Figure 1.

Apparently paradoxical gene-phenotype associations in the context of disease stratified genetic studies. We simulated genotype, continuous risk factor values and disease status in a general population sample according to our liability scale model and set the genetic effect on the risk factor ($\gamma$) to zero. We observed that the estimated effect of the ‘B’ allele of a genetic marker on a continuous trait is negative both in cases and controls. Disease carriers also have higher trait value than controls. However, when combining the two strata the marker is—as expected— not associated with the trait. The reason for this apparent paradox is that the proportion of disease risk allele ‘B’) carriers is higher in the case group. Thus when merging cases into the control group the mean trait value of the BB group increases much more than it does in the other genotype groups. This concept is recognized as Simpson's paradox (40).