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Table 1 Simulation results for the 1-aminoanthraquinone dataset using the benchmark dose method (reference model: Probit)

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

Exclusion
criteriaa
Selectionb Reliability (Mean distance)c Rank Validityd
(%)
Rank BMDL calculabilitye (%) Non-exclusion and BMDL calculationf (%) True dose-responseg (%)
None Lowest BMDL 0.4 5 100.0 1 95.6 95.6 0.1
Lowest BMD 0.3 2 100.0 1 95.6 95.6 0.1
Lowest AIC 120.9 15 88.4 15 95.6 95.6 34.1
MA-all 6.2 9 99.6 8 95.6 95.6 NA
MA-3 4.7 7 99.8 7 100.0 100.0 NA
MA AIC < 3 9.0 11 98.8 11 100.0 100.0 NA
KS Lowest BMDL 0.4 5 100.0 1 95.6 95.6 0.1
Lowest BMD 0.3 2 100.0 1 95.6 95.6 0.1
Lowest AIC 120.9 15 88.4 15 95.6 95.6 34.1
MA-all 6.1 8 99.6 8 95.6 95.6 NA
KS, BMD/BMDL Lowest BMDL 0.3 4 100.0 1 95.6 79.1 0.5
Lowest BMD 0.2 1 100.0 1 95.6 79.1 0.5
Lowest AIC 121.0 17 88.4 15 95.6 79.1 38.4
MA-all 6.3 10 99.3 10 95.6 79.1 NA
KS, BMDU/BMDL Lowest BMDL 27.2 13 91.0 12 95.6 49.0 18.4
Lowest BMD 27.1 12 91.0 12 95.6 49.0 18.4
Lowest AIC 148.3 18 79.4 18 95.6 49.0 35.3
MA-all 33.9 14 90.2 14 95.6 49.0 NA
  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, 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 as 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