                              BMD Analysis (Cmax)

                                   Kan Shao
                               September 5, 2013

Becci et al 1982, Table 5, Sternabrae (missing), Litter size
                               Dose, Cmax (mg/L)
                                       N
                                    Effect
                                       0
                                      24
                                       1
                                     202.4
                                      22
                                       0
                                     641.1
                                      23
                                       4
                                    2049.6
                                      22
                                      17

                            BMD Estimation Results
                                       
Model
P-Value
AIC
BMD 
(BMR=10%)
BMDL
(BMR=10%) 
BMD
(BMR=5%)
BMDL 
(BMR=5%)
Gamma
0.29
60.88
563.27
333.82
420.35
209.39
Logistic
0.42
59.93
653.38
475.06
424.13
282.05
LogLogistic
0.29
60.86
558.66
344.90
421.06
228.25
LogProbit
0.32
60.59
552.53
352.30
436.81
252.13
Multistage
0.53
59.17
548.73
315.68
382.87
168.76
Probit
0.45
59.72
594.26
439.12
380.16
256.35
Weibull
0.26
61.16
566.77
319.70
399.58
190.16
Quantal-Linear
0.04
66.13
220.23
153.18
107.22
74.57
Note: Quantal-Linear cannot fit properly. Multistage model (degree 2) is the best fitted model and should be selected.

Becci et al 1982, Table 5, Vertebrae (Incomplete ossification), Litter size
                               Dose, Cmax (mg/L)
                                       N
                                    Effect
                                       0
                                      24
                                      12
                                     202.4
                                      22
                                      11
                                     641.1
                                      23
                                      14
                                    2049.6
                                      22
                                      18

                            BMD Estimation Results
                                       
Model
P-Value
AIC
BMD 
(BMR=10%)
BMDL
(BMR=10%) 
BMD
(BMR=5%)
BMDL 
(BMR=5%)
Gamma
0.84
121.46
347.23
117.60
204.7
57.25
Logistic
0.97
119.49
271.17
170.45
135.45
85.27
LogLogistic
0.87
121.45
361.44
65.84
227.21
31.19
LogProbit
0.99
119.43
393.99
210.39
273.97
146.30
Multistage
0.80
121.49
302.83
117.31
153.46
57.11
Probit
0.97
119.49
280.19
182.93
139.97
91.50
Weibull
0.83
121.47
333.97
117.52
188.83
57.21
Quantal-Linear
0.94
119.55
212.68
116.58
103.54
56.75
Note: LogProbit Model is the best fitted model, but the BMDLs exceed the range of 3-fold. So, the lowest BMDL should be selected. 
