Goodness-of-Fit Checks for Joint Models

TL;DR

This paper tackles the lack of systematic goodness-of-fit tools for joint models of longitudinal and time-to-event data. It proposes a Bayesian posterior predictive checks framework that assesses the longitudinal mean, variance, and correlation, survival distributions via empirical CDFs and probability integral transforms, and the longitudinal-survival association via time-dependent concordance, across settings that include existing subjects, new covariate-only subjects, dynamic predictions, and cross-validated assessment. The framework is demonstrated in the Bio-SHiFT heart failure study and through simulations, showing that it can identify misspecifications that traditional criteria may miss and guide model refinement, with an implementation available in the JMbayes2 R package. Overall, the approach provides a flexible, comprehensive toolkit for diagnosing joint model fit and improving predictive reliability in clinical settings.

Abstract

Joint models for longitudinal and time-to-event data are widely used in many disciplines. Nonetheless, existing model comparison criteria do not indicate whether a model adequately fits the data or which components may be misspecified. We introduce a Bayesian posterior predictive checks framework for assessing a joint model's fit to the longitudinal and survival processes and their association. The framework supports multiple settings, including existing subjects, new subjects with only covariates, dynamic prediction at intermediate follow-up times, and cross-validated assessment. For the longitudinal component, goodness-of-fit is assessed through the mean, variance, and correlation structure, while the survival component is evaluated using empirical cumulative distributions and probability integral transforms. The association between processes is examined using time-dependent concordance statistics. We apply these checks to the Bio-SHiFT heart failure study, and a simulation study demonstrates that they can identify model misspecification that standard information criteria fail to detect. The proposed methodology is implemented in the freely available R package JMbayes2.

Figures (1)

• Figure 1: Top-left panel: posterior-posterior predictive checks for the mean function of eGFR using 50 simulated datasets from the joint model that assumes linear subject-specific profiles and the value functional form; the grey lines are the loess curves of the simulated data, and the superimposed black line is the loess curve of the observed data. Top-right panel: posterior-posterior predictive checks for the semi-variogram function of NGAL using 50 simulated datasets from the joint model that assumes nonlinear subject-specific profiles and the value functional form; the grey lines are the loess curves of the simulated data, and the superimposed black line is the loess curve of the observed data. Bottom-left panel: posterior-prior predictive checks for the composite event outcome using 50 simulated datasets from the joint model that assumes linear subject-specific profiles and the area functional form; the grey lines are the eCDF curves of the simulated data, the superimposed black line is the Kaplan-Meier curve of the observed data, and the dashed black line is the 95% confidence interval of the Kaplan-Meier estimate. Bottom-right panel: posterior-prior predictive checks for the concordance statistic between NGAL and the composite event using 50 simulated datasets from the joint model that assumes nonlinear subject-specific profiles and the area functional form; the grey lines are the loess curves of the simulated data, and the superimposed black line is the loess curve of the observed data.