Doubly robust methods for handling confounding by cluster

In clustered designs such as family studies, the exposure-outcome association is usually confounded by both cluster-constant and cluster-varying confounders. The influence of cluster-constant confounders can be eliminated by studying the exposure-outcome association within (conditional on) clusters, but additional regression modeling is usually required to control for observed cluster-varying confounders. A problem is that the working regression model may be misspecified, in which case the estimated within-cluster association may be biased. To reduce sensitivity to model misspecification we propose to augment the standard working model for the outcome with an auxiliary working model for the exposure. We derive a doubly robust conditional generalized estimating equation (DRCGEE) estimator for the within-cluster association. This estimator combines the two models in such a way that it is consistent if either model is correct, not necessarily both. Thus, the DRCGEE estimator gives the researcher two chances instead of only one to make valid inference on the within-cluster association. We have implemented the estimator in an R package and we use it to examine the association between smoking during pregnancy and cognitive abilities in offspring, in a sample of siblings.