We are motivated by studying the effect that the expression of inflammatory genes has on the risk of colorectal cancer. Gene expression, however, is likely confounded with other risk factors for cancer. But because meiosis within families is considered a random process, the genotypes can potentially be used as instruments for the actual inflammation levels. The problem we address here is that designs are typically based on case-control sampling for these settings. We show first that, in contrast to settings with no confounding, modeled with conditional logistic regression, instrumental variables causal effects are generally incorrectly estimated if the design effect is ignored, as they are not invariant under such designs. We show, second, how in general the framework of principal stratification is useful to validly estimate the causal effects under such designs. We demonstrate these results with the effect of inflammation on colorectal cancer.
Group for Research in Decision Analysis