A Bayesian Approach for Nonignorable Dropout in Bivariate Longitudinal Models

2026-06-24

AI Summary

This study addresses missing data in bivariate longitudinal settings arising from non-random dropout—particularly when the two response variables exhibit asynchronous dropout times and complex distributional features such as skewness and heavy tails. The authors propose an innovative Bayesian nonparametric joint modeling approach that simultaneously characterizes the observation processes and dropout mechanisms for both variables. By incorporating identification constraints based on dropout indicators and sensitivity parameters, the method achieves partial identification of the missing data distribution under nonignorable missingness. Assigning priors to the sensitivity parameters enables systematic sensitivity analyses across a range of plausible missingness scenarios. This work represents the first extension of Bayesian nonparametric modeling to bivariate longitudinal dropout contexts and demonstrates its practical utility through successful application to a cost-effectiveness clinical trial on intellectual disability interventions, yielding robust evidence to inform health policy decisions.

Abstract

Longitudinal data collected in clinical trials are almost always incomplete due to some of the participants dropping out from the study during the planned follow-up. A common strategy to handle nonresponse expresses missingness in terms of a dropout process, which is jointly analysed with the outcome process to facilitate the formulation of the missingness assumptions. However, when the outcome is multivariate, the identification of the dropout process becomes problematic, especially when individuals have different dropout times for each type of response, and sensitivity analysis is difficult. The modelling task may be also be complicated by data complexities (e.g. skewness and spikes) which are difficult to capture through standard parametric methods. An example of this analysis framework occurs in trial-based economic evaluations, where a longitudinal bivariate response, formed by suitably-defined measures of effectiveness and costs, is analysed to inform policymakers about the cost-effectiveness of alternative interventions. We present a novel Bayesian nonparametric approach to handle a missing bivariate longitudinal outcome by jointly modelling the dropout process associated with each type of response while also taking into account the complexities of the data. We specify a flexible nonparametric model for the observed data and partially identify the distribution of the missing data with identifying restrictions conditional on the dropout indicators and sensitivity parameters. We explore alternative nonignorable scenarios through different priors for the sensitivity parameters. Our approach is motivated by, and applied to, data from a trial assessing the cost-effectiveness of a new treatment for intellectual disability and challenging behaviour.

Problem

• nonignorable dropout
• bivariate longitudinal data
• missing data
• sensitivity analysis
• data complexity

Innovation

• Bayesian nonparametrics
• nonignorable dropout
• bivariate longitudinal data
• sensitivity analysis
• missing data