Table 1.

Illustrative example of collapsing an effect across the risk factor distribution: non-equality of subject-specific and population-averaged odds ratios and equality of relative risks

Logistic-linear model: logit π = −2 + X log(2)
Risk factor (x)	P (Y = 1|X = x)	P (Y = 1|X = x + 1)	Odds ratio
0.2	0.135	0.237	2
0.4	0.152	0.263	2
1.4	0.263	0.417	2
1.8	0.320	0.485	2
Average	0.217	0.351	1.94

Log-linear model: log π = −2 + X log(2)
Risk factor (x)	P (Y = 1|X = x)	P (Y = 1|X = x + 1)	Relative risk
0.2	0.155	0.311	2
0.4	0.179	0.357	2
1.4	0.357	0.714	2
1.8	0.471	0.943	2
Average	0.291	0.581	2