Table C.12.
Result for the incidence of hepatocellular carcinomas reported by Moser et al. (2009) and NTP (1993), using study as a covariate and using model averaging
| Model | Included covariate(s) | Number of parameters | Log‐likelihood | AIC | BMD – study.Moser | BMDL – study.Moser | BMDU – study.Moser | BMD – study.NTP | BMDL – study.NTP | BMDU – study.NTP | Converged | Accepted AIC | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Null | 1 | −165.92 | 333.84 | NA | NA | NA | NA | NA | NA | Yes | ||
| 2 | Full | 7 | −125.20 | 264.40 | NA | NA | NA | NA | NA | NA | Yes | ||
| 3 | Logistic | 2 | −126.28 | 256.56 | 6.26 | 5.46 | 7.14 | 6.26 | 5.46 | 7.14 | Yes | Yes | |
| 4 | Logistic | a | 3 | −126.05 | 258.10 | 5.91 | 5.00 | 7.19 | 5.91 | 5.00 | 7.19 | Yes | Yes |
| 5 | Logistic | b | 3 | −125.22 | 256.44 | 5.13 | 4.22 | 6.66 | 6.73 | 5.75 | 7.80 | Yes | Yes |
| 6 | Logistic | a, b | 4 | −125.20 | 258.40 | 5.14 | 4.22 | 6.65 | 6.61 | 5.30 | 8.08 | Yes | Yes |
| 7 | Probit | 2 | −126.30 | 256.60 | 5.74 | 5.00 | 6.59 | 5.74 | 5.00 | 6.59 | Yes | Yes | |
| 11 | Log‐logistic | 3 | −125.95 | 257.90 | 6.44 | 4.81 | 7.95 | 6.44 | 4.81 | 7.95 | Yes | Yes | |
| 12 | Log‐logistic | a | 4 | −125.93 | 259.86 | 6.45 | 4.83 | 7.94 | 6.45 | 4.83 | 7.94 | Yes | No |
| 13 | Log‐logistic | b | 4 | −124.55 | 257.10 | 5.87 | 4.62 | 7.19 | 7.90 | 5.85 | 9.91 | Yes | Yes |
| 14 | Log‐logistic | a, b | 5 | −124.52 | 259.04 | 5.88 | 4.62 | 7.18 | 8.01 | 5.88 | 10.94 | Yes | No |
| 15 | Log‐probit | 3 | −125.87 | 257.74 | 6.49 | 4.94 | 7.91 | 6.49 | 4.94 | 7.91 | Yes | Yes | |
| 16 | Log‐probit | a | 4 | −125.84 | 259.68 | 6.49 | 4.95 | 7.90 | 6.49 | 4.95 | 7.90 | Yes | No |
| 17 | Log‐probit | b | 4 | −124.50 | 257.00 | 5.90 | 4.66 | 7.22 | 7.82 | 5.91 | 9.59 | Yes | Yes |
| 18 | Log‐probit | a, b | 5 | −124.49 | 258.98 | 5.90 | 4.66 | 7.22 | 7.88 | 5.91 | 10.38 | Yes | No |
| 19 | Weibull | 3 | −126.04 | 258.08 | 6.36 | 4.62 | 7.99 | 6.36 | 4.62 | 7.99 | Yes | Yes | |
| 20 | Weibull | a | 4 | −126.03 | 260.06 | 6.36 | 4.62 | 7.99 | 6.36 | 4.62 | 7.99 | Yes | No |
| 21 | Weibull | b | 4 | −124.60 | 257.20 | 5.80 | 4.53 | 7.15 | 7.99 | 5.76 | 10.14 | Yes | Yes |
| 22 | Weibull | a, b | 5 | −124.56 | 259.12 | 5.82 | 4.53 | 7.13 | 8.13 | 5.80 | 11.29 | Yes | No |
| 23 | Gamma | 3 | −125.93 | 257.86 | 6.44 | 4.77 | 7.94 | 6.44 | 4.77 | 7.94 | Yes | Yes | |
| 24 | Gamma | a | 4 | −125.91 | 259.82 | 6.45 | 4.78 | 7.93 | 6.45 | 4.78 | 7.93 | Yes | No |
| 25 | Gamma | b | 4 | −124.52 | 257.04 | 5.86 | 4.61 | 7.19 | 7.88 | 5.85 | 9.73 | Yes | Yes |
| 26 | Gamma | a, b | 5 | −124.50 | 259.00 | 5.87 | 4.61 | 7.18 | 7.97 | 5.87 | 10.57 | Yes | No |
| 27 | Two‐stage | 3 | −126.23 | 258.46 | 5.80 | 5.09 | 6.71 | 5.80 | 5.09 | 6.71 | Yes | No | |
| 28 | Two‐stage | a | 4 | −126.23 | 260.46 | 5.79 | 5.08 | 6.72 | 5.79 | 5.08 | 6.72 | Yes | No |
| 29 | Two‐stage | b | 4 | −125.88 | 259.76 | 5.09 | 3.99 | 6.96 | 5.99 | 5.17 | 7.06 | Yes | No |
| 30 | Two‐stage | a, b | 5 | −125.87 | 261.74 | 5.07 | 3.98 | 6.96 | 6.01 | 5.17 | 7.16 | Yes | No |
AIC: Akaike information criterion; BMD: benchmark dose; BMDL: benchmark dose lower confidence limit; BMDU: benchmark dose upper confidence limit.