7%
                                     34.5%
                                     33.4%
                                     81.9%
                                     82.9%
                                     86.3%
                                     88.2%
                                     87.3%
                                     88.3%
* Values in red are statistically significant at the 95% level.  Estimates shaded green are in the expected direction, those shaded yellow are in the opposite direction.

Table 2 compares the estimates for selected variables from the "Ex WA" model in Table 1 with a model that includes only vehicles in crashes in which at least one involved vehicle was so disabled from the crash that it had to be towed from the crash scene (i.e. excludes non-severe crashes, labeled "Ex NS" in the table). Again, values in red are statistically significant at the 95% level, while the estimates shaded green are in the expected direction, and those shaded yellow are in the opposite direction (estimated coefficients for all variables included in the model are shown in Appendix A.)

As Kahane and LBNL noted in their 2012 studies, certain vehicle technologies, such as ABS and ESC, should reduce crash frequency, while others, such as side airbags in cars and CUVs/minivans, and supplementary frontal bumpers (BLOCKER1) or greater bumper overlap (BLOCKER2) on light trucks, should reduce casualty risk once a crash has occurred.  And one might expect that, all else held equal, mass reduction would reduce braking distance, and footprint reduction (or more specifically wheelbase) would improve maneuverability, both of which would result in reduced crash frequency.  On the other hand, one might expect that the added mass of AWD might increase braking distance, and thus increase crash frequency, while decreasing risk per crash in the subject vehicle but perhaps increasing societal risk per crash. 

Table 2 presents the estimated effects on crash frequency (crashes per VMT) and casualty risk per crash by vehicle type.  For cars, two-door cars are associated with a higher crash frequency (5.48%) and risk per crash (1.24%) than four-door cars, in the "Ex WA" model.  Excluding the most severe crashes (the "Ex NS" model) has little effect on the TWODOOR variable (5.93%, 1.40%).

As expected, the four side airbag variables all are associated with a decrease in risk per crash (although only two are statistically-significant) in the "Ex WA" model; however, two are also associated with an unexpected decrease in crash frequency, and COMBO is associated with an unexpected increase in crash frequency.  Excluding the most severe crashes in the "Ex NS" model has little effect on these variables.

The crash avoidance technologies ABS and ESC are associated with a large decrease in crash frequency, as expected, in the "Ex WA" model (a 5.73% and 16.7% decrease, respectively); however, they also are associated with large unexpected decreases in risk per crash (a 1.98% decrease for ABS, and a 12.4% decrease for ESC).  Excluding the most severe crashes has little effect on crash frequency for ABS (from a 5.73% decrease to a 7.62% decrease) or ESC (from a 16.7% decrease to a 16.4% decrease); excluding severe crashes has little effect on casualty risk per crash for ESC (from a 12.4% decrease to a 12.2% decrease), but results in a small decrease in risk per crash for ABS (from a 1.98% decrease to a 1.39% decrease).

Regarding driver gender, male drivers are associated with an expected large increase in crash frequency (6.66%), but no effect on risk per crash, in the "Ex WA" model.  Excluding severe crashes increases the expected large increase in crash frequency to 10.2%, but also results in a large decrease in risk per crash (to 4.53%), in the "Ex NS" model.  This result is expected, as men are assumed to be more robust and better able to withstand injury than women in a severe crash.  Regarding driver age, the youngest and oldest drivers are associated with the largest increase in crash frequency, as expected, in the "Ex WA" model; and seven of the eight age groups are also associated with increases in risk per crash, suggesting that drivers older than 50 are less robust than 50-year old drivers.  Excluding the most severe crashes increases the association between driver age and crash frequency for the youngest and oldest drivers, while decreasing the association between driver age and risk per crash.  

Under the "Ex WA" model, driving at night, in a rural county, and on a high-speed road are each associated with large increases in crash frequency (32.4%, 20.9%, and 60.4%, respectively), but even larger increases in risk per crash (43.1%, 48.4%, and 82.9%), particularly on high-speed roads. Excluding the most severe crashes shifts some of the estimated effect from risk per crash to crash severity, for each variable in the "Ex NS" model; however, each variable is still associated with a fairly large increase in risk per crash (33.7% for night, 44.1% for rural roads, and 60.6% for high-speed roads).  For example, driving on a high speed road is associated with a 60% increase in crash frequency and a 83% using all crashes; excluding the most severe crashes increases the association of driving on a high speed road to a 98% increase in crash frequency, while reducing the association to a 61% increase in risk per crash.  

Table 2. Estimated effect on crash frequency (crashes per mile traveled) and casualty risk per crash, excluding crashes in Washington ("Ex WA") and excluding non-severe crashes ("Ex NS")
Variable
                       Crash frequency (crashes per VMT)
                             Casualties per crash

                                     Cars
                                 Light Trucks
                                 CUVs/minivans
                                     Cars
                                 Light Trucks
                                 CUVs/minivans

                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
UNDRWT00
                                     2.02%
                                     2.08%
                                     1.46%
                                     1.65%
                                       -- 
                                       -- 
                                                                          0.22%
                                                                          0.13%
                                                                         -0.15%
                                                                         -0.42%
                                       -- 
                                       -- 
OVERWT00
                                     1.37%
                                     1.17%
                                     0.86%
                                     0.98%
                                       -- 
                                       -- 
                                                                         -1.03%
                                                                         -0.65%
                                                                         -0.73%
                                                                         -1.16%
                                       -- 
                                       -- 
LBS100
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.85%
                                     0.95%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -0.22%
                                                                         -0.26%
FOOTPRNT
                                     0.86%
                                     1.48%
                                     1.12%
                                     1.07%
                                    -0.40%
                                    -0.03%
                                                                          0.36%
                                                                         -0.29%
                                                                         -0.14%
                                                                         -0.11%
                                                                          0.87%
                                                                          1.17%
TWODOOR
                                     5.48%
                                     5.93%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          1.24%
                                                                          1.40%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
SUV
                                       -- 
                                       -- 
                                    -0.47%
                                    -0.27%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          1.50%
                                                                          0.19%
                                       -- 
                                       -- 
HDPU
                                       -- 
                                       -- 
                                    -3.72%
                                    -3.35%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -0.94%
                                                                         -2.25%
                                       -- 
                                       -- 
BLOCKER1
                                       -- 
                                       -- 
                                    -1.09%
                                    -0.35%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          0.67%
                                                                          1.64%
                                       -- 
                                       -- 
BLOCKER2
                                       -- 
                                       -- 
                                    -0.28%
                                    -2.04%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -4.75%
                                                                         -2.69%
                                       -- 
                                       -- 
MINIVAN
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     1.96%
                                    -1.67%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          14.4%
                                                                          24.3%
ROLLCURT
                                    -1.88%
                                    -1.74%
                                       -- 
                                       -- 
                                    -0.81%
                                    -0.74%
                                                                         -3.91%
                                                                         -3.75%
                                       -- 
                                       -- 
                                                                         -1.81%
                                                                         -1.80%
CURTAIN
                                     0.00%
                                     0.20%
                                       -- 
                                       -- 
                                    -2.94%
                                    -0.58%
                                                                         -2.94%
                                                                         -3.48%
                                       -- 
                                       -- 
                                                                         -3.03%
                                                                         -5.99%
COMBO
                                     2.55%
                                     2.82%
                                       -- 
                                       -- 
                                    -0.79%
                                    -1.60%
                                                                         -1.66%
                                                                         -1.58%
                                       -- 
                                       -- 
                                                                          5.49%
                                                                          7.26%
TORSO
                                    -5.07%
                                    -5.93%
                                       -- 
                                       -- 
                                    -4.59%
                                    -7.09%
                                                                         -10.4%
                                                                         -9.12%
                                       -- 
                                       -- 
                                                                         -2.91%
                                                                         -0.26%
ABS
                                    -5.73%
                                    -7.62%
                                       -- 
                                       -- 
                                    -19.0%
                                    -19.0%
                                                                         -1.98%
                                                                         -1.39%
                                       -- 
                                       -- 
                                                                         -9.08%
                                                                         -6.16%
ESC
                                    -16.7%
                                    -16.4%
                                    -15.1%
                                    -19.8%
                                    -1.28%
                                    -5.08%
                                                                         -12.4%
                                                                         -12.2%
                                                                         -18.3%
                                                                         -14.4%
                                                                         -10.2%
                                                                         -7.65%
AWD
                                       -- 
                                       -- 
                                     39.4%
                                     37.6%
                                     8.84%
                                     10.5%
                                       -- 
                                       -- 
                                                                          1.07%
                                                                          0.42%
                                                                         -4.14%
                                                                         -6.69%
DRVMALE
                                     6.66%
                                     10.2%
                                    -1.12%
                                    -0.54%
                                     2.02%
                                     3.76%
                                                                         -0.01%
                                                                         -4.53%
                                                                         -0.06%
                                                                         -1.94%
                                                                          8.09%
                                                                          7.50%
M14_30
                                     4.36%
                                     5.51%
                                     3.76%
                                     4.42%
                                     5.03%
                                     6.06%
                                                                          1.02%
                                                                         -0.07%
                                                                          0.63%
                                                                         -0.32%
                                                                          0.52%
                                                                         -0.78%
M30_50
                                     0.33%
                                     0.66%
                                     0.40%
                                     0.56%
                                     0.18%
                                     0.40%
                                                                          0.02%
                                                                         -0.25%
                                                                         -0.17%
                                                                         -0.37%
                                                                         -0.15%
                                                                         -0.35%
M50_70
                                     0.16%
                                     0.35%
                                     0.31%
                                     0.34%
                                     0.63%
                                     0.85%
                                                                          1.27%
                                                                          1.22%
                                                                          1.11%
                                                                          1.16%
                                                                          1.28%
                                                                          1.12%
M70_96
                                     3.93%
                                     4.86%
                                     4.42%
                                     5.05%
                                     3.27%
                                     4.03%
                                                                          2.36%
                                                                          1.66%
                                                                          1.87%
                                                                          1.52%
                                                                          1.95%
                                                                          1.17%
F14_30
                                     3.46%
                                     4.70%
                                     3.53%
                                     4.72%
                                     3.61%
                                     4.85%
                                                                          0.75%
                                                                         -0.20%
                                                                          0.62%
                                                                         -0.44%
                                                                          1.24%
                                                                          0.03%
F30_50
                                    -0.05%
                                     0.06%
                                     0.03%
                                    -0.11%
                                     0.00%
                                    -0.04%
                                                                         -0.43%
                                                                         -0.67%
                                                                         -0.12%
                                                                         -0.14%
                                                                         -0.18%
                                                                         -0.23%
F50_70
                                     0.70%
                                     1.13%
                                     0.91%
                                     0.93%
                                     1.09%
                                     1.34%
                                                                          1.08%
                                                                          0.86%
                                                                          1.32%
                                                                          1.39%
                                                                          2.08%
                                                                          1.86%
F70_96
                                     4.33%
                                     5.21%
                                     3.31%
                                     3.42%
                                     3.36%
                                     4.18%
                                                                          1.86%
                                                                          1.23%
                                                                         -0.16%
                                                                         -0.03%
                                                                          0.58%
                                                                         -0.18%
NITE
                                     32.4%
                                     41.1%
                                     37.2%
                                     47.3%
                                     25.2%
                                     30.5%
                                                                          43.1%
                                                                          33.7%
                                                                          40.9%
                                                                          29.2%
                                                                          32.0%
                                                                          29.7%
RURAL
                                     20.9%
                                     23.8%
                                     19.3%
                                     22.1%
                                     15.2%
                                     19.1%
                                                                          48.4%
                                                                          44.1%
                                                                          41.4%
                                                                          37.5%
                                                                          43.3%
                                                                          42.9%
SPDLIM55
                                     60.4%
                                     98.0%
                                     41.7%
                                     79.6%
                                     33.4%
                                     68.5%
                                                                          82.9%
                                                                          60.6%
                                                                          88.2%
                                                                          62.3%
                                                                          88.3%
                                                                          71.7%
* Values in red are statistically significant at the 95% level.  Estimates shaded green are in the expected direction, those shaded yellow are in the opposite direction.

The results described above for cars are similar for light trucks and CUVs/minivans:  

     :: The two measures to make light trucks more compatible with car-like frontal structures, a secondary bumper (BLOCKER1) and greater overlap in bumper heights between light trucks and cars (BLOCKER2), are expected to have little association with crash frequency, but decrease casualty risk per crash.  In the baseline model BLOCKER1 is associated with an unexpected decrease in crash frequency but not risk per crash, while BLOCKER2 has the expected relationship, no effect on crash frequency but a decrease in risk per crash.  However, after removing non-severe crashes in the "Ex NS" model, BLOCKER2 is associated with a decrease in both crash frequency and risk per crash.
     
     :: For CUVs, three of the four side airbag variables are associated with an expected decrease in risk per crash; however, combination side airbags are associated with a statistically-significant increase in risk per crash, even after excluding non-severe crashes (from a 5.49% increase to a 7.26% increase.  All four side airbag variables are associated with an unexpected decrease in crash frequency, particularly curtain (a 2.94% decrease) and torso side airbags (a 4.59% decrease).  Excluding non-severe crashes decreases the estimated effect of curtain side airbags on crash frequency (from a 2.94% decrease to a 0.58% decrease, but increases the effect of torso side airbags (from a 4.59% decrease to a 7.09% decrease) on crash frequency.
     
     :: ABS in CUVs/minivans, and ESC in light trucks, is associated with a decrease in crash frequency, as expected, but an unexpected decrease in risk per crash.  ESC in CUVs/minivans is associated with a much higher decrease in risk per crash than in crash frequency; removing non-severe crashes, increases the effect on crash frequency (from a 1.28% decrease to a 5.08% decrease), and decreases the effect on risk per crash from a 10.2% decrease to a 7.65% decrease), but the effect on crash frequency is still lower than that on risk per crash.
     
     :: AWD is associated with a large expected increase in crash frequency in both light trucks and CUVs/minivans, as well as an unexpected decrease in risk per crash in CUVs/minivans; these results do not change after excluding non-severe crashes.
     
     :: Male drivers have no effect on crash frequency or risk per crash in light trucks, but for CUVs/minivans are associated with an expected increase in crash frequency, as well as an unexpected increase in risk per crash.  As with cars, the youngest and oldest drivers are associated with an increase in crash frequency in light trucks and CUVs/minivans, which increases after non-severe crashes are excluded. 
     
     :: As with cars, driving at night, in a rural county, and on a high-speed road are each associated with large expected increases in crash frequency, but even larger unexpected increases in risk per crash, in light trucks and CUVS/minivans.  Excluding non-severe crashes shifts only some of the estimated effect from risk per crash to crash frequency, for each variable.   

Table 3 compares the results from the simultaneous two-stage model, which simultaneously estimates the two components of U.S. fatality risk per VMT, crash frequency and fatality risk per crash.  As in Tables 1 and 2, values in red are statistically significant at the 95% level, while the estimates shaded green are in the expected direction, and those shaded yellow are in the opposite direction.

Comparing the "Ex WA" estimates in Table 2 with the "Base" model estimates in Table 3, we see that the simultaneous two-stage model estimates several substantial differences in the effectiveness of side airbags in fatality risk per crash: a smaller decrease in fatality risk per crash for torso airbags in cars (a 1.36% vs. 10.4% decrease), and a large increase in risk per crash for combination side airbags (a 9.48% decrease vs. a 5.49% increase) and a large increase in risk per crash for torso side airbags (a 5.61% increase vs. a 2.91% decrease) in CUVs/minivans.  While the two-stage fatality model estimates comparable decreases in crash frequency, as expected, from ABS and ESC to those in the casualty model for all three types of vehicles, the two-stage fatality model estimates larger decreases in risk per crash for ABS in cars (a 5.14% decrease vs. a 1.98% decrease), but unexpected increases in risk per crash for ESC in cars (a 6.22% increase rather than a 12.4% decrease), for ABS in CUVs/minivans (a 5.39% increase rather than a 9.08% decrease), and for ESC in light trucks (a 2.53% decrease rather than a 18.3% decrease) and CUVs/minivans (a 1.39% decrease rather than a 10.2% decrease).  For AWD, the two-stage fatality model estimates a similar increase in crash frequency in light trucks and CUVs/minivans to the baseline casualty risk model, as expected, but also estimates unexpected, very large reductions in risk per crash (a 49.2% decrease for light trucks, and a 30.3% decrease for CUVs/minivans).  

Table 3. Simultaneous two-stage model estimated effect on U.S. crash frequency (crashes per mile traveled) and fatality risk per crash, baseline and excluding non-severe crashes
Variable
                       Crash frequency (crashes per VMT)
                             Casualties per crash

                                     Cars
                                 Light Trucks
                                 CUVs/minivans
                                     Cars
                                 Light Trucks
                                 CUVs/minivans

                                     Base
                                     Ex NS
                                     Base
                                     Ex NS
                                     Base
                                     Ex NS
                                     Base
                                     Ex NS
                                     Base
                                     Ex NS
                                     Base
                                     Ex NS
UNDRWT00
                                     1.83%
                                     1.89%
                                     1.47%
                                     1.65%
                                       -- 
                                       -- 
                                                                         -0.62%
                                                                         -1.08%
                                                                         -1.11%
                                                                         -1.35%
                                       -- 
                                       -- 
OVERWT00
                                     1.25%
                                     0.95%
                                     0.95%
                                     0.96%
                                       -- 
                                       -- 
                                                                         -1.05%
                                                                         -1.20%
                                                                         -1.53%
                                                                         -1.59%
                                       -- 
                                       -- 
LBS100
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.84%
                                     0.78%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -1.55%
                                                                         -1.40%
FOOTPRNT
                                     0.99%
                                     1.66%
                                     1.14%
                                     1.07%
                                    -0.35%
                                     0.18%
                                                                          1.14%
                                                                          0.62%
                                                                         -1.43%
                                                                         -1.48%
                                                                          2.45%
                                                                          1.67%
TWODOOR
                                     5.13%
                                     5.77%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          2.03%
                                                                          1.15%
                                       
                                       
                                       -- 
                                       -- 
SUV
                                       -- 
                                       -- 
                                    -2.32%
                                     0.01%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          16.7%
                                                                          12.8%
                                       -- 
                                       -- 
HDPU
                                       -- 
                                       -- 
                                    -3.08%
                                    -3.57%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          5.37%
                                                                          5.83%
                                       -- 
                                       -- 
BLOCKER1
                                       -- 
                                       -- 
                                    -0.93%
                                    -1.38%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -1.86%
                                                                         -1.01%
                                       -- 
                                       -- 
BLOCKER2
                                       -- 
                                       -- 
                                    -0.70%
                                    -2.26%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -1.18%
                                                                          0.29%
                                       -- 
                                       -- 
MINIVAN
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     2.70%
                                    -3.43%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -8.83%
                                                                         -5.31%
ROLLCURT
                                    -1.19%
                                    -1.16%
                                       -- 
                                       -- 
                                    -0.66%
                                    -0.59%
                                                                         -0.38%
                                                                         -1.04%
                                       -- 
                                       -- 
                                                                         -1.42%
                                                                         -1.05%
CURTAIN
                                    -0.04%
                                     0.58%
                                       -- 
                                       -- 
                                    -3.87%
                                    -0.97%
                                                                         -0.06%
                                                                         -1.21%
                                       -- 
                                       -- 
                                                                          1.11%
                                                                         -1.92%
COMBO
                                     2.00%
                                     2.54%
                                       -- 
                                       -- 
                                     0.00%
                                    -2.68%
                                                                         -2.45%
                                                                         -4.36%
                                       -- 
                                       -- 
                                                                         -9.48%
                                                                         -6.70%
TORSO
                                    -6.35%
                                    -6.32%
                                       -- 
                                       -- 
                                    -4.48%
                                    -7.71%
                                                                         -1.36%
                                                                         -3.36%
                                       -- 
                                       -- 
                                                                          5.61%
                                                                          11.5%
ABS
                                    -5.99%
                                    -8.44%
                                       -- 
                                       -- 
                                    -19.4%
                                    -17.8%
                                                                         -5.14%
                                                                         -3.68%
                                       -- 
                                       -- 
                                                                          5.39%
                                                                          2.38%
ESC
                                    -17.1%
                                    -16.6%
                                    -17.1%
                                    -19.1%
                                    -1.52%
                                    -4.71%
                                                                          6.22%
                                                                          3.09%
                                                                         -2.53%
                                                                         -0.90%
                                                                         -1.39%
                                                                         -2.79%
AWD
                                       -- 
                                       -- 
                                     44.8%
                                     31.5%
                                     10.0%
                                     8.05%
                                       -- 
                                       -- 
                                                                         -49.2%
                                                                         -47.0%
                                                                         -30.3%
                                                                         -32.6%
DRVMALE
                                     5.54%
                                     9.77%
                                    -2.86%
                                    -1.68%
                                     0.53%
                                     2.59%
                                                                          30.9%
                                                                          23.1%
                                                                          24.4%
                                                                          21.5%
                                                                          36.3%
                                                                          32.5%
M14_30
                                     4.48%
                                     5.45%
                                     3.71%
                                     4.36%
                                     4.93%
                                     5.89%
                                                                          0.24%
                                                                         -0.79%
                                                                         -0.07%
                                                                         -0.82%
                                                                         -1.01%
                                                                         -2.28%
M30_50
                                     0.50%
                                     0.73%
                                     0.44%
                                     0.64%
                                     0.26%
                                     0.49%
                                                                          0.97%
                                                                          0.71%
                                                                          0.79%
                                                                          0.53%
                                                                          0.71%
                                                                          0.60%
M50_70
                                     0.11%
                                     0.30%
                                     0.24%
                                     0.26%
                                     0.59%
                                     0.83%
                                                                          2.34%
                                                                          2.17%
                                                                          1.16%
                                                                          1.09%
                                                                          1.59%
                                                                          1.53%
M70_96
                                     4.26%
                                     4.93%
                                     4.33%
                                     4.79%
                                     3.47%
                                     4.04%
                                                                          4.00%
                                                                          2.99%
                                                                          3.35%
                                                                          2.89%
                                                                          3.66%
                                                                          2.49%
F14_30
                                     3.68%
                                     4.77%
                                     3.46%
                                     4.72%
                                     3.64%
                                     4.97%
                                                                         -0.53%
                                                                         -1.69%
                                                                          0.37%
                                                                         -0.98%
                                                                          1.36%
                                                                         -0.25%
F30_50
                                     0.05%
                                     0.11%
                                     0.01%
                                    -0.12%
                                    -0.01%
                                    -0.08%
                                                                          0.09%
                                                                         -0.03%
                                                                          0.27%
                                                                          0.35%
                                                                         -0.40%
                                                                         -0.12%
F50_70
                                     0.74%
                                     1.08%
                                     0.81%
                                     0.82%
                                     1.04%
                                     1.22%
                                                                          2.67%
                                                                          2.24%
                                                                          2.62%
                                                                          2.53%
                                                                          2.55%
                                                                          2.50%
F70_96
                                     4.51%
                                     5.24%
                                     3.68%
                                     3.46%
                                     3.42%
                                     4.12%
                                                                          3.55%
                                                                          2.62%
                                                                          2.21%
                                                                          2.67%
                                                                          3.93%
                                                                          3.25%
NITE
                                     31.2%
                                     37.1%
                                     41.0%
                                     44.6%
                                     30.5%
                                     29.8%
                                                                           119%
                                                                           110%
                                                                          93.0%
                                                                          90.1%
                                                                          86.2%
                                                                          96.5%
RURAL
                                     24.3%
                                     22.4%
                                     23.9%
                                     19.4%
                                     25.1%
                                     20.8%
                                                                           162%
                                                                           177%
                                                                           145%
                                                                           159%
                                                                           149%
                                                                           167%
SPDLIM55
                                     66.7%
                                     97.4%
                                     51.4%
                                     80.8%
                                     44.6%
                                     69.7%
                                                                           205%
                                                                           153%
                                                                           222%
                                                                           164%
                                                                           232%
                                                                           186%
* Values in red are statistically significant at the 95% level.  Estimates shaded green are in the expected direction, those shaded yellow are in the opposite direction.

For the most part, the estimated effects of driver age in the two-stage fatality risk model are comparable to those in the casualty risk model; however, the two-stage fatality risk model estimates large, unexpected increases in risk per crash for male drivers, for each vehicle type (31% for cars, 24% for light trucks, and 36% for CUVs/minivans).  Similarly, the large unexpected increases in risk per crash in the casualty risk model are even higher in the two-stage fatality risk model.

The effect of removing non-severe crashes from the analysis using the two-stage fatality model can be seen by comparing the two sets of estimates in Table 3.  As in Table 2, removing the non-severe crashes somewhat improves the estimated effects for some variables, but does not "correct" the unexpected results from the baseline model.  For example, combination and torso side airbags in cars are associated with larger decreases in risk per crash after removing non-severe crashes (from a 2.45% to a 4.36% decrease for combination side airbags, and from a 1.36% decrease to a 3.36% decrease for torso side airbags); however, combination side airbags continue to be associated with an increase, and torso side airbags with a decrease, in crash frequency in cars.  The crash avoidance technologies continue to be associated with expected large decreases in crash frequency, but also a large decrease in risk per crash in cars.

While removing severe crashes somewhat decreases the unexpected increases in risk per crash for male drivers, and in some cases driving at night, in rural counties, or on high-speed roads, these unexpected increases in risk per crash remain quite large in the two-stage fatality model after removing severe crashes.

These results suggest that accounting for crash severity, by excluding crashes where all involved vehicles were able to be driven away from the crash scene, for the most part has little effect on the unexpected relationships between crash frequency, casualty risk per crash, and vehicle characteristics, driver age and gender, and crash circumstances, in either the two separate crash frequency and casualty risk per crash models developed in Phase 2 (Table 2), or the simultaneous two-stage U.S. fatality risk model (Table 3).




Appendix A: Detailed regression model results

Table A-1. Estimated effect on crash frequency (crashes per mile traveled) and casualty risk per crash, NHTSA baseline model ("Base") and excluding crashes in WA ("Ex WA")
Variable
                       Crash frequency (crashes per VMT)
                             Casualties per crash

                                     Cars
                                 Light Trucks
                                 CUVs/minivans
                                     Cars
                                 Light Trucks
                                 CUVs/minivans

                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
                                     Base
                                     Ex WA
UNDRWT00
                                     1.97%
                                     2.02%
                                     1.43%
                                     1.46%
                                       -- 
                                       -- 
                                     0.17%
                                     0.22%
                                    -0.12%
                                    -0.15%
                                       -- 
                                       -- 
OVERWT00
                                     1.34%
                                     1.37%
                                     0.93%
                                     0.86%
                                       -- 
                                       -- 
                                    -1.01%
                                    -1.03%
                                    -0.71%
                                    -0.73%
                                       -- 
                                       -- 
LBS100
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.93%
                                     0.85%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                    -0.26%
                                    -0.22%
FOOTPRNT
                                     0.85%
                                     0.86%
                                     1.09%
                                     1.12%
                                    -0.53%
                                    -0.40%
                                     0.42%
                                     0.36%
                                    -0.17%
                                    -0.14%
                                     0.79%
                                     0.87%
TWODOOR
                                     4.98%
                                     5.48%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     1.29%
                                     1.24%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
SUV
                                       -- 
                                       -- 
                                    -0.80%
                                    -0.47%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     1.85%
                                     1.50%
                                       -- 
                                       -- 
HDPU
                                       -- 
                                       -- 
                                    -3.40%
                                    -3.72%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                    -0.28%
                                    -0.94%
                                       -- 
                                       -- 
BLOCKER1
                                       -- 
                                       -- 
                                    -0.21%
                                    -1.09%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.60%
                                     0.67%
                                       -- 
                                       -- 
BLOCKER2
                                       -- 
                                       -- 
                                    -0.69%
                                    -0.28%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                    -4.82%
                                    -4.75%
                                       -- 
                                       -- 
MINIVAN
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     2.68%
                                     1.96%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     13.0%
                                    14.36%
ROLLCURT
                                    -1.93%
                                    -1.88%
                                       -- 
                                       -- 
                                    -0.89%
                                    -0.81%
                                    -3.97%
                                    -3.91%
                                       -- 
                                       -- 
                                    -1.85%
                                    -1.81%
CURTAIN
                                    -0.10%
                                     0.00%
                                       -- 
                                       -- 
                                    -3.40%
                                    -2.94%
                                    -3.02%
                                    -2.94%
                                       -- 
                                       -- 
                                    -3.63%
                                    -3.03%
COMBO
                                     2.36%
                                     2.55%
                                       -- 
                                       -- 
                                    -0.37%
                                    -0.79%
                                    -1.58%
                                    -1.66%
                                       -- 
                                       -- 
                                     5.13%
                                     5.49%
TORSO
                                    -5.43%
                                    -5.07%
                                       -- 
                                       -- 
                                    -4.81%
                                    -4.59%
                                    -10.4%
                                    -10.4%
                                       -- 
                                       -- 
                                    -2.80%
                                    -2.91%
ABS
                                    -6.14%
                                    -5.73%
                                       -- 
                                       -- 
                                    -19.6%
                                    -19.0%
                                    -1.82%
                                    -1.98%
                                       -- 
                                       -- 
                                    -9.11%
                                    -9.08%
ESC
                                    -16.8%
                                    -16.7%
                                    -15.7%
                                    -15.1%
                                    -1.20%
                                    -1.28%
                                    -12.0%
                                    -12.4%
                                    -18.2%
                                    -18.3%
                                    -10.1%
                                    -10.2%
AWD
                                       -- 
                                       -- 
                                     44.9%
                                     39.4%
                                     10.7%
                                     8.84%
                                       -- 
                                       -- 
                                     0.96%
                                     1.07%
                                    -4.86%
                                    -4.14%
DRVMALE
                                     6.43%
                                     6.66%
                                    -0.95%
                                    -1.12%
                                     1.90%
                                     2.02%
                                    -0.28%
                                    -0.01%
                                    -0.14%
                                    -0.06%
                                     7.94%
                                     8.09%
M14_30
                                     4.41%
                                     4.36%
                                     3.83%
                                     3.76%
                                     5.11%
                                     5.03%
                                     1.05%
                                     1.02%
                                     0.64%
                                     0.63%
                                     0.58%
                                     0.52%
M30_50
                                     0.35%
                                     0.33%
                                     0.39%
                                     0.40%
                                     0.18%
                                     0.18%
                                     0.02%
                                     0.02%
                                    -0.16%
                                    -0.17%
                                    -0.15%
                                    -0.15%
M50_70
                                     0.16%
                                     0.16%
                                     0.33%
                                     0.31%
                                     0.61%
                                     0.63%
                                     1.30%
                                     1.27%
                                     1.12%
                                     1.11%
                                     1.26%
                                     1.28%
M70_96
                                     3.98%
                                     3.93%
                                     4.42%
                                     4.42%
                                     3.40%
                                     3.27%
                                     2.37%
                                     2.36%
                                     1.87%
                                     1.87%
                                     1.87%
                                     1.95%
F14_30
                                     3.49%
                                     3.46%
                                     3.57%
                                     3.53%
                                     3.62%
                                     3.61%
                                     0.73%
                                     0.75%
                                     0.60%
                                     0.62%
                                     1.25%
                                     1.24%
F30_50
                                    -0.04%
                                    -0.05%
                                     0.01%
                                     0.03%
                                    -0.01%
                                     0.00%
                                    -0.45%
                                    -0.43%
                                    -0.14%
                                    -0.12%
                                    -0.25%
                                    -0.18%
F50_70
                                     0.71%
                                     0.70%
                                     0.93%
                                     0.91%
                                     1.10%
                                     1.09%
                                     1.09%
                                     1.08%
                                     1.34%
                                     1.32%
                                     2.06%
                                     2.08%
F70_96
                                     4.37%
                                     4.33%
                                     3.37%
                                     3.31%
                                     3.43%
                                     3.36%
                                     1.84%
                                     1.86%
                                    -0.37%
                                    -0.16%
                                     0.65%
                                     0.58%
NITE
                                     32.4%
                                     32.4%
                                     37.8%
                                     37.2%
                                     25.2%
                                     25.2%
                                     44.2%
                                     43.1%
                                     42.2%
                                     40.9%
                                     32.1%
                                     32.0%
RURAL
                                     21.3%
                                     20.9%
                                     20.3%
                                     19.3%
                                     15.6%
                                     15.2%
                                     48.5%
                                     48.4%
                                     42.2%
                                     41.4%
                                     43.7%
                                     43.3%
SPDLIM55
                                     62.1%
                                     60.4%
                                     41.9%
                                     41.7%
                                     34.5%
                                     33.4%
                                     81.9%
                                     82.9%
                                     86.3%
                                     88.2%
                                     87.3%
                                     88.3%
VEHAGE
                                     0.43%
                                     0.43%
                                    -0.02%
                                    -0.04%
                                     1.45%
                                     1.57%
                                     1.89%
                                     1.87%
                                     2.30%
                                     2.35%
                                     1.05%
                                     0.88%
BRANDNEW
                                     6.24%
                                     6.44%
                                     0.84%
                                     1.20%
                                     0.38%
                                     0.87%
                                     3.20%
                                     3.17%
                                     2.76%
                                     2.76%
                                     3.04%
                                     2.90%
CY2002
                                    -8.09%
                                    -7.77%
                                    -9.70%
                                    -9.20%
                                    -10.9%
                                    -9.12%
                                     4.16%
                                     4.34%
                                     10.2%
                                     9.91%
                                     11.7%
                                     11.9%
CY2003
                                    -6.03%
                                    -5.66%
                                    -3.12%
                                    -2.49%
                                    -5.21%
                                    -3.84%
                                     5.96%
                                     6.03%
                                     5.41%
                                     5.59%
                                     10.6%
                                     11.6%
CY2004
                                    -4.01%
                                    -3.62%
                                    -1.93%
                                    -1.51%
                                    -3.01%
                                    -2.00%
                                     1.81%
                                     1.75%
                                     1.94%
                                     1.63%
                                    -2.21%
                                    -1.68%
CY2005
                                    -1.64%
                                    -1.42%
                                    -0.16%
                                     0.34%
                                    -0.13%
                                     0.71%
                                     1.53%
                                     1.50%
                                     1.63%
                                     1.62%
                                    -0.42%
                                    -0.08%
CY2007
                                     3.89%
                                     3.98%
                                     2.73%
                                     2.86%
                                     3.58%
                                     3.66%
                                    -7.63%
                                    -7.76%
                                    -8.26%
                                    -8.42%
                                    -4.43%
                                    -3.67%
CY2008
                                     3.97%
                                     4.17%
                                     2.01%
                                     1.98%
                                     5.28%
                                     5.30%
                                    -10.1%
                                    -10.2%
                                    -12.2%
                                    -12.3%
                                    -7.48%
                                    -6.89%
AL
                                     143%
                                     144%
                                     91.5%
                                     92.4%
                                     130%
                                     130%
                                    -8.93%
                                    -9.02%
                                    -23.9%
                                    -23.8%
                                    -26.1%
                                    -26.1%
KS
                                     63.1%
                                     63.3%
                                     38.4%
                                     40.9%
                                     58.8%
                                     59.5%
                                    -85.7%
                                    -85.7%
                                    -87.4%
                                    -87.4%
                                    -88.1%
                                    -88.1%
KY
                                     157%
                                     158%
                                     134%
                                     138%
                                     198%
                                     199%
                                    -78.5%
                                    -78.5%
                                    -81.6%
                                    -81.6%
                                    -82.1%
                                    -82.1%
MD
                                    -1.84%
                                    -1.96%
                                    -14.2%
                                    -13.3%
                                     -4.9%
                                     -4.7%
                                    -60.3%
                                    -60.4%
                                    -54.4%
                                    -54.4%
                                    -51.0%
                                    -51.1%
MI
                                     97.3%
                                     97.6%
                                     62.1%
                                     64.8%
                                     78.0%
                                     78.9%
                                    -89.2%
                                    -89.2%
                                    -91.0%
                                    -91.0%
                                    -89.5%
                                    -89.5%
MO
                                     98.5%
                                     98.8%
                                     59.8%
                                     63.0%
                                     89.9%
                                     90.8%
                                    -70.8%
                                    -70.9%
                                    -71.8%
                                    -71.9%
                                    -73.3%
                                    -73.3%
NE
                                     85.4%
                                     85.4%
                                     55.4%
                                     58.7%
                                     65.4%
                                     66.0%
                                    -74.4%
                                    -74.4%
                                    -73.7%
                                    -73.7%
                                    -77.1%
                                    -77.1%
NJ
                                     85.0%
                                     84.7%
                                     66.9%
                                     69.1%
                                     79.1%
                                     79.4%
                                    -91.8%
                                    -91.8%
                                    -91.9%
                                    -91.9%
                                    -92.5%
                                    -92.5%
PA
                                    -28.2%
                                    -28.2%
                                    -25.5%
                                    -23.9%
                                    -25.3%
                                    -24.9%
                                    -75.6%
                                    -75.6%
                                    -75.4%
                                    -75.4%
                                    -76.5%
                                    -76.5%
WA
                                     23.4%
                                       -- 
                                     31.3%
                                       -- 
                                     45.1%
                                       -- 
                                    -87.4%
                                       -- 
                                    -86.5%
                                       -- 
                                    -87.1%
                                       -- 
WI
                                     49.5%
                                     49.6%
                                     34.8%
                                     37.8%
                                     36.8%
                                     37.4%
                                    -74.5%
                                    -74.5%
                                    -76.6%
                                    -76.6%
                                    -76.8%
                                    -76.8%
WY
                                     138%
                                     138%
                                     32.4%
                                     36.6%
                                     96.2%
                                     97.8%
                                    -75.0%
                                    -75.0%
                                    -77.6%
                                    -77.6%
                                    -75.5%
                                    -75.5%
Values in red are statistically significant at the 95% level.
Table A-2. Estimated effect on crash frequency (crashes per mile traveled) and casualty risk per crash, excluding crashes in WA ("Ex WA") and excluding non-severe crashes ("Ex NS")
Variable
                       Crash frequency (crashes per VMT)
                             Casualties per crash

                                     Cars
                                 Light Trucks
                                 CUVs/minivans
                                     Cars
                                 Light Trucks
                                 CUVs/minivans

                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
                                     Ex WA
                                     Ex NS
UNDRWT00
                                     2.02%
                                     2.08%
                                     1.46%
                                     1.65%
                                       -- 
                                       -- 
                                                                          0.22%
                                                                          0.13%
                                                                         -0.15%
                                                                         -0.42%
                                       -- 
                                       -- 
OVERWT00
                                     1.37%
                                     1.17%
                                     0.86%
                                     0.98%
                                       -- 
                                       -- 
                                                                         -1.03%
                                                                         -0.65%
                                                                         -0.73%
                                                                         -1.16%
                                       -- 
                                       -- 
LBS100
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     0.85%
                                     0.95%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -0.22%
                                                                         -0.26%
FOOTPRNT
                                     0.86%
                                     1.48%
                                     1.12%
                                     1.07%
                                    -0.40%
                                    -0.03%
                                                                          0.36%
                                                                         -0.29%
                                                                         -0.14%
                                                                         -0.11%
                                                                          0.87%
                                                                          1.17%
TWODOOR
                                     5.48%
                                     5.93%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          1.24%
                                                                          1.40%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
SUV
                                       -- 
                                       -- 
                                    -0.47%
                                    -0.27%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          1.50%
                                                                          0.19%
                                       -- 
                                       -- 
HDPU
                                       -- 
                                       -- 
                                    -3.72%
                                    -3.35%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -0.94%
                                                                         -2.25%
                                       -- 
                                       -- 
BLOCKER1
                                       -- 
                                       -- 
                                    -1.09%
                                    -0.35%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          0.67%
                                                                          1.64%
                                       -- 
                                       -- 
BLOCKER2
                                       -- 
                                       -- 
                                    -0.28%
                                    -2.04%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                         -4.75%
                                                                         -2.69%
                                       -- 
                                       -- 
MINIVAN
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                     1.96%
                                    -1.67%
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                                                          14.4%
                                                                          24.3%
ROLLCURT
                                    -1.88%
                                    -1.74%
                                       -- 
                                       -- 
                                    -0.81%
                                    -0.74%
                                                                         -3.91%
                                                                         -3.75%
                                       -- 
                                       -- 
                                                                         -1.81%
                                                                         -1.80%
CURTAIN
                                     0.00%
                                     0.20%
                                       -- 
                                       -- 
                                    -2.94%
                                    -0.58%
                                                                         -2.94%
                                                                         -3.48%
                                       -- 
                                       -- 
                                                                         -3.03%
                                                                         -5.99%
COMBO
                                     2.55%
                                     2.82%
                                       -- 
                                       -- 
                                    -0.79%
                                    -1.60%
                                                                         -1.66%
                                                                         -1.58%
                                       -- 
                                       -- 
                                                                          5.49%
                                                                          7.26%
TORSO
                                    -5.07%
                                    -5.93%
                                       -- 
                                       -- 
                                    -4.59%
                                    -7.09%
                                                                         -10.4%
                                                                         -9.12%
                                       -- 
                                       -- 
                                                                         -2.91%
                                                                         -0.26%
ABS
                                    -5.73%
                                    -7.62%
                                       -- 
                                       -- 
                                    -19.0%
                                    -19.0%
                                                                         -1.98%
                                                                         -1.39%
                                       -- 
                                       -- 
                                                                         -9.08%
                                                                         -6.16%
ESC
                                    -16.7%
                                    -16.4%
                                    -15.1%
                                    -19.8%
                                    -1.28%
                                    -5.08%
                                                                         -12.4%
                                                                         -12.2%
                                                                         -18.3%
                                                                         -14.4%
                                                                         -10.2%
                                                                         -7.65%
AWD
                                       -- 
                                       -- 
                                     39.4%
                                     37.6%
                                     8.84%
                                     10.5%
                                       -- 
                                       -- 
                                                                          1.07%
                                                                          0.42%
                                                                         -4.14%
                                                                         -6.69%
DRVMALE
                                     6.66%
                                     10.2%
                                    -1.12%
                                    -0.54%
                                     2.02%
                                     3.76%
                                                                         -0.01%
                                                                         -4.53%
                                                                         -0.06%
                                                                         -1.94%
                                                                          8.09%
                                                                          7.50%
M14_30
                                     4.36%
                                     5.51%
                                     3.76%
                                     4.42%
                                     5.03%
                                     6.06%
                                                                          1.02%
                                                                         -0.07%
                                                                          0.63%
                                                                         -0.32%
                                                                          0.52%
                                                                         -0.78%
M30_50
                                     0.33%
                                     0.66%
                                     0.40%
                                     0.56%
                                     0.18%
                                     0.40%
                                                                          0.02%
                                                                         -0.25%
                                                                         -0.17%
                                                                         -0.37%
                                                                         -0.15%
                                                                         -0.35%
M50_70
                                     0.16%
                                     0.35%
                                     0.31%
                                     0.34%
                                     0.63%
                                     0.85%
                                                                          1.27%
                                                                          1.22%
                                                                          1.11%
                                                                          1.16%
                                                                          1.28%
                                                                          1.12%
M70_96
                                     3.93%
                                     4.86%
                                     4.42%
                                     5.05%
                                     3.27%
                                     4.03%
                                                                          2.36%
                                                                          1.66%
                                                                          1.87%
                                                                          1.52%
                                                                          1.95%
                                                                          1.17%
F14_30
                                     3.46%
                                     4.70%
                                     3.53%
                                     4.72%
                                     3.61%
                                     4.85%
                                                                          0.75%
                                                                         -0.20%
                                                                          0.62%
                                                                         -0.44%
                                                                          1.24%
                                                                          0.03%
F30_50
                                    -0.05%
                                     0.06%
                                     0.03%
                                    -0.11%
                                     0.00%
                                    -0.04%
                                                                         -0.43%
                                                                         -0.67%
                                                                         -0.12%
                                                                         -0.14%
                                                                         -0.18%
                                                                         -0.23%
F50_70
                                     0.70%
                                     1.13%
                                     0.91%
                                     0.93%
                                     1.09%
                                     1.34%
                                                                          1.08%
                                                                          0.86%
                                                                          1.32%
                                                                          1.39%
                                                                          2.08%
                                                                          1.86%
F70_96
                                     4.33%
                                     5.21%
                                     3.31%
                                     3.42%
                                     3.36%
                                     4.18%
                                                                          1.86%
                                                                          1.23%
                                                                         -0.16%
                                                                         -0.03%
                                                                          0.58%
                                                                         -0.18%
NITE
                                     32.4%
                                     41.1%
                                     37.2%
                                     47.3%
                                     25.2%
                                     30.5%
                                                                          43.1%
                                                                          33.7%
                                                                          40.9%
                                                                          29.2%
                                                                          32.0%
                                                                          29.7%
RURAL
                                     20.9%
                                     23.8%
                                     19.3%
                                     22.1%
                                     15.2%
                                     19.1%
                                                                          48.4%
                                                                          44.1%
                                                                          41.4%
                                                                          37.5%
                                                                          43.3%
                                                                          42.9%
SPDLIM55
                                     60.4%
                                     98.0%
                                     41.7%
                                     79.6%
                                     33.4%
                                     68.5%
                                                                          82.9%
                                                                          60.6%
                                                                          88.2%
                                                                          62.3%
                                                                          88.3%
                                                                          71.7%
VEHAGE
                                     0.43%
                                     1.32%
                                    -0.04%
                                     0.45%
                                     1.57%
                                     2.69%
                                                                          1.87%
                                                                          1.24%
                                                                          2.35%
                                                                          2.34%
                                                                          0.88%
                                                                         -0.56%
BRANDNEW
                                     6.44%
                                     7.66%
                                     1.20%
                                     0.89%
                                     0.87%
                                     0.11%
                                                                          3.17%
                                                                          4.17%
                                                                          2.76%
                                                                          5.23%
                                                                          2.90%
                                                                          1.94%
CY2002
                                    -7.77%
                                    -13.6%
                                    -9.20%
                                    -15.5%
                                    -9.12%
                                    -15.9%
                                                                          4.34%
                                                                          3.94%
                                                                          9.91%
                                                                          11.3%
                                                                          11.9%
                                                                          8.29%
CY2003
                                    -5.66%
                                    -15.3%
                                    -2.49%
                                    -12.0%
                                    -3.84%
                                    -14.9%
                                                                          6.03%
                                                                          7.31%
                                                                          5.59%
                                                                          8.52%
                                                                          11.6%
                                                                          11.0%
CY2004
                                    -3.62%
                                    -8.66%
                                    -1.51%
                                    -5.42%
                                    -2.00%
                                    -7.00%
                                                                          1.75%
                                                                          1.10%
                                                                          1.63%
                                                                          2.01%
                                                                         -1.68%
                                                                         -2.26%
CY2005
                                    -1.42%
                                    -4.68%
                                     0.34%
                                    -1.77%
                                     0.71%
                                    -4.53%
                                                                          1.50%
                                                                          2.18%
                                                                          1.62%
                                                                          2.10%
                                                                         -0.08%
                                                                         -2.62%
CY2007
                                     3.98%
                                     3.90%
                                     2.86%
                                     3.83%
                                     3.66%
                                     3.72%
                                                                         -7.76%
                                                                         -7.85%
                                                                         -8.42%
                                                                         -8.69%
                                                                         -3.67%
                                                                         -2.77%
CY2008
                                     4.17%
                                     4.24%
                                     1.98%
                                     3.48%
                                     5.30%
                                     4.70%
                                                                         -10.2%
                                                                         -10.4%
                                                                         -12.3%
                                                                         -12.8%
                                                                         -6.89%
                                                                         -6.21%
AL
                                     144%
                                     55.5%
                                     92.4%
                                     22.1%
                                     130%
                                     43.2%
                                                                          -9.0%
                                                                          57.2%
                                                                         -23.8%
                                                                          38.9%
                                                                         -26.1%
                                                                          38.7%
KS
                                     63.3%
                                     6.50%
                                     40.9%
                                     -7.5%
                                     59.5%
                                     5.84%
                                                                         -85.7%
                                                                         -75.9%
                                                                         -87.4%
                                                                         -78.0%
                                                                         -88.1%
                                                                         -79.1%
KY
                                     158%
                                     35.1%
                                     138%
                                     18.3%
                                     199%
                                     45.4%
                                                                         -78.5%
                                                                         -61.0%
                                                                         -81.6%
                                                                         -64.9%
                                                                         -82.1%
                                                                         -65.5%
MD
                                    -1.96%
                                    -11.8%
                                    -13.3%
                                    -22.8%
                                    -4.69%
                                    -10.5%
                                                                         -60.4%
                                                                         -65.1%
                                                                         -54.4%
                                                                         -58.4%
                                                                         -51.1%
                                                                         -55.6%
MI
                                     97.6%
                                     9.39%
                                     64.8%
                                    -9.66%
                                     78.9%
                                     2.47%
                                                                         -89.2%
                                                                         -78.8%
                                                                         -91.0%
                                                                         -81.2%
                                                                         -89.5%
                                                                         -78.9%
MO
                                     98.8%
                                     28.7%
                                     63.0%
                                     4.31%
                                     90.8%
                                     19.3%
                                                                         -70.9%
                                                                         -54.4%
                                                                         -71.9%
                                                                         -54.3%
                                                                         -73.3%
                                                                         -57.0%
NE
                                     85.4%
                                    -1.57%
                                     58.7%
                                    -13.0%
                                     66.0%
                                    -7.52%
                                                                         -74.4%
                                                                         -52.6%
                                                                         -73.7%
                                                                         -52.3%
                                                                         -77.1%
                                                                         -55.3%
NJ
                                     84.7%
                                     31.0%
                                     69.1%
                                     16.6%
                                     79.4%
                                     23.5%
                                                                         -91.8%
                                                                         -87.5%
                                                                         -91.9%
                                                                         -87.1%
                                                                         -92.5%
                                                                         -87.5%
PA
                                    -28.2%
                                    -27.0%
                                    -23.9%
                                    -22.4%
                                    -24.9%
                                    -21.5%
                                                                         -75.6%
                                                                         -79.0%
                                                                         -75.4%
                                                                         -77.9%
                                                                         -76.5%
                                                                         -79.9%
WA
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
                                       -- 
WI
                                     49.6%
                                     7.61%
                                     37.8%
                                    -3.91%
                                     37.4%
                                    -3.15%
                                                                         -74.5%
                                                                         -64.5%
                                                                         -76.6%
                                                                         -66.6%
                                                                         -76.8%
                                                                         -66.1%
WY
                                     138%
                                     53.2%
                                     36.6%
                                    -13.7%
                                     97.8%
                                     23.5%
                                                                         -75.0%
                                                                         -56.6%
                                                                         -77.6%
                                                                         -65.2%
                                                                         -75.5%
                                                                         -57.1%
* Values in red are statistically significant at the 95% level. 


Appendix B: Discussion of crash frequency and risk per crash results in Kahane 2012

Below is the discussion of DRI's estimates of crash frequency and risk per crash included in Kahane 2012.

   For passenger cars and truck-based LTVs, overall and for many of the individual crash types, these analyses tend to show that (1) mass reduction lowers F/A [i.e. risk per crash], but (2) increases A/VMT [i.e. crash frequency].
   
   The analyses appear to be computationally valid. The sum of the F/A and the A/VMT coefficients is usually close to the baseline coefficients in NHTSA's analysis.
   
   However, in most of their tables, Van Auken and Zellner label the column of F/A coefficients as the "effect of mass reduction on crashworthiness and crash compatibility" and the A/VMT coefficients as its "effect on crash avoidance." In other words, the tables say mass reduction benefits crashworthiness and harms crash avoidance. NHTSA believes these are not accurate characterizations of the coefficients and they lead, in turn, to misunderstandings. Specifically, the ICCT in their public comment argue that the observed benefit to crashworthiness and harm to crash avoidance is counterintuitive and may be evidence of a flaw in the baseline analysis, such as a need for additional or different control variables.
   
   NHTSA believes the metric of fatalities per reported crash (F/A) does not measure just crashworthiness but also certain important aspects of crash avoidance, namely the severity of a crash. In addition, it could be influenced by how often crashes are reported or not reported.
   
   Conceptually, crashworthiness is the likelihood that an occupant will survive, given an impact to a vehicle that in turn results in a particular physical insult to the occupant. It is quite appropriate for the regression analyses to control for driver age and gender, because it is known that, given the same physical insult, a person is more likely to die with each year that he or she gets older. Furthermore, from young adulthood up to middle age, a female is more likely to die from the same physical insult as a male of the same age. Crash-data analyses have shown increases in fatality risk of 2 to 4 percent for each year that a person gets older. Young adult females are 20 to 30 percent more vulnerable than males of the same age; that differences decreases over time and eventually reverses by late middle age, but averaging across all ages, females are still 5 to 20 percent more vulnerable than males of the same age.
   
   In other words, if these F/A regressions truly modeled crashworthiness, the analyses of the crash types where most fatalities are in the case vehicle (rollover, fixed-object, heavy-truck, and the various types of collisions where the other vehicle is heavier) should have coefficients like -0.03 for M14_30, F14_30, M30_50, and F30_50, each of which measure how many years the driver is younger than 30 or 50, respectively. They should have coefficients like +0.03 for M50_70, F50_70, M70_96, and F70_96, which measure how many years the driver is older than 50 or 70. They should have a coefficient like -0.10 for DRVMALE, because a male is less vulnerable than a female. In crashes where the fatalities are uncommon in the case vehicle (hitting a pedestrian or a much lighter vehicle), the coefficients should all be close to zero, because the age or gender of the driver will not affect how the pedestrian reacts to a physical insult.
   Instead, the regressions rather consistently estimate positive or near-zero coefficients for M14_30, F14_30, M30_50, and F30_50 and positive coefficients for DRVMALE. They say F/A decreases as the occupant ages up to age 50 and F/A is lower for females than males.
   
   A more blatant example: on purely crashworthiness considerations, whether it is light or dark outside ought to have little effect on the risk of death from a given physical insult, except perhaps to the extent it affects EMS arrival. But NITE is consistently associated with an extraordinary increase in F/A.
   
   Of course, it is obvious what is going on. These crash data have no measure of crash severity, such as delta v. M14_30, F14_30, M30_50, F30_50, DRVMALE, and NITE all act as surrogates for crash severity. They not only indicate crashworthiness (ability to survive a physical insult) but also, and in some cases primarily, crash avoidance  -  namely, the ability of age 30-50 drivers, females, and daytime drivers to stay out of situations that lead to fatal crashes, while having their share of fender-benders. Driving at night, on the other hand, is a way to avoid fender-benders characteristic of rush-hour traffic and thereby increases F/A.
   
   Just as many of the control variables in the F/A regressions measure effects of crash avoidance in addition to (and sometimes in place of) crashworthiness, by the same token, there is no particular reason that the coefficients for UNDRWT00, OVERWT00, and FOOTPRNT measure the effects of crashworthiness exclusively and not also crash avoidance. Control variables such as M14_30, F14_30, M30_50, F30_50, DRVMALE, NITE, and also SPDLIM55 and RURAL may account for much of the effect of crash severity on risk per reported crash, but it is unknown exactly how much.
   
   A salient feature of NHTSA's approach, where the numerator is fatalities and the denominator VMT, is to take crash-reporting rates out of the formula for calculating risk.  A fatality is a fatality and a mile of travel is a mile of travel  -  unlike contact events that may or may not be police-reported, depending on the vehicle, the driver, the locality, or the circumstances of the moment.  These analyses of F/A and A/VMT appear to be computationally valid, but NHTSA doubts they truly measure the "effect of mass reduction on crashworthiness" and "effect of mass reduction on crash avoidance." 

References

Kahane, C.J. 2012. Relationships Between Fatality Risk, Mass, and Footprint in Model Year 2000-2007 Passenger Cars and LTVs.  Final report prepared for the National Center for Statistics and Analysis, National Highway Traffic Safety Administration, DOT HS 811 665; August.

Wenzel, Tom. 2012. An Analysis of the Relationship between Casualty Risk per Crash and Vehicle Mass and Footprint for Model Year 2000-2007 Light-Duty Vehicles.  Final report prepared for the Office of Energy Efficiency and Renewable Energy, US Department of Energy.  Lawrence Berkeley National Laboratory;  August.  LBNL-5697E.  

Wenzel, Tom. 2013. Assessment of DRI's Two-Stage Logistic Regression Model Used to Simultaneously Estimate the Relationship between Vehicle Mass or Size Reduction and U.S. Fatality Risk, Crashworthiness/Compatibility, and Crash Avoidance.  Draft report prepared for the Office of Energy Efficiency and Renewable Energy, US Department of Energy.  Lawrence Berkeley National Laboratory.  January

Wenzel, Tom. 2014. Sensitivity of Light-Duty Vehicle Crash Frequency per Vehicle Mile of Travel to Additional Vehicle and Driver Variables.  Draft report prepared for the Office of Energy Efficiency and Renewable Energy, US Department of Energy; Lawrence Berkeley National Laboratory, 2014; February.



