Likelihood Inference of Some Cure Rate Models and Applications

Abstract

<p>In this thesis, we perform a survival analysis for right-censored data of populations with a cure rate. We consider two cure rate models based on the Geometric distribution and Poisson distribution, which are the special cases of the Conway-Maxwell distribution. The models are based on the assumption that the number of competing causes of the event of interest follows Conway-Maxwell distribution. For various sample sizes, we implement a simulation process to generate samples with a cure rate. Under this setup, we obtain the maximum likelihood estimator (MLE) of the model parameters by using the gamlss R package. Using the asymptotic distribution of the MLE as well as the parametric bootstrap method, we discuss the construction of confidence intervals for the model parameters and their performance is then assessed through Monte Carlo simulations.</p>