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.

Parameter Estimation of Rayleigh Distribution Based on MCEM Algorithm

MCEM algorithm produces based on the evolution of the EM algorithm. According to the MCEM algorithm theory, the iterative formula of parameter estimation of Rayleigh was derived based on MCEM algorithm, meanwhile the computer simulation algorithm was designed. Computer simulation shows that , in the case of the small sample, parameter estimation of MCEM algorithm is more stable and precise than MLE algorithm.

PARAMETER ESTIMATE WITH ONLY ONE COMPLETE FAILURE OBSERVATION USING MONTE CARLO EM ALGORITHM

In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likelihood estimation of parameters becomes a difficult problem. Mao and Chen published a real data set of the lifetime of a certain type of bearings which only contains one failure data. They used a Bayesian method to analyze the data and obtained some results for model parameter estimation. However, in their method the choice of prior distribution will affect heavily the final results. In this paper, we propose a Monte Carlo EM (MCEM) algorithm to estimate reliability model parameters using the Weibull distribution. Based on the same data set of Mao and Chen, we obtain some results using the MCEM algorithm. Our results do not depend on the choice of arbitrary prior distributions.