Two‐part hidden Markov models for semicontinuous longitudinal data with nonignorable missing covariates

摘要

This study develops a two‐part hidden Markov model (HMM) for analyzing semicontinuous longitudinal data in the presence of missing covariates. The proposed model manages a semicontinuous variable by splitting it into two random variables: a binary indicator for determining the occurrence of excess zeros at all occasions and a continuous random variable for examining its actual level. For the continuous longitudinal response, an HMM is proposed to describe the relationship between the observation and unobservable finite‐state transition processes. The HMM consists of two major components. The first component is a transition model for investigating how potential covariates influence the probabilities of transitioning from one hidden state to another. The second component is a conditional regression model for examining the state‐specific effects of covariates on the response. A shared random effect is introduced to each part of the model to accommodate possible unobservable heterogeneity among observation processes and the nonignorability of missing covariates. A Bayesian adaptive least absolute shrinkage and selection operator (lasso) procedure is developed to conduct simultaneous variable selection and estimation. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative dataset. New insights into the pathology of Alzheimer's disease and its potential risk factors are obtained.