Analysis of bivariate longitudinal discrete data: A joint continuous-time Markov chains approach
Properly understanding the course of disease, particularly the transition rate from one disease stage to another, is important for prognosis. Continuous-time Markov chain (CTMC) methods have been widely used to estimate the transition rates between stages of various diseases, but challenges arise when applied to Alzheimer's disease (AD) or other diseases where there can be both improvement and worsening of symptoms overtime. We propose a new methodology for analyzing bivariate ternary outcome processes under a CTMC framework in AD studies. Because treatments have been shown to improve cognitive impairment among individuals with AD, our proposed method incorporates and irreducible transition rate matrix into our model and, hence, offers flexibility in allowing either disease progression or regression. To reduce bias, we extend the univariate analysis to a joint model framework to accommodate results of two different diagnostic tests administered simultaneously, which further enhances detecting the disease early and properly classifying the stage of AD. The proposed model adopts a shared-parameter to connect the two outcome sequences and obtain parameter estimates using an expectation-maximization algorithm. Simulation studies showed that our joint model more accurately estimated transition rates with satisfactory coverage probability when the correlation between two processes was presented. The correlation process between two outcomes also was evaluated. We observed an unignorable proportion of regressive transitions, implying that the previous progressive assumption was inappropriate and might limit the analysis to assess the possible regression of disease. We also incorporate the covariates into the joint continuous-time Markov chain model to study the covariate effects on the disease transition. Our innovative approach groups the effects of covariates with favorable clinical interpretations to avoid possible numerical instability in parameter estimation. Our application of joint continuous-time Markov chain to a large cohort of patients with Alzheimer disease (AD) described the natural history of AD and interpreted covariate effects on disease transition. Our proposed model is unique with its ability to describe the transition rates and consider covariate effects on both progression and regression of disease, and enjoys the computational and predictive advantages.
Wu, Chih-Hsien, "Analysis of bivariate longitudinal discrete data: A joint continuous-time Markov chains approach" (2016). Texas Medical Center Dissertations (via ProQuest). AAI10126217.