Reviewer:
Charles M. Farmer, Ph.D.
Director of Statistical Services
Insurance Institute for Highway Safety
Arlington, VA
cfarmer@iihs.org
703-247-1590
703-247-1587 FAX

January 4, 2011

Summary of Results

NHTSA analyses in 1997 and 2003 estimated the effects on fatality risk of historical changes in the average size and weight of the vehicle fleet.  As size and weight tended to change concurrently (and proportionally), it made sense to model the effects of only one of these parameters, namely vehicle curb weight.  It was argued that any attempt to estimate the individual effects of size and weight would be confounded by the high correlation between the two parameters (i.e., multicollinearity).

However, the processes of design and manufacture have evolved such that vehicle weight now can be reduced with little or no change to vehicle size.  The relevant question, then, is how fatality risk would be affected by a change in vehicle weight while holding size essentially constant.  The latest NHTSA analysis tackled this question.

The data used were similar to those from the 2003 analysis: crashes occurring during the years 1995-2000 and involving 1991-1999 model passenger vehicles.  Logistic regression analyses were conducted to predict the effect on fatality risk of a 100-pound weight reduction while maintaining the vehicle footprint (wheelbase times track width).  For cars weighing less than 2950 pounds the effect was an estimated 2.21 percent increase in fatalities (301/13608).  For cars weighing at least 2950 pounds the effect was a 0.90 percent increase in fatalities (98/10884).  For light trucks and vans (LTVs) weighing less than 3870 pounds the effect was a 0.17 percent increase in fatalities (14/8057).  For LTVs weighing at least 3870 pounds the effect was a 1.90 percent decrease in fatalities (280/14705).

Fatality Increase (%) per 100-Pound Mass Reduction While Maintaining Footprint
                                       
                       Actual Regression Result Scenario
                            Upper-Estimate Scenario
                            Lower-Estimate Scenario
Cars < 2,950 pounds
                                                                           2.21
                                                                           2.21
                                                                           1.02
Cars > 2,950 pounds
                                                                           0.90
                                                                           0.90
                                                                           0.44
LTVs < 3,870 pounds
                                                                           0.17
                                                                           0.55
                                                                           0.41
LTVs > 3,870 pounds
                                                                          -1.90
                                                                          -0.62
                                                                          -0.73


Summary of Methodology

For each vehicle make/model/body style/model year in each calendar year the national count of registered vehicles was divided into categories corresponding to combinations of driver gender, driver age (4 groups), night/day, rural road/urban, and high speed road/other.  These divisions mirrored the distribution of gender, age, and roadway categories of drivers involved in two-vehicle police-reported crashes for which the other driver was judged to be solely at fault.  Thus the exposure of vehicles in the study was estimated not only for the various vehicle characteristics, but also for driver and roadway characteristics.  Based on odometer readings from NHTSA-investigated crashes, annual mileage of LTVs seems to be higher for bigger vehicles.  The registration counts for LTVs were further adjusted to account for these estimated mileage differences.

Fatal crash involvements for each make/model/body style/model year in each calendar year were classified according to 6 mutually exclusive crash types: first-event rollovers, collisions with fixed objects, collisions with pedestrians/bicycles/motorcycles, collisions with heavy trucks, collisions with cars, and collisions with LTVs.

Fatal crash involvement records were combined with the not-at-fault records to produce the data set for analyses.  Logistic regressions were used to estimate the odds that a record was from a fatal crash based on driver gender, driver age, night/day, rural road/urban, high speed road/other, presence of a driver airbag, presence of antilock brakes (ABS), the curb weight of the vehicle, and the footprint.  Fatal crash involvements were weighted in the regression by the number of fatalities in the crash and not-at-fault involvements were weighted by the registration counts.  Odds ratios from the regression therefore approximated differences in the fatality rate per vehicle (or per mile) per year.

General Comments

The only difference between this analysis and that of the 2003 study is the addition of vehicle footprint to the logistic regressions.  Earlier analyses have avoided adding size measures to the statistical models because of concerns about multicollinearity.  These concerns still exist (as evidenced by the relatively high correlation between weight and footprint), but the analysis proceeds anyway.  Researchers should look for a better way to lessen the effects of multicollinearity.

One suggestion would be to use more recent data in the hope that curb weight and footprint are less correlated than they used to be.  I realize that building this data set is a major undertaking, but it is possible now to study fatal crashes of 2001-2008 model passenger vehicles during the years 2005-2009.  Such a future analysis is mentioned on page 533 of the report.  I encourage NHTSA to pursue it.

The stated purpose of the analysis was to develop parameters for the Volpe model, i.e., the percentage change in crash fatalities per 100 pound weight reduction while maintaining footprint.  Much of the text, however, is devoted to a comparison of the NHTSA methodology to that presented by Dynamic Research Inc. (DRI).  Section 2.3 of the report demonstrates that breaking the regression analysis into two stages (as DRI does) causes parameter estimates for curb weight to change from negative to positive.  For example, the parameter estimate for curb weight of relatively heavy cars colliding with LTVs was -0.0114 when using a single-stage logistic regression of fatality risk.  However, when estimation was broken into fatalities per crash followed by crashes per vehicle, the combined curb weight parameter was 0.0292.

The latest NHTSA analysis has a believability advantage over the DRI analyses because the results are consistent with those predicted by the laws of physics.  That is, to the extent that other factors are adequately controlled, increased size should reduce peak forces on occupants for any given crash delta velocity by increasing crush distance over which the delta velocity occurs; in analogous manner, increased mass (i.e,, momentum/inertia) should reduce peak forces for a given amount of crush distance by lessening the delta velocity in crashes with movable/deformable objects.  Analyses that find otherwise need to explain how these physical effects have been overcome or masked.

Also, the NHTSA analysis is self consistent.  The analysis that estimates the two separate parameters for size and weight yields estimated fatal crash effects (when statistically recombined) that are consistent with the overall effect associated with the original logistic regression for size/weight combined.  

Despite these advantages, I find myself wondering why the DRI analysis did not yield similar results.  Theoretically, it should have.  NHTSA suggests that part of the genuine effect of mass is momentarily "lost" when fatality rates are analyzed per 1,000 reported crash involvements or per 1,000 reported induced-exposure involvements, because that effect is "hidden" in the rate of reported involvements per 1,000 registration years.  Heavier cars have fewer reported crash involvements per registration year.  Reported crash rates decrease by about 2 percent reduction per 100-pound increase.  Because log-linear effects are additive across the two regression steps, this 2-percent effect is basically "lost" from the analysis of fatalities per 1,000 induced-exposure crashes.

This demonstrates how the NHTSA and DRI analyses can produce contradictory results, but it does not clearly explain how these differences come about.  Both methods are logical.  In fact, if a data set existed containing all crashes and vehicle travel miles for each combination of driver gender, driver age, night/day, rural road/urban, high speed road/other, presence of a driver airbag, presence of antilock brakes (ABS), curb weight of the vehicle, and footprint, then parameter estimates from a two-stage regression should sum exactly to that from a single-stage regression.  Why does the two-stage method applied here yield different results?  Is it due to aggregating the data by make, model, body type, model year, state, and calendar year and employing average values for driver characteristics?  Is it due to differences in the independent variables included for the first-stage and second-stage regression models?

I am somewhat concerned that dropping driver age from the second-stage regression model shifts the results back in line with those of NHTSA (see Table 2-8).  (It would be helpful if the parameter estimates from each stage were reported rather than just the sum.)  The decile results (Section 2.4) also ignore driver age, and also agree with NHTSA's logistic regressions.  Is driver age the confounding factor?

One should keep in mind that these effects are being estimated without a clear understanding of why different vehicles of the same size have different weights.  Weights might vary because of variations in engine size.  More horsepower per weight tends to increase crash risk  -  this would be one way  that increased weight might increase fatal crash risk, counteracting the momentum exchange relationship.  Excluding muscle and sporty cars did not significantly change the estimates in this report.  However, trends toward greater horsepower have extended beyond these vehicle segments.

The model years 1991-1999 saw large improvements in occupant protection driven largely by structural improvements and safety equipment like side airbags.  These improvements would increase vehicle mass (and hence reduce fatality rates) but they also might account for some of the lower fatality rates directly.

Results are given separately for the four vehicle classes: passenger cars weighing less than 2950 pounds, passenger cars weighing at least 2950 pounds, LTVs weighing less than 3870 pounds, and LTVs weighing at least 3870 pounds.  However, CAFE regulations affect all four classes simultaneously.  It would be nice to know the effect of a 100-pound weight reduction in all vehicles.  Given the double counting of some fatalities, I'm not sure how to accomplish this from Tables 4-1 through 4-4.  Do the fatality changes and baseline fatalities simply combine for an estimated 0.28 percent overall increase in fatalities (133/47254)?

According to Table 2-15, the effect of reducing footprints by 0.65 square feet while maintaining weight is a 3.64 percent increase in fatalities for passenger cars weighing less than 2950 pounds (496/13608) and a 6.84 percent increase for passenger cars weighing at least 2950 pounds (745/10884).  According to Table 3-2, the effect of reducing footprints by 0.975 square feet while maintaining weight is a 2.26 percent increase in fatalities for LTVs weighing less than 3870 pounds (182/8057) and a 2.14 percent increase for LTVs weighing at least 3870 pounds (315/14705).  Conversely, increasing the vehicle footprint while maintaining weight should be beneficial.  I think it's important to determine how much footprint increase would be necessary to counteract the negative effect of a 100-pound weight reduction.  That is, how can designers reduce vehicle weight without harming society?

Finally, it would be helpful if NHTSA made available on its web site the complete set of data used to produce the main results.  This would make it easier for other researchers to understand the methodology and to try out suggested improvements to the analysis.  It also would make it easier for NHTSA to respond to these suggestions.

Specific Comments (quotes from the study are in italics)

   1. (p. 486, bullet 2) Although substituting footprint for track width and wheelbase produces similar or at best marginally lower VIF scores (the test for curb weight, track width, and wheelbase produced VIF scores of 6.4, 3.0, and 6.5, whereas the test for curb weight and footprint produced scores of 6.1 and 5.8), the literature suggests that combining parameters is generally advisable for alleviating multicollinearity. Would it not make sense to go further and combine curb weight with footprint?  A combined measure of curb weight per square foot would solve the problem of multicollinearity and still allow for testing the effect of reducing weight while maintaining footprint.
   2. (p. 496, para. 2) Should increases the chance of coefficients in the lighter <--> fatalities direction for mass because the effect of mass is essentially split between the two regressions instead read increases the chance of coefficients in the lighter <--> fewer fatalities direction for mass because the effect of mass is essentially split between the two regressions?
   3.  (p. 529, Table 3-5) Should the heading NUMBER OF FOOTPRINT DECILES WHERE FOOTPRINT HAS NEGATIVE CORRELATION WITH THE FATAL-CRASH RATE instead read NUMBER OF CURB WEIGHT DECILES WHERE FOOTPRINT HAS NEGATIVE CORRELATION WITH THE FATAL-CRASH RATE?
   4. Peer reviewers were charged with deciding whether the analytical methods were appropriate and whether the material was presented in a clear and concise manner.  I believe the methods are appropriate, but they are not definitive.  Although the current NHTSA analysis yields results that are internally consistent and consistent with expectations from the physics of car crashes, alternative methods to estimate the separate effects of size and weight can and should be considered in the future.  Thinking of this as a work in progress is some justification for the length of the report.  It was very clearly written, but I would not call it concise. 

Peer Review Recommendation

Acceptable with minor revisions (as indicated)
