Seemingly Unrelated Multi-State processes: a Bayesian semiparametric approach

TL;DR

This paper introduces a Bayesian semiparametric joint modeling approach for multiple related multi-state processes, capturing their dependence via random effects and graph structures, with applications in disease progression analysis.

Contribution

It proposes a novel SUMS model with flexible random effects and graphical dependence, advancing multi-state modeling in complex, related processes.

Findings

Effective modeling of disease progression in mental health.

Flexible random effects capture clustering and outliers.

Graph structures describe inter-process dependencies.

Abstract

Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular statistical technique, in particular when the exact transition times are not observed. The key quantities of interest are the transition rates, capturing the instantaneous risk of moving from one state to another. The main contribution of this work is to propose a joint semiparametric model for several possibly related multi-state processes (Seemingly Unrelated Multi-State, SUMS, processes), assuming a Markov structure for the transitions over time. The dependence between different processes is captured by specifying a joint random effect distribution on the transition rates of each process. We assume a flexible random effect distribution, which allows for clustering of the individuals, overdispersion and outliers. Moreover, we employ a graph structure to describe the dependence among processes, exploiting tools from the Gaussian Graphical model literature. It is also possible to include covariate effects. We use our approach to model disease progression in mental health. Posterior inference is performed through a specially devised MCMC algorithm.