A discrete time event-history approach to informative drop-out in multivariate latent Markov models with covariates

TL;DR

This paper introduces an event-history extension to multivariate latent Markov models to handle informative drop-out in longitudinal data, ensuring unbiased estimates by modeling drop-out as an interval-censored event with correlated random effects.

Contribution

It develops a novel EH-LM model with a unified Markov chain for random effects, extending maximum likelihood estimation with an efficient EM algorithm for multivariate data with informative drop-out.

Findings

Successfully applied to medical data on cirrhosis.

Achieved unbiased parameter estimates in presence of drop-out.

Extended Baum-Welch recursion for efficient computation.

Abstract

Latent Markov (LM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-varying unobserved heterogeneity, which is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the LM approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in LM modeling is avoided by correlated random effects, included in the different model components, which follow a common Markov chain. In order to perform maximum likelihood estimation of the proposed model by the Expectation-Maximization algorithm, we extend the usual backward-forward recursions of Baum and Welch. The algorithm has the same complexity of the one adopted in cases of non-informative drop-out. Standard errors for the parameter estimates are derived by using the Oakes' identity. We illustrate the proposed approach through an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, the first of which is continuous and the second is binary.