. 2020 Dec 17;8:e10557. doi: 10.7717/peerj.10557

Table 3. Estimated benchmark dose (BMD) and benchmark dose lower limit (BMDL) for different continuous data sets, different models and different levels of BMR using PROAST, BMDS and bmd.

PROAST and BMDS uses profile likelihood intervals for estimating BMDL while the R package bmd uses the delta method, inverse regression or bootstrap. For all data sets, the relative definition of BMD was used.

					BMD			BMDL
Data set	Std	Rep	Model	BMR	PROAST	BMDS	bmd	PROAST profile	BMDS profile	bmd delta	bmd inverse	bmd bootstrap
A	1	10	Log–logistic^a	0.05	0.088	0.144	0.144	0	0.050	0.037	0.082	0.051
				0.1	0.129	0.200	0.200	0	0.080	0.077	0.119	0.080
			Weibull²	0.05	0.040	0.126	0.126	0	0.018	0.004	0.063	0.017
				0.1	0.070	0.183	0.183	0	0.034	0.038	0.097	0.032
	0.1	10	Log–logistic	0.05	0.101	0.107	0.107	0.091	0.105	0.097	0.097	0.096
				0.1	0.148	0.154	0.154	0.135	0.151	0.142	0.140	0.140
			Weibull	0.05	0.049	0.074	0.074	0.041	0.060	0.061	0.061	0.061
				0.1	0.086	0.115	0.115	0.073	0.097	0.099	0.098	0.098
	0.1	3	Log–logistic	0.05	0.092	0.097	0.097	0.080	0.078	0.075	0.077	0.079
				0.1	0.138	0.140	0.140	0.121	0.1156	0.114	0.114	0.117
			Weibull	0.05	0.043	0.066	0.066	0.031	0.040	0.037	0.043	0.043
				0.1	0.076	0.105	0.105	0.058	0.067	0.066	0.072	0.072
B	1	10	Log–logistic	0.05	0.003	0.092	0.092	0	0.005	0	0.035	0.005
				0.1	0.008	0.148	0.149	0	0.011	0	0.06	0.012
			Weibull	0.05	0	0.045	0.045	0	0.015	0	0.014	0.003
				0.1	0.002	0.085	0.085	0	0.030	0	0.029	0.007
	0.1	10	Log–logistic	0.05	0.033	0.032	0.032	0.019	0.023	0.024	0.023	0.023
				0.1	0.07	0.067	0.067	0.043	0.050	0.054	0.051	0.05
			Weibull	0.05	0.008	0.056	0.016	0.003	0.051	0.011	0.011	0.011
				0.1	0.022	0.112	0.038	0.012	0.102	0.029	0.027	0.027
	0.1	3	Log–logistic	0.05	0.029	0.036	0.036	0.016	0.028	0.024	0.023	0.023
				0.1	0.064	0.074	0.074	0.038	0.051	0.055	0.051	0.051
			Weibull	0.05	0.008	0.056	0.019	0.004	0.049	0.012	0.012	0.012
				0.1	0.023	0.113	0.044	0.012	0.099	0.031	0.029	0.03
C	1	10	Log–logistic^c	0.05	–	0.717	0.717	–	0.047	0	0.261	0.079
				0.1	–	0.971	0.971	–	0.098102	0	0.369	0.155
			Weibull	0.05	–	0.666	0.666	–	0.051	0	0.224	0.067
				0.1	–	0.930	0.930	–	0.102	0	0.329	0.134
	0.1	10	Log–logistic	0.05	0.847	0.843	0.843	0.737	0.832	0.683	0.696	0.693
				0.1	1.137	1.126	1.126	1.010	1.111	0.954	0.953	0.957
			Weibull	0.05	0.827	0.833	0.833	0.705	0.677	0.651	0.679	0.677
				0.1	1.155	1.132	1.132	1.010	0.950	0.929	0.948	0.952
	0.1	3	Log–logistic	0.05	1.724	3.262	2.621	1.070	3.219	0	1.501	0.821
				0.1	2.054	3.491	2.905	1.380	3.459	0	1.684	1.107
			Weibull	0.05	2.007	3.533	2.647	1.090	3.431	0	1.513	0.802
				0.1	2.382	3.753	2.956	1.450	3.329	0	1.716	1.095

Notes.

Hill model for BMDS and PROAST. The Hill model was fitted as an unrestricted model in BMDS.

Exponential model in BMDS and PROAST. The exponential model was fitted as a restricted model in BMDS.

No model fitted for this data set using PROAST.