Penalized generalized quasi-likelihood based variable selection for longitudinal data

Abstract

High-dimensional longitudinal data with a large number of covariates, have become increasingly common in many bio-medical applications. The identification of a sub-model that adequately represents the data is necessary for easy interpretation. Also, the inclusion of redundant variables may hinder the accuracy and efficiency of estimation and inference. The joint likelihood function for longitudinal data is challenging, particularly in correlated discrete data. To overcome this problem Wang et al. (Biometrics 68:353-360, 2012) introduced penalized GEEs (PGEEs) with a non-convex penalty function which requires only the first two marginal moments and a working correlation matrix. This method works reasonably well in high-dimensional problems; however, there is a risk of model mis-specification such as variance function and correlation structure and in such situations, we propose variable selection based on penalized generalized quasilikelihood (PGQL). Simulation studies show that when model assumptions are true, the PGQL method has performance comparable with that of PGEEs. However, when the model is mis-specified, the PGQL method has clear advantages over the PGEEs method. We have implemented the proposed method in a real case example.