A simulation study on the impact of censoring on standard errors in the clustered joint model

Abstract

This simulation study rigorously evaluated the impact of censoring on standard error (SE) estimation in clustered joint models for longitudinal binary and survival outcomes. Joint models were vital in biomedical research for analysing interdependent repeated measures and event times, but their performance in clustered settings (e.g., multicenter trials) under censoring remained under explored. We focused on scenarios like adolescent HIV studies, where binary viral load suppression (longitudinal) and time to treatment interruption (survival) were modelled jointly with shared random effects to account for within-cluster correlation. Using Monte Carlo simulations (200–1000 replications) with 10 clusters of 20 subjects, we systematically varied right-censoring rates (5%–35%), cluster sizes, and random-effects structures. Performance metrics including bias, root mean squared error (RMSE), empirical standard errors (ESE), asymptotic standard errors (ASE), and coverage probabilities (CP) were compared. Results revealed that censoring significantly distorted SE estimation, with ASE increasingly underestimating ESE for key parameters as censoring intensified. For WHO stage parameters (e.g., β₂, β₃), ASEESE agreement held reasonably until 20% censoring, but deteriorated thereafter. The ART regimen parameter (γ_s) exhibited substantial bias and RMSE inflation beyond 20% censoring (e.g., bias: 0.0675, RMSE: 0.1441 at 30% censoring), with CP falling to 89.5%. Conversely, age parameters (γ_a) showed reduced bias under higher censoring. Variance components (log(σ_u), log(σ_v)) displayed significant ASE-ESE discrepancies at all censoring levels. We identified a critical threshold near 20% censoring, beyond which inference reliability declined markedly for treatment-related parameters. Spline-smoothed error trends further illustrated parameter-specific sensitivities. These findings cautioned against relying solely on asymptotic SE approximations in high-censoring or complex clustered designs and underscored the need for robust variance estimation. The study provided practical guidance: research focused on clinical covariates (e.g., ART) should limit censoring below 20%, while demographic parameters tolerated higher rates.