Joint modeling of longitudinal measurements and survival outcomes in heart valve transplantation data

A joint modeling technique for longitudinal data and time-to-event data is advanced statistical methodology to analyze repeated measurements and time-to-event outcomes. In the present article, a shared random effects approach is considered to account for both longitudinal data and survival outcomes. The longitudinal data is submodeled by a linear mixed-effects model that captures the individual response over time. Whereas the time-to-event sub-model uses the generalized exponential distribution as the baseline distribution for the proportional hazard model to incorporate survival times as well as time-independent covariates. To estimate model parameters, the Expectation-Maximization approach has been used, which is effective with latent random effects since random effects are unobservable in nature. In the E-step, the expected log-likelihood is derived based on current parameter estimates, and in the M-step, we maximize this likelihood to update the parameters. To show the efficacy of the proposed approach, an extensive simulation study has been conducted. Furthermore, the model is tested on a real-world medical dataset, heart valve data, to demonstrate its efficacy in analyzing the link between longitudinal responses and survival outcomes.