Simulation study of viable scenarios for potential numerical convergence issues in fitting joint models for longitudinal and survival data

Studies concerning the characteristics of phenomena/experiments over time, such as longitudinal studies or those focused on the time until an event of interest occurs, are increasingly essential in various fields. There may be instances where the investigation of the relationship between one or more longitudinal responses and an event of interest is warranted, a task achievable through the joint model of longitudinal and survival data. However, these models may have convergence problems and be computationally demanding, making their use unfeasible in many cases. In consideration of these factors, the objective of this study is to conduct a Monte Carlo simulation study involving various censoring percentages and correlation structures. The proposed cross-coverage probability will be employed as a diagnostic tool to identify circumstances conducive to numerical convergence, aiming to obtain maximum likelihood estimates for joint models applied to longitudinal and survival data. The results indicated similarity in terms of inference among the models, accounting for the impact of both the correlation structure and the censoring percentage. It was determined that the cross-coverage probability contributes to diagnosing the favorable behavior of the data, thereby facilitating the implementation of joint modeling.