Table 2.
Case-control data from the advanced colorectal adenoma study of Moslehi et al [27]. Columns 1 and 2 show the levels of smoking and NAT2 acetylation (based on SNP rs1495741). Columns 5, 6, and 7 show the estimated log odds and the standard errors in parentheses based on three models. Note that the full logistic model is a saturated model. Therefore, for this model, the estimated log odds is equal to the observed log odds, and the estimtated standard error is the square root of the sum of the inverse of the number of cases and the number of controls. We refer to these standard errors as the “within class” standard errors. The value of λ used to fit the additive GJ model is shown in parentheses in the last column. The last three rows of the table show the maximum log-likelihood, mean squared error (MSE), Akaike’s AIC, and the Bayes information criterion for the three models.
| 1 | 2 | 3 | 4 | 5–7 Estimated log odds (std error) from three models | ||
|---|---|---|---|---|---|---|
| Smoking | NAT2 acetylation | Case | Control | Full logistic | Additive logistic | Optimal additive GJ (λ = −4.62) |
| Never | Rapid/Intermediate | 92 | 124 | −0.298 (0.138) |
−0.319 (0.111) |
−0.197 (0.078) |
| Never | Slow | 140 | 158 | −0.121 (0.116) |
−0.106 (0.101) |
−0.153 (0.095) |
| Past | Rapid/Intermediate | 108 | 116 | −0.071 (0.134) |
−0.226 (0.109) |
−0.132 (0.080) |
| Past | Slow | 134 | 153 | −0.133 (0.118) |
−0.013 (0.102) |
−0.070 (0.094) |
| Current | Rapid/Intermediate | 60 | 52 | 0.143 (0.189) |
0.499 (0.143) |
0.163 (0.172) |
| Current | Slow | 115 | 42 | 1.007 (0.180) |
0.712 (0.137) |
1.007 (0.180) |
| Maximum log-likelihood | −875.308 | −879.646 | −875.868 | |||
| MSE | 0.0221 | 0.0561 | 0.0186 | |||
| AIC | 1762.617 | 1767.293 | 1761.735 | |||
| BIC | 1793.61 | 1787.955 | 1787.563 | |||