Semi-Markov Models for Multistate Data Analysis with Periodic Observations

Abstract

Semi-Markov models are useful to describe transitions in health or disease status in medical research. Estimating latent risk functions among disease statuses with data collected at periodic intervals can be difficult because of incomplete transition information. This study presents a pseudo likelihood approach to analyzing multistate data under a time homogeneous semi-Markov model when transition epochs are incomplete. We first estimate mean sojourn times for each observed time interval based on a competing risk model and its Markov process, and then use those estimated mean sojourn times as the length of transition epochs in observed likelihoods. We use an HIV cohort study to illustrate the method.