|
Exclusiona
|
Selectionb
|
Reliabilityc (Mean distance)
|
Rank
|
Validityd (%)
|
Rank
|
BMDL calculabilitye
(%)
|
Non-exclusion and BMDL calculationf (%)
|
True dose-responseg (%)
|
|---|
|
None
|
Lowest BMDL
|
0.4
|
17
|
99.9
|
1
|
99.8
|
99.8
|
0.0
|
|
Lowest BMD
|
0.3
|
13
|
99.7
|
5
|
99.8
|
99.8
|
0.1
|
|
Lowest AIC
|
0.1
|
2
|
89.0
|
16
|
99.8
|
99.8
|
38.3
|
|
MA-all
|
0.2
|
10
|
98.2
|
11
|
99.8
|
99.8
|
NA
|
|
MA-3
|
0.1
|
1
|
93.9
|
14
|
100.0
|
100.0
|
NA
|
|
MA AIC < 3
|
0.2
|
8
|
97.8
|
13
|
100.0
|
100.0
|
NA
|
|
KS
|
Lowest BMDL
|
0.4
|
17
|
99.9
|
1
|
99.8
|
99.8
|
0.0
|
|
Lowest BMD
|
0.3
|
13
|
99.7
|
5
|
99.8
|
99.8
|
0.1
|
|
Lowest AIC
|
0.1
|
2
|
89.0
|
15
|
99.8
|
99.8
|
38.3
|
|
MA-all
|
0.2
|
9
|
98.4
|
10
|
99.8
|
99.8
|
NA
|
|
KS, BMD/BMDL
|
Lowest BMDL
|
0.3
|
16
|
99.9
|
1
|
99.8
|
98.7
|
0.0
|
|
Lowest BMD
|
0.3
|
12
|
99.7
|
5
|
99.8
|
98.7
|
0.2
|
|
Lowest AIC
|
0.1
|
5
|
88.7
|
17
|
99.8
|
98.7
|
38.7
|
|
MA-all
|
0.2
|
7
|
98.7
|
9
|
99.8
|
98.7
|
NA
|
|
KS, BMDU/BMDL
|
Lowest BMDL
|
0.3
|
15
|
99.9
|
1
|
99.8
|
93.9
|
0.0
|
|
Lowest BMD
|
0.2
|
11
|
99.6
|
8
|
99.8
|
93.9
|
0.2
|
|
Lowest AIC
|
0.1
|
4
|
88.5
|
18
|
99.8
|
93.9
|
39.0
|
|
MA-all
|
0.2
|
6
|
98.2
|
11
|
99.8
|
93.9
|
NA
|
- 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 three smallest 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 as 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
