On The Interplay between Exposure Misclassification and Informative Cluster Size

Abstract

A recent multigenerational study of diethylstilbestrol and attention deficit hyperactivity disorder exhibited signs of both informative cluster size-the outcome was more prevalent in small families-and exposure misclassification-self-report of familial diethylstilbestrol exposure was substantially mismeasured. Motivated by this, we study the effect of exposure misclassification when cluster size is potentially informative and, in particular, when misclassification is differential by cluster size. We find that: misclassification in an exposure that is related to cluster size induces informativeness when cluster size would otherwise be non-informative; and misclassification that is differential by informative cluster size may attenuate, inflate or possibly reverse the sign of estimates. To mitigate these issues, we propose an observed likelihood correction for joint models of cluster size and outcomes, and an expected estimating equations correction. We evaluate these approaches in simulations and in application to the motivating data from the second Nurses Health Study, NHS II.