Regularized Latent Class Model for Joint Analysis of High‐Dimensional Longitudinal Biomarkers and a Time‐to‐Event Outcome

Although many modeling approaches have been developed to jointly analyze longitudinal biomarkers and a time‐to‐event outcome, most of these methods can only handle one or a few biomarkers. In this article, we propose a novel joint latent class model to deal with high dimensional longitudinal biomarkers. Our model has three components: a class membership model, a survival submodel, and a longitudinal submodel. In our model, we assume that covariates can potentially affect biomarkers and class membership. We adopt a penalized likelihood approach to infer which covariates have random effects and/or fixed effects on biomarkers, and which covariates are informative for the latent classes. Through extensive simulation studies, we show that our proposed method has improved performance in prediction and assigning subjects to the correct classes over other joint modeling methods and that bootstrap can be used to do inference for our model. We then apply our method to a dataset of patients with idiopathic pulmonary fibrosis, for whom gene expression profiles were measured longitudinally. We are able to identify four interesting latent classes with one class being at much higher risk of death compared to the other classes. We also find that each of the latent classes has unique trajectories in some genes, yielding novel biological insights.