Joint modeling of longitudinal count and time-to-event data with excess zero using accelerated failure time model: an application with CD4 cell counts

Abstract

Longitudinal count and time to event (TTE) data are often associated in some ways. Hence, using joint models for analyzing these data constitutes an attractive modeling framework which is applied in many different fields of statistics and clinical studies. Also, Accelerated Failure Time (AFT) models can be used for the analysis of TTE data to estimate the effects of covariates on acceleration/deceleration of the survival time. So, we assume that the time variable is modeled in this article with Weibull AFT distribution. Furthermore, to develop the joint modeling strategy of these kinds of data, a correlated generalized linear mixed effect model (GLMEM) is applied using a member of the family of power series (PS) distributions in the longitudinal count submodel. Both of longitudinal count and TTE data may have excess zeros. The adequate of this approach in joint modeling with considering two censoring mechanism, right and left is illustrated using some simulation studies. Finally, we implement these proposed joint models on real AIDS data set.

Keywords:

• Longitudinal count data
• time to event (TTE) data
• joint model
• Accelerated Failure Time (AFT)
• Generalized Linear Mixed Effect Model (GLMEM)
• Power Series Distribution (PSD)