New Approaches for Variable Selection in Longitudinal Studies: An Application to Genetic Association Studies and Bone Loss

We study the problem of variable selection in the context of longitudinal studies by linear mixed effect models when the dimensionality of predictors subject to selection is high. We consider a fully Bayesian formulation of the problem with spike-and-slab a prior distributions which is an appealing solution, however, we find it computationally demanding. As an alternative, we propose a general penalized log-likelihood framework based on marginalized observation equation and a heterogeneous error term. The parameters of the model are estimated by a block wise coordinate gradient descent algorithm. Given the formulation of the considered linear mixed effect models as random slope and intercept models, we consider yet another variable selection procedure which is more ad hoc but has an advantage of computational speed. The procedure consists of two steps and is based on assessing the significance of co-variates from biased predictors of subject-specific random effects. We study the impact of this mis-specification on the accuracy of variable selection. We demonstrate the applicability of the proposed frameworks by studying the association between single nucleotide polymorphisms and bone loss that contributes to the development of osteopenia and osteoporosis in post-menopausal women and aged men and is a strong risk factor for bones fractures and its related mortality. The data is obtained from the longitudinal Dubbo Osteoporosis Epidemiology Study.