Parametric Methods for Analysis of Survival Times with Applications to Organ Transplantation

Abstract

In this dissertation, we have two main objectives. First, we introduce a hybrid method to model hazard function. Different approaches have been used for modeling survival times including parametric, semi-parametric, and non-parametric models. Non-parametric and semi-parametric models are commonly used for survival time analysis due to their flexibility. However, the parametric models are in high demand because of their predictive power. A challenging task is to extend semi-parametric methods and design full parametric models for analysis of survival times by estimating a set of unknown parameters. In the proposed method, the nonparametric estimate of the survival function by Kaplan Meier and the parametric estimate of the logistic function in the Cox proportional hazard by partial likelihood method are combined to estimate a parametric baseline hazard function. We compare the estimated baseline hazard using the proposed method and the Cox model. The performance of each method is measured based on the estimated parameters of the baseline distribution as well as the goodness of fit of the model. The focus of the second goal is to study graft failure in solid organ transplantation. We have studied the impact of donor’s and receiver’s factors such as age, gender, and ethnicity on organ survival. Six different organ types including kidney, liver, heart, lung, pancreas, and intestine are investigated in this study. The dataset includes transplanted organs in the US between 1987 and 2010.