Penalized generalized linear mixed models for longitudinal outcomes in genetic association studies

This work is motivated by analyses of longitudinal data collected from participants in the Quebec Longitudinal Study of Child Development (QLSCD) and the Quebec Newborn Twin Study (QNTS) to identify important genetic predictors for emotional and behavioral difficulties in childhood and adolescence. We propose a lasso penalized mixed model for continuous and binary longitudinal traits that allows the inclusion of multiple random effects to account for random individual effects not attributable to the genetic similarity between individuals. Through simulation studies, we show that replacing the estimated genetic relatedness matrix (GRM) by a sparse matrix introduces bias in the variance components estimates, but that the obtained computational gain is major while the impact on the performance of the penalized model to retrieve important predictors is negligible. We compare the performance of the proposed penalized mixed model to a standard lasso and to a univariate mixed model association test and show that the proposed model always identifies causal predictors with greater precision. Finally, we show an application of the proposed methodology to predict three externalizing behavorial scores in the combined QLSCD and QNTS longitudinal cohorts.