Table 3.

Case-control data from the bladder cancer study of Rothman et al [28]. 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 = −3.2)
Never	Rapid/Intermediate	760	1679	−0.793 (0.044)	−0.912 (0.032)	−0.825 (0.027)
Never	Slow	1202	2758	−0.831 (0.035)	−0.756 (0.029)	−0.808 (0.028)
Past	Rapid/Intermediate	1859	2300	−0.213 (0.031)	−0.194 (0.026)	−0.199 (0.023)
Past	Slow	3455	3559	−0.030 (0.024)	−0.041 (0.021)	−0.034 (0.023)
Current	Rapid/Intermediate	1165	1254	−0.074 (0.041)	−0.004 (0.030)	−0.086 (0.033)
Current	Slow	2258	1865	0.191 (0.031)	0.150 (0.027)	0.194 (0.031)
Maximum log-likelihood				−16178.38	−16186.88	−16179.04
MSE				0.0012	0.0052	0.0011
AIC				32368.76	32381.76	32368.08
BIC				32417.30	32414.12	32408.52