TABLE 5.

The thyroid epithelial cell vacuolization data

	a	b	d	ζ	BMD	BMDL	BMDU	AICc	Weight
Inv Exp	0.107 (0.037)	13.628 (8.707)	1.312 (0.246)	—	2.287 (0.785)	1.298	4.127	187.262	0.347
Gamma	0.096 (0.035)	6.377 (5.511)	0.297 (0.095)	13.392 (8.645)	1.225 (0.536)	0.525	2.340	192.065	0.031
Lomax	0.100 (0.034)	108.112 (126.342)	3.028 (1.253)	0.324 (0.232)	3.164 (2.062)	0.940	7.024	188.244	0.212
Inverse Lomax	0.106 (0.037)	1.925 (7.024)	1.328 (0.255)	27.721 (94.074)	2.282 (0.784)	1.313	4.126	189.351	0.122
LN	0.099 (0.036)	0.075 (0.038)	1.090 (0.184)	—	1.271 (0.547)	0.562	2.434	189.850	0.095
LSN	0.117 (0.041)	0.517 (0.098)	0.606 (0.084)	40.200 (179.513)	3.009 (0.487)	1.989	3.988	188.591	0.179
Logistic	−2.327 (0.434)	0.594 (0.292)	0.586 (0.132)	—	0.001 (0.003)	0.001	0.029	194.904	0.008
Probit	−1.337 (0.218)	0.322 (0.151)	0.604 (0.128)	—	0.001 (0.003)	0.001	0.029	195.719	0.005
The direct approach: standard errors estimate (23) and Wald-type limits					2.443 (1.306)	0.295	4.590
The direct approach: bootstrap standard error and percentile limits					2.443 (0.931)	0.707	3.734
The indirect approach: bootstrap standard error and percentile limits					2.153 (0.910)	0.261	3.074

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