A Copula Approach to Joint Modeling of Longitudinal Measurements and Survival Times Using Monte Carlo Expectation-Maximization with Application to AIDS Studies

Abstract

Joint modeling of longitudinal measurements and time to event data is often performed by fitting a shared parameter model. Another method for joint modeling that may be used is a marginal model. As a marginal model, we use a Gaussian model for joint modeling of longitudinal measurements and time to event data. We consider a regression model for longitudinal data modeling and a Weibull proportional hazard model for event time data modeling. A Gaussian copula is used to consider the association between these two models. A Monte Carlo expectation-maximization approach is used for parameter estimation. Some simulation studies are conducted in order to illustrate the proposed method. Also, the proposed method is used for analyzing a clinical trial dataset.

Key Words:

• Copula models
• Expectation-maximization algorithm
• Longitudinal model
• Non-ignorability
• Shared parameter model
• Time to event model