Simulation-based assessment of model selection criteria during the application of benchmark dose method to quantal response data

Yoshii, Keita; Nishiura, Hiroshi; Inoue, Kaoru; Yamaguchi, Takayuki; Hirose, Akihiko

doi:10.1186/s12976-020-00131-w

Theoretical Biology and Medical Modelling

Table 2 Simulation results for the 2-ethylhexyl vinyl ether dataset (reference model: Probit)

From: Simulation-based assessment of model selection criteria during the application of benchmark dose method to quantal response data

Exclusion^a	Selection^b	Reliability^c (Mean distance)	Rank	Validity^d (%)	Rank	BMDL calculability^e (%)	Non-exclusion and BMDL calculation^f (%)	True dose-response^g (%)
None	Lowest BMDL	17.8	7	100.0	1	85.2	85.2	0
	Lowest BMD	17.8	7	100.0	1	85.2	85.2	0
	Lowest AIC	20.7	15	66.7	9	85.2	85.2	33.4
	MA-all	6.2	6	66.7	9	85.2	85.2	NA
	MA-3	3.6	1	66.7	9	100.0	100.0	NA
	MA AIC < 3	5.1	2	66.7	9	100.0	100.0	NA
KS	Lowest BMDL	17.8	7	100.0	1	85.2	85.2	0
	Lowest BMD	17.8	7	100.0	1	85.2	85.2	0
	Lowest AIC	20.7	15	66.7	9	85.2	85.2	33.4
	MA-all	6.2	5	66.7	9	85.2	85.2	NA
KS, BMD/BMDL	Lowest BMDL	17.8	7	100.0	1	85.2	85.2	0
	Lowest BMD	17.8	7	100.0	1	85.2	85.2	0
	Lowest AIC	20.7	15	66.7	9	85.2	85.2	33.4
	MA-all	6.1	4	66.7	9	85.2	85.2	NA
KS, BMDU/BMDL	Lowest BMDL	17.8	7	100.0	1	85.2	85.2	0
	Lowest BMD	17.8	7	100.0	1	85.2	85.2	0
	Lowest AIC	20.7	15	66.7	9	85.2	85.2	0
	MA-all	6.1	3	66.7	9	85.2	85.2	33.4

^aExclusion criteria: KS, Kolmogorov-Smirnov test of goodness-of-fit; BMD/BMDL, ratio of benchmark dose (BMD₁₀) to benchmark dose lower bound (BMDL₁₀) with values > 10 excluded; BMDU/BMDL, ratio of benchmark dose upper bound (BMDU₁₀) to BMDL₁₀ with values > 10 excluded. ^bModel selection criteria: Lowest BMDL, model with the lowest value of BMDL₁₀; Lowest BMD, model with the lowest value of BMD₁₀; Lowest AIC, e model with the lowest AIC value; MA-all, model averaging of all converged models; MA-3, model averaging of three models with the three lowest AIC values; MA-AIC, model averaging of all models with AIC values < 3 compared with the best model that yielded the minimum AIC. ^cReliability (Mean distance), measured by the mean distance between unbiased BMDL₁₀ and calculated BMDL₁₀ followed by rank. ^dValidity (%), measured as the iterations that satisfied calculated BMDL₁₀ lower than unbiased BMD₁₀ followed by rank. ^eBMDL calculability (%), measured as the iterations that yielded BMDL in the model selection criterion. ^fNon-exclusion and BMDL calculation (%), measured as the iterations that yielded BMDL in the model selection criterion along with exclusion criteria. ^gTrue dose response (%), measured by the default model selected by the model selection criterion. Note: Validity (%), BMDL calculability (%), non-exclusion and BMDL calculation (%), and true dose response (%) were converted into rates of iterations divided by 9000, nine models in 1000 simulation data. NA, not applicable

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ISSN: 1742-4682

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