Analysis of Longitudinal Categorical Data Using a Continuous Time Semi-Markov Chain Model

• Activity Number: 264 - New Statistical Methods for Longitudinal Data Analysis
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kusha Mohammadi* and Wenyaw Chan and Valory N Pavlik
• Companies: Univeristy of Texas- Health Science Center at Houston and University of Texas-Health Science Center at Houston and Baylor College of Medicine
• Keywords: Semi-Markov Model; Longitudinal Data; Categorical Outcome

Abstract

Longitudinal studies have been paramount to studying dynamic diseases and interventions in public health. Over the years, many statistical developments have contributed to improvements in modeling the dynamics of transitions among disease states. Particularly, the multi-state Markov model has been utilized to estimate the transition rates between multi-categorical responses. However, the Markov property, which assumes the sojourn time to be exponential distributed, may not be realistic in practice. In this research, we consider the semi-Markov framework to analyze longitudinal categorical outcomes that allow for unspecified waiting time distributions. To estimate the parameters of the semi-Markov model, we propose a partial likelihood approach for a three to four stage process. We evaluated our method assuming the sojourn time follows a gamma, Weibull or exponential distribution and examined their sensitivities to our method. The proposed method was evaluated through extensive simulation written with Rcpp package and parallel computing. A longitudinal application of Alzheimer’s disease care-giver stress level was used to illustrate the proposed partial likelihood approach.