Joint Analysis of Longitudinal Data and Zero-Inflated Recurrent Events

Abstract

Longitudinal data together with recurrent events are commonly encountered in clinical trials. In many applications, these two processes are highly correlated. When there exist a large portion of subjects not experiencing recurrent events of interest, it is possible that some of these subjects are unsusceptible to the events. Therefore, we assume the underlying population is composed of two subpopulations: one subpopulation susceptible to the recurrent events, and the other unsusceptible. In this article, we propose a joint model of longitudinal outcomes and zero-inflated recurrent event data. Our model consists of three submodels: (1) a generalized linear mixed model for the longitudinal process; (2) a proportional intensities model for the recurrent event process in the susceptible subpopulation; and (3) a logistic regression model for the probability such that a subject belongs to the unsusceptible subpopulation. We consider associations (1) between longitudinal outcomes and the zero-inflation rate; and (2) between longitudinal outcomes and the intensity rate of recurrent events in the susceptible subpopulation. Estimation is carried out by maximizing the log-likelihood function using Gaussian quadrature techniques, which can be conveniently implemented in SAS Proc NLMIXED. Simulation studies demonstrate that the proposed method performs well. We apply the method to a clinical trial.

KEYWORDS:

• Frailty model
• Gaussian quadrature
• Piecewise constant baseline
• Unsusceptible population

Supplementary Materials

Supplementary materials contain codes for both data generation in the simulation study and the proposed estimation procedure.

Acknowledgments

The authors thank the Associate Editor and two referees for their careful reading and helpful comments that have led to an improved article.

Disclosure Statement

Both authors are employees and stock holders of Eli Lilly and Company.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.