A latent class approach for joint modeling of a time-to-event outcome and multiple longitudinal biomarkers subject to limits of detection

Multiple biomarkers on different biological pathways are often measured over time to investigate the complex mechanism of disease development and progression. Identification of informative subpopulation patterns of longitudinal biomarkers and clinical endpoint may assist in risk stratification and provide insights into new therapeutic targets. Motivated by a multicenter study to assess the inflammatory markers of sepsis in patients with community-acquired pneumonia, we propose a joint latent class analysis of multiple biomarkers and a time-to-event outcome while accounting for censored biomarker measurements due to detection limits. The interrelationship between biomarker trajectories and clinical endpoint is fully captured by a latent class structure, which reveals the subpopulation profiles of biomarkers and clinical outcome. The estimation of joint latent class models becomes more complicated when biomarkers are subject to detection limits. Based on a Metropolis–Hastings method, we develop a Monte Carlo Expectation–Maximization (MCEM) algorithm to estimate model parameters. We demonstrate the satisfactory performance of our MCEM algorithm using simulation studies, and apply our method to the motivating study to examine the heterogeneous patterns of cytokine responses to pneumonia and associated mortality risks.