Joint model for repeated measurements and competing risks data using flexible shared random effects

In advanced clinical trials, clinicians collect data on both time-to-event outcomes with respective causes and longitudinal characteristics during each follow-up visit. Such experiments motivate researchers to develop feasible models suitable for the inference of the obtained data. In this article, a joint model is designed for longitudinal data or repeated measurement data and time-to-event data generated in the presence of competing risks. For the longitudinal data, a linear mixed-effects model is considered to capture the fixed effects of covariates on longitudinal measurements, while the random effects account for between-individual variation over the visiting time points. For the competing risks process, a generalized exponential distribution is used, with the scale parameter modeled as an exponential function of a linear combination of covariates. To link these two processes, a shared random effects association structure is employed. The parameters of the joint model are estimated using the maximum likelihood technique via the Expectation-Maximization algorithm, where the random effects are treated as latent variables. Additionally, a simulation study is conducted to evaluate the performance of the joint model. Finally, the model is applied to real-life data from the SANAD trial, demonstrating its practical utility.