[Paper Review] A Bayesian Joint model for Longitudinal DAS28 Scores and Competing Risk Informative Drop Out in a Rheumatoid Arthritis Clinical Trial

Violeta Hennessey, Luis León‐Novelo+4 more|arXiv (Cornell University)|Jan 25, 2018

Statistical Methods in Clinical Trials37 references3 citations

TL;DR

This paper proposes a Bayesian joint model that simultaneously analyzes longitudinal DAS28 scores and competing risk informative dropout in a rheumatoid arthritis clinical trial. By linking a longitudinal random change-point model for DAS28 with a time-to-event hazard model for dropout due to inefficacy, adverse events, or administrative reasons, the method corrects for bias in treatment effect estimation caused by informative dropout, with Model 6—sharing all trajectory parameters—showing the best fit (DIC = 391.04).

ABSTRACT

Rheumatoid arthritis clinical trials are strategically designed to collect the disease activity score of each patient over multiple clinical visits, meanwhile a patient may drop out before their intended completion due to various reasons. The dropout terminates the longitudinal data collection on the patients activity score. In the presence of informative dropout, that is, the dropout depends on latent variables from the longitudinal process, simply applying a model to analyze the longitudinal outcomes may lead to biased results because the assumption of random dropout is violated. In this paper we develop a data driven Bayesian joint model for modeling DAS28 scores and competing risk informative drop out. The motivating example is a clinical trial of Etanercept and Methotrexate with radiographic Patient Outcomes (TEMPO, Keystone et.al).

Motivation & Objective

• To address bias in longitudinal DAS28 analysis caused by informative dropout in rheumatoid arthritis clinical trials.
• To model the complex interplay between longitudinal disease activity trends and multiple competing causes of patient dropout.
• To develop a flexible, data-driven Bayesian joint model that accounts for random change-points in DAS28 trajectories and time-to-event dropout processes.
• To compare multiple model specifications and identify the optimal configuration that best fits the TEMPO clinical trial data.
• To demonstrate that separate analysis of longitudinal data overestimates treatment effects when dropout is informative, especially in the methotrexate group.

Proposed method

• Uses a Bayesian hierarchical framework to jointly model DAS28 scores and time-to-dropout with competing risks (inefficacy, adverse events, administrative).
• Employs a longitudinal random change-point model where DAS28 scores follow two linear trends—before and after a subject-specific change-point—capturing early improvement and later stabilization.
• Models time-to-dropout using a log-normal hazard model with a shared random effect linking the longitudinal and survival components.
• Incorporates a selection model structure where dropout hazard depends on latent longitudinal outcomes (e.g., disease activity at dropout, baseline, or pre/post change-point trends).
• Uses Markov Chain Monte Carlo (MCMC) with Gibbs sampling to estimate posterior distributions, with convergence assessed via trace plots, autocorrelation, and potential scale reduction.
• Selects the best-fitting model using Deviance Information Criterion (DIC), with Model 6—sharing all trajectory parameters (αi, β1i, β2i)—selected as optimal.

Experimental results

Research questions

• RQ1 How does informative dropout due to treatment inefficacy or adverse events bias the estimation of treatment effects in longitudinal DAS28 data?
• RQ2 Which model specification best captures the joint dynamics of DAS28 trajectories and competing risk dropout in the TEMPO clinical trial?
• RQ3 Does a joint modeling approach that links longitudinal DAS28 scores with time-to-dropout improve the reliability of treatment effect estimates compared to separate analysis?
• RQ4 How do different assumptions about the dependence of dropout on latent longitudinal processes (e.g., baseline DAS28, change-point trends) affect model fit and inference?
• RQ5 Can a Bayesian random change-point model effectively capture the non-linear improvement pattern in DAS28 scores while accounting for competing risks of dropout?

Key findings

• Model 6, which shares all trajectory parameters (αi, β1i, β2i) between the longitudinal and dropout models, achieved the lowest DIC (391.04), indicating the best fit to the data.
• Separate analysis (Model 1) overestimated treatment effectiveness in the methotrexate group, where dropout due to inefficacy was highest (18.4%), compared to 17.5% in the etanercept group and 5.6% in the combo-therapy group.
• The joint model revealed that dropout due to inefficacy was more strongly associated with poor early disease activity response (β1i) than with baseline disease activity (αi), suggesting early response predicts dropout risk.
• The joint model (Model 6) produced more conservative and reliable treatment effect estimates than separate analysis, especially in treatment groups with high dropout rates.
• Convergence and mixing were achieved for all six models, with acceptable autocorrelation and effective sample sizes, confirming the stability of MCMC sampling.
• The population-level curves from Model 6 (dashed lines) showed a more realistic and less optimistic trajectory for the methotrexate group compared to Model 1 (solid lines), highlighting the bias correction from joint modeling.