Document Type


Date of Degree

Fall 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Zhang, Ying

Second Advisor

Romitti, Paul A.

First Committee Member

Cavanaugh, Joseph E.

Second Committee Member

Methews, Michael P.

Third Committee Member

Mathews, Katherine D.


Joint modeling of a single event time response with a longitudinal covariate dates back to the 1990s. The three basic types of joint modeling formulations are selection models, pattern mixture models and shared parameter models. The shared parameter models are most widely used. One type of a shared parameter model (Joint Model I) utilizes unobserved random effects to jointly model a longitudinal sub-model and a survival sub-model to assess the impact of an internal time-dependent covariate on the time-to-event response.

Motivated by the Muscular Dystrophy Surveillance, Tracking and Research Network (MD STARnet), we constructed a new model (Joint Model II), to jointly analyze correlated bivariate time-to-event responses associated with an internal time-dependent covariate in the Frequentist paradigm. This model exhibits two distinctive features: 1) a correlation between bivariate time-to-event responses and 2) a time-dependent internal covariate in both survival models. Developing a model that sufficiently accommodates both characteristics poses a challenge. To address this challenge, in addition to the random variables that account for the association between the time-to-event responses and the internal time-dependent covariate, a Gamma frailty random variable was used to account for the correlation between the two event time outcomes. To estimate the model parameters, we adopted the Expectation-Maximization (EM) algorithm. We built a complete joint likelihood function with respect to both latent variables and observed responses. The Gauss-Hermite quadrature method was employed to approximate the two-dimensional integrals in the E-step of the EM algorithm, and the maximum profile likelihood type of estimation method was implemented in the M-step. The bootstrap method was then applied to estimate the standard errors of the estimated model parameters. Simulation studies were conducted to examine the finite sample performance of the proposed methodology. Finally, the proposed method was applied to MD STARnet data to assess the impact of shortening fractions and steroid use on the onsets of scoliosis and mental health issues.

Public Abstract

Duchenne/Becker Muscular Dystrophy (DBMD) is a recessive X-linked form of muscular dystrophy with a prevalence rate of 1/3600 among male subjects. Individuals with DBMD suffer muscular degeneration, ceased ambulation and eventually death.

In the Muscular Dystrophy Surveillance, Tracking And Research Network (MD STARnet) surveillance data on male subjects from Iowa, Georgia, Colorado, Arizona and New York State were collected. Using MD STARnet data, we were interested in two time-to-event responses: 1) onset of mental health issues, including anger control, anxiety and depression and 2) onset of scoliosis, defined by a patients' Cobb Angle greater than 10 degrees. The goal of the study was to investigate the association between two time-dependent covariates, shortening fraction and steroid use, and the onsets of mental health issues and scoliosis. These associations indicate whether the two time-dependent covariates are risk factors for the onsets of mental health issues and scoliosis.

The challenge in this study was the lack of existing methods in the Frequentist paradigm that are capable of dealing with bivariate time-to-event responses while accounting for the impact of the two time-dependent covariates on the bivariate survival responses. We proposed a joint model of bivariate event time data to tackle this difficulty and applied the proposed model to MD STARnet data. Jointly modeling the two survival responses was important in this context. Not only did it allow us to ascertain the correlation between the two survival responses, it also enhanced the efficiency of the inference about the effect of time-dependent covariates on the survival responses.


Joint Modeling, Time-to-event data analysis


ix, 103 pages


Includes bibliographical references (pages 99-103).


Copyright © 2015 Ke Liu

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Biostatistics Commons