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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

Exclusiona Selectionb Reliabilityc (Mean distance) Rank Validityd (%) Rank BMDL calculabilitye
(%)
Non-exclusion and BMDL calculationf (%) True dose-responseg (%)
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
  1. 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