A joint continuous time Markov model of the longitudinal data for the bivariate binary outcome with application on mother's stress and child's illness

Xiaoying Yu, The University of Texas School of Public Health


Collecting multiple binary responses over time is very common in the longitudinal studies for biomedical research. Traditionally, researchers or statisticians analyze one outcome at a time and report its result. A transition model is used when the research interest focuses on the transition between two outcome statuses and how the covariates affect the transition rates. Continuous time Markov chain (CTMC) model is recommended when the timing of the transition is uncertain. However, the independent analysis on each process may not yield efficient results, or there are situations which require analyzing two processes simultaneously. Though the joint models have been proposed in many areas, the research for transition models is still limited. ^ The aim of this dissertation is to develop a frequentist approach to estimate model parameters for the joint modeling using CTMC. In Chapter II, joint transition model using shared random effects and the likelihood function was formulated. The Adaptive Gaussian Quadrature was used for the numerical integration for each integral of the random effects and a Dual Quasi-Newton algorithm was used to optimize the log-likelihood function. Empirical studies were conducted to examine the validity of the proposed method and to compare the performance of parameter estimation between the proposed model and the traditional separate-model approach. The derivation of the transition odds ratio (OR) and the programming algorithm for the estimation were also given. We find that the proposed method is more efficient in estimating parameters of interest in general, especially in the small sample size. A joint model with separate random effects for forward and backward transitions accounts for different degrees of the heterogeneity for different transitions and shows large improvements in estimation when compared to separate random effects models. ^ A dataset from the Mothers' Stress and Children's Morbidity Study (MSCM) was used to illustrate our methodologies. We applied the method to the data with one covariate in Chapter II and expand the model to include more covariates in Chapter III. Sophisticated analyses were performed, including model selection and comparison, interpretation on the final model, and transition OR over time and individual predictions based on the final model.^

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Recommended Citation

Yu, Xiaoying, "A joint continuous time Markov model of the longitudinal data for the bivariate binary outcome with application on mother's stress and child's illness" (2015). Texas Medical Center Dissertations (via ProQuest). AAI3720135.