Continuous Time Survival in Latent Variable Models

We describe a general multivariate, multilevel framework for continuous time survival analysis that includes joint modeling of survival time variables and continuous and categorical observed and latent variables. The proposed framework is implemented in the Mplus software package. The survival time variables are modeled with nonparametric or parametric proportional hazard distributions and include right censoring. The proposed modeling framework includes finite mixtures of Cox regression models with and without class-specific baseline hazards, multilevel Cox regression models, and multilevel frailty models. We illustrate the framework with several simulation studies. Comparison is made with discrete time survival models. We also investigate the effect of ties on the proposed estimation method. Simulation studies are conducted to compare the methods implemented in Mplus with those implemented in SAS.