Shrinkage parameter estimation for penalized logistic regression analysis of case-control data

In genetic epidemiology, rare variant case-control studies aim to investigate the association between rare genetic variants and human diseases. Rare genetic variants lead to sparse covariates that are predominately zeros and this sparseness leads to estimators of log-odds-ratio parameters that are biased away from their null value of zero. Different penalized-likelihood methods have been developed to mitigate this sparse-data bias for case-control studies. In this project, we study penalized logistic regression using a class of log-F priors indexed by a shrinkage parameter m to shrink the biased MLE towards zero. We propose a simple method to select the value of m based on a marginal likelihood. The marginal likelihood is maximized by the Monte Carlo EM algorithm. Properties of the proposed method are evaluated in a simulation study, and the method is applied to a real dataset from the ADNI-1 study.