TABLE 3.

The cell proliferation data with full design

Model	a	b	c	d	ζ	σ	BMD	BMDL	BMDU	AIC	Weight
Exp	7.285 (0.097)	0.322 (0.085)	1.388 (0.040)	1.012 (0.228)	—	0.394 (0.043)	0.083 (0.065)	0.025	0.333	50.859	0.197
Inv Exp	7.284 (0.097)	1.696 (0.478)	1.654 (0.289)	0.434 (0.188)	—	0.400 (0.044)	0.125 (0.085)	0.091	0.449	52.207	0.101
Hill	7.288 (0.098)	2.937 (0.931)	1.435 (0.075)	1.1524 (0.334)	—	0.396 (0.043)	0.098 (0.081)	0.014	0.401	51.447	0.147
LN	7.289 (0.097)	0.525 (0.111)	1.445 (0.099)	0.646 (0.204)	—	0.397 (0.043)	0.122 (0.087)	0.017	0.439	51.738	0.127
Logistic	0.949 (0.100)	0.420 (0.107)	10.103 (0.237)	0.956 (0.214)	—	0.393 (0.043)	0.077 ( 0.061)	0.011	0.320	50.758	0.208
Probit	0.588 (0.057)	0.245 (0.061)	10.089 (0.226)	0.920 (0.197)	—	0.393 (0.043)	0.071 (0.057)	0.011	0.306	50.647	0.220
The direct approach: standard errors estimate (23) and Wald-type limits							0.091 (0.073)	0.014	0.409
The direct approach: bootstrap standard error and percentile limits							0.091 (0.103)	0.011	0.325
The indirect approach: bootstrap standard error and percentile limits							0.091 (0.101)	0.019	0.318

Note: Estimates for all fitted models (with one representative for nested models), the model-specific BMD estimates, 90% profile likelihood based BMDL and BMDU, corrected AIC, and corresponding weight for averaging. Model-averaged BMD estimates based on the direct approach with 90% Wald and percentile bootstrap BMDL and BMDU limits, and based on the indirect approach with 90% percentile bootstrap BMDL and BMDU limits. Estimates for the standard error are shown: using formula (23) and the bootstrap for the direct estimate and only the bootstrap for the indirect estimate. B = 3, 000 bootstrap samples were generated.

Abbreviations: Exp, exponential; Inv Exp, inverse exponential; LN, log-normal; LSN, log-skew-normal model.