Maximum likelihood inference on a mixed conditionally and marginally specified regression model for genetic epidemiologic studies with two‐phase sampling

Summary. Two‐phase stratified sampling designs can reduce the cost of genetic epidemiologic studies by limiting expensive ascertainments of genetic and environmental exposure to an efficiently selected subsample (phase II) of the main study (phase I). Family history and some covariate information, which may be cheaply gathered for all subjects at phase I, can be used for sampling of informative subjects at phase II. We develop alternative maximum likelihood methods for analysis of data from such studies by using a novel regression model that permits the estimation of ‘marginal’ risk parameters that are associated with the genetic and environmental covariates of interest, while simultaneously characterizing the ‘conditional’ risk of the disease associated with family history after adjusting for the other covariates. The methods and appropriate asymptotic theories are developed with and without an assumption of gene–environment independence, allowing the distribution of the environmental factors to remain non‐parametric. The performance of the alternative methods and of sampling strategies is studied by using simulated data involving rare and common genetic variants. An application of the methods proposed is illustrated by using a case–control study of colorectal adenoma embedded within the prostate, lung, colorectal and ovarian cancer screening trial.