Analysis of Correlated Recurrent and Terminal Events Data in SAS

Recurrent events data have been increasingly important in clinical studies. There are many methods to analyze this type of data. Several papers have been presented about how to perform repeated events analysis in SAS. In clinical studies, we may encounter recurrent disease episodes in patients with a terminal event such as death, and the terminal event is often strongly correlated with the recurrent event process. In this paper, using a simulated organ transplant dataset as example, we demonstrate how to model and analyze correlated recurrent and terminal events data in SAS. . INTRODUCTION Recurrent event data are commonly encountered in clinical and observational studies, such as repeated tumor occurrences, repeated hospitalizations and multiple rejection episodes after organ transplant. The observation of recurrent events could be disrupted by loss to follow-up, end of study, or a terminal event such as death. Analysis focus is usually either on failure time using standard survival analysis or recurrent event process using Mean Cumulative Function for the number of events to model the process [1]. In many instances, the terminal events may have interaction with the recurrent process, thus need to be treated as informative censoring. Analyzing the data based on recurrent events or terminal event separately may lead to biased estimates when such informative censoring exists. It is important to take into account of both terminal events and recurrent events when suspects of their interaction reasonably arise based on domain knowledge. Frailty models have been proposed and successfully used in the analysis of correlated failure time data. The frailty approach aims to account for heterogeneity caused by unmeasured covariates. They are extensions of the proportional hazard model. The recurrent event process can be modeled by a random effects ( frailty) proportional hazards model. In the presence of dependent terminal event, the random effects are also incorporated into the model for the terminal events [2]. Such models are conceptually shared frailty models. They are useful for assessing the covariate effects on both processes as well as the level of their correlation. A novel Gaussian quadrature estimation method has been proposed by Liu and Huang [3] for various frailty proportional hazards models. This estimation method is relatively straightforward and has been implemented in SAS Proc NLMIXED. Based on their work, we present in this paper a simple SAS macro to conduct the analysis and generate additional hazard and survival plots for the analysis. DEFINITION As proposed in [2], a random effect was shared by the proportional hazard models of both recurrent events and terminal events as seen below: (t) )r Z exp( ) ( 0 i i T v t ri + = β (1) ) ( ) exp( ) ( 0 t v Z t i i T i λ γ β λ + = (2) where β are coefficients of observed covariates Z, r0(t) and λ0(t) are baseline hazards for recurrent and terminal event processes, respectively. The correlation between these two processes is introduced by the shared frailty ν i , which can have a different impact on ri (t) and λi (t) due to coefficient γ. Statistics & Analysis NESUG 2008