Statistical Inference Using competing Risks Data

Abstract

In this thesis, we analyse competing risks data using the two-parameter bathtub (TPBT) distribution. The hazard rate of the TPBT distribution can be either increasing or a bathtub-shaped, which allows it to be a good fit for several data sets. In competing risks data, it is assumed that the object (system) is under attack of many risks (causes of failure) that compete to destroy it. In this study, we assume that the system will be destroyed by only one cause and all risks are independent. We discuss two models. The first does not allow covariates while the second does. We used the maximum likelihood and Bayes methods to estimate the model parameters, the relative risks and some of the reliability measures of the system. The likelihood equations of the unknown parameters have no analytic solution and numerical methods will be used to get the maximum likelihood estimations. Also, the posterior distribution of the parameters is not in a convenient form, therefore we used Markov Chain Monte Carlo (MCMC) method to simulate random draws from the posterior distribution and then use it to obtain the Bayes estimates of the parameters, the relative risks and the system’s reliability measures. Furthermore, to study the performance of the two estimation techniques used, we provided a simulation study. This paper is illustrated on two real data sets.