Likelihood Inference in Case-control Studies of a Rare Disease Under Independence of Genetic and Continuous Non-genetic Covariates
In genetic association studies, there is increasing interest in understanding the joint effects of genetic and nongenetic factors. For rare diseases, the case-control study is the standard design and logistic regression is the standard method of inference. However, the power to detect statistical interaction is a concern, even with relatively large samples. Under independence of genetic and nongenetic covariates, improved precision of interaction estimators is possible, but logistic regression does not make use of this assumption and consequently is not statistically efficient. To increase efficiency, we develop a semiparametric likelihood approach that incorporates the independence assumption. Our approach is based on classic arguments for case-control inference and allows for the distribution of nongenetic factors to be completely unspecified. We also describe a strategy for relaxing the independence assumption. Under either independence or the proposed dependence model, inference for association parameters is conveniently obtained by fitting a conditional logistic regression. The statistical properties of the proposed methodology are investigated by simulation and connections to previous work are discussed.