CURE RATE AND DESTRUCTIVE CURE RATE MODELS UNDER PROPORTIONAL HAZARDS LIFETIME DISTRIBUTIONS

Abstract

Cure rate models are widely used to model time-to-event data in the presence of long-term survivors. Cure rate models, since introduced by Boag (1949), have gained significance over time due to remarkable advancements in the drug industry resulting in cures for a number of diseases. In this thesis, cure rate models are considered under a competing risk scenario wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution, under the assumption of proportional hazards (PH) lifetime for the susceptibles. This provides a natural extension of the work of Balakrishnan & Pal (2013) who had considered independently and identically distributed (i.i.d.) lifetimes in this setup. By linking covariates to the lifetime through PH assumption, we obtain a flexible cure rate model. First, the baseline hazard is assumed to be of the Weibull form. Parameter estimation is carried out using EM algorithm and the standard errors are estimated using Louis' method. The performance of estimation is assessed through a simulation study. A model discrimination study is performed using Likelihood-based and Information-based criteria since the COM-Poisson model includes geometric, Poisson and Bernoulli as special cases. The details are covered in Chapter 2. As a natural extension of this work, we next approximate the baseline hazard with a piecewise linear functions (PLA) and estimated it non-parametrically for the COM-Poisson cure rate model under PH setup. The corresponding simulation study and model discrimination results are presented in Chapter 3. Lastly, we consider a destructive cure rate model, introduced by Rodrigues et. al (2011), and study it under the PH assumption for the lifetimes of susceptibles. In this, the initial number of competing causes are modeled by a weighted Poisson distribution. We then focus mainly on three special cases, viz., destructive exponentially weighted Poisson, destructive length-biased Poisson and destructive negative binomial cure rate models, and all corresponding results are presented in Chapter 4.