A mixture of transition models for heterogeneous longitudinal ordinal data: with applications to longitudinal bacterial vaginosis data

Abstract

Markov models used to analyze transition patterns in discrete longitudinal data are based on the limiting assumption that individuals follow the common underlying transition process. However, when one is interested in diseases with different disease or severity subtypes, explicitly modeling subpopulation-specific transition patterns may be appropriate. We propose a model which captures heterogeneity in the transition process through a finite mixture model formulation and provides a framework for identifying subpopulations at different risks. We apply the procedure to longitudinal bacterial vaginosis study data and demonstrate that the model fits the data well. Further, we show that under the mixture model formulation, we can make the important distinction between how covariates affect transition patterns unique to each of the subpopulations and how they affect which subgroup a participant will belong to. Practically, covariate effects on subpopulation-specific transition behavior and those on subpopulation membership can be interpreted as effects on short-term and long-term transition behavior. We further investigate models with higher-order subpopulation-specific transition dependence.

Keywords: Markov model; bacterial vaginosis; heterogeneity; longitudinal data; mixture model; mover stayer model.