A nested frailty model for bivariate recurrent events: a Poisson modelling approach

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University of New Brunswick


Survival analysis is used to study the time until the occurrence of an event of interest. Some events of interest can occur more than once in a subject. These events are termed recurrent events. In this thesis, we consider survival analysis of bivariate recurrent events in which each subject may experience two distinct types of recurrent events. For example, in the peritonitis dialysis study conducted in Taichung Veterans General Hospital in Taiwan, both Gram-positive and Non-Gram-positive peritonitis are observed on 575 patients over time. Each of these two types of peritonitis may occur more than once in a patient. Clearly these two types of recurrent events are clustered by subject. In addition, the recurrent events of each type are further clustered by the type of events. To characterize those clustering effects in our analysis, we incorporate two levels of nested frailties into Cox survival models to analyze bivariate recurrent events jointly. There are many different approaches to the estimation of nested frailty Cox survival models in the literature. In this thesis, we propose a Poisson modelling approach to the estimation of our nested frailty Cox Survival models for bivariate recurrent events. This approach enables us to develop an optimal model estimation based on orthodox best linear unbiased predictor of frailties in an auxiliary frailty Poisson model. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved frailties. Our approach deals with an unspecified baseline hazard function. In addition, the treatment of ties and stratification is explicitly incorporated in our approach in the same way as in the standard Cox model. The usefulness of our proposed method is illustrated through analysis of peritonitis dialysis data and a simulation study.