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

Family studies to identify disease-related genes often collect families wit h multiple cases. If environmental exposures or other measured covariates a re 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 re duces to standard conditional logistic regression. We show that the simpler conditional logistic regression typically yields biased estimators of expo sure effects, and we describe conditions under which the conditional logist ic approach has little or no bias.