Penalized Logistic Regression Analysis for Genetic Association Studies of Binary Phenotypes

Abstract

AbstractIncreasingly, logistic regression methods for genetic association studies of binary phenotypes must be able to accommodate rare genetic variants. Rare variants represent sparse covariates that are predominately zeros, and this sparseness leads to maximum likelihood estimators (MLEs) of log-OR parameters that are biased away from their null value of zero. Different penalized-likelihood methods have been developed to mitigate sparse-data bias. 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. For a given m, log-F -penalized logistic regression may be easily implemented using data augmentation and standard software. We propose a two-step approach to the analysis of a genetic association study: first, a set of approximately independent variants is used to estimate m; and second, the estimated m is used for log-F -penalized logistic regression analyses of all variants. Our estimate of m is the maximizer of a marginal likelihood obtained by integrating the latent log-ORs out of the joint distribution of the parameters and observed data. We consider two approximate approaches to maximizing the marginal likelihood: (i) a Monte Carlo EM algorithm and (ii) a Laplace approximation to each integral, followed by derivative-free optimization of the approximation. We evaluate the statistical properties of our proposed two-step method and compared its performance to other shrinkage methods by a simulation study.