A joint logistic regression and covariate‐adjusted continuous‐time Markov chain model

• Published in: Statistics in medicine Vol. 36; no. 28; pp. 4570 - 4582
• Main Authors: Rubin, Maria Laura, Chan, Wenyaw, Yamal, Jose‐Miguel, Robertson, Claudia Sue
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 10.12.2017
• Subjects: Brain Injuries, Traumatic - therapy; Computer Simulation; continuous‐time Markov chain; Cross-Sectional Studies; Humans; joint model; Likelihood Functions; Logistic Models; logistic regression; longitudinal data; Longitudinal Studies; Markov analysis; Markov Chains; Medical statistics; Physiology; Prognosis; Randomized Controlled Trials as Topic; transition rates; Treatment Outcome; continuous-time Markov chain; logistic regression; joint model; transition rates; longitudinal data
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.7387

The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross‐sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross‐sectional response, where the unobserved transition rates of a two‐state continuous‐time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6‐month outcome based on physiological data collected post‐injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long‐term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd.