Analysis of the HIV/AIDS Data Using Joint Modeling of Longitudinal (k,l)-Inflated Count and Time to Event Data in Clinical Trials

Generalized linear mixed effect models (GLMEMs) are widely applied for the analysis of correlated non-Gaussian data such as those found in longitudinal studies. On the other hand, the Cox (proportional hazards, PHs) and the accelerated failure time (AFT) regression models are two well-known approaches in survival analysis to modeling time to event (TTE) data. In this article, we develop joint modeling of longitudinal count (LC) and TTE data and consider extensions with fixed effects and parametric random effects in our proposed joint models. The LC response is inflated in two points k and l (k < l) and we use some members of (k, l)-inflated power series distribution (PSD) as the distribution of this response. Also, for modeling of TTE process, the PHs model of Cox and the AFT model, based on a flexible hazard function, are separately proposed. One of the goals of the present paper is to evaluate and compare the performance of joint models of (k, l)-inflated LC and TTE data under two mentioned approaches via extensive simulations. The estimation is through the penalized likelihood method, and our concentration is on efficient computation and effective parameter selection. To assist efficient computation, the joint likelihoods of the observations and the latent variables of the random effects are used instead of the marginal likelihood of the observations. Finally, a real AIDS data example is presented to illustrate the potential applications of our joint models.