Serniparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies

We consider the problem of maximum-likelihood estimation in case-control studies of gene-environment associations with disease when genetic and environmental exposures can be assumed to be independent in the underlying population. Traditional logistic regression analysis may not be efficient in this setting. We study the semiparametric maximum likelihood estimates of logistic regression parameters that exploit the gene-environment independence assumption and leave the distribution of the environmental exposures to be nonparametric. We use a profile-likelihood technique to derive a simple algorithm for obtaining the estimator and we study the asymptotic theory. The results are extended to situations where genetic and environmental factors are independent conditional on some other factors. Simulation studies investigate small-sample properties. The method is illustrated using data from a case-control study designed to investigate the interplay of BRCA1/2 mutations and oral contraceptive use in the aetiology of ovarian cancer.