Inference for covariates that accounts for ascertainment and random genetic effects in family studies

SUMMARY Family studies to identify disease-related genes often collect families with multiple cases. If environmental exposures or other measured covariates are also important, they should be incorporated into these genetic analyses to control for confounding and increase statistical power. We propose a two-level mixed effects model that allows us to estimate environmental effects while accounting for varying genetic correlations among family members and adjusting for ascertainment by conditioning on the number of cases in the family. We describe a conditional maximum likelihood analysis based on this model. When genetic effects are negligible, this conditional likelihood reduces to standard conditional logistic regression. We show that the simpler conditional logistic regression typically yields biased estimators of exposure effects, and we describe conditions under which the conditional logistic approach has little or no bias.