# A Bayesian Multilevel Joint Modeling of Longitudinal and Survival Outcomes in Cluster Randomized Controlled Trial Studies

## TL;DR

This paper introduces a new statistical model for analyzing mental health interventions delivered in group settings, showing that ignoring group structures leads to biased results.

## Contribution

The paper introduces a multilevel joint model (MJM) that accounts for clustering in CRCTs, enabling accurate evaluation of longitudinal and survival outcomes.

## Key findings

- The PAX program significantly improved mental health trajectories and reduced mental disorder diagnoses.
- Ignoring hierarchical structures leads to biased inferences and underestimation of intervention effects.
- The MJM outperformed traditional joint models in accuracy and standard error estimation.

## Abstract

Cluster randomized controlled trials (CRCTs) are commonly used when interventions are delivered at the group level. Since data from CTCTs are inherently multilevel, methods that properly account for clustering are required. Joint modeling (JM) of longitudinal and survival data allows for simultaneous evaluation of intervention effects on repeated measures and time‐to‐event outcomes, offering a comprehensive view of intervention effects. However, existing JMs do not accommodate clustered data structures typically of CRCTs. This study introduces a multilevel joint model (MJM) to simultaneously evaluate intervention effects on correlated longitudinal and survival outcomes. The model was applied to empirical data from a large CRCT evaluating the PAX Good Behavior Game, a classroom‐based mental health intervention involving 4189 Grade 1 students across 313 classrooms during the 2011–2012 school year. Mental health was assessed at three time points: pre‐PAX (January 2012), post‐PAX (June 2012), and Grade 5 (June 2016). Time‐to‐first mental disorder diagnosis was tracked through March 2024. Simulation studies further evaluated the MJM's performance under varying conditions, including censoring rates, cluster sizes, group‐level variances, and survival model specifications. Results indicated the PAX program significantly improved mental health trajectories and reduced the risk of mental disorder diagnoses. The MJM outperformed traditional JMs by producing more accurate estimates and standard errors. Both empirical and simulation findings demonstrated that ignoring hierarchical structures leads to biased inferences and underestimation of intervention effects. The proposed MJM offers a robust and flexible analytic framework for analyzing data from CRCTs, emphasizing the importance of accounting for clustering in evaluating group‐based interventions.