On some likelihood lnference for the destructive COM-Poison cure rate model with generalised gamma lifetime

Abstract

In this thesis, based on a competing causes scenario, the destructive Conway-Maxwell Poisson (COM-Poisson) cure rate model is studied. The model assumes the occurrence of the event under study to undergo a destructive process of the initial competing causes and only the undamaged portion relating to the initial number of competing causes is recorded. This provides a real and practical way of interpreting the occurrence of the event under study in a biological system. This research assumes the distribution of competing causes to be COM-Poisson which includes some of the commonly used discrete distributions as its particular cases. Furthermore, we propose to model the lifetime by the generalised gamma distribution, which includes some of the commonly used lifetime distributions as its particular cases. The main contribution of this thesis is to develop the expectation maximisation (EM) algorithm to determine the maximum likelihood estimates (MLEs) of the model parameters and to carry out the likelihood inference assuming the data to be right censored. Model discrimination within the COM-Poisson and generalised gamma families are carried out to select a parsimonious distribution for the competing cause and the lifetime that jointly provides an adequate fit to the data. We develop the estimation procedure using both profile likelihood and complete likelihood approaches and make a comparison between the two techniques through the EM algorithm. The performance of the proposed method of inference is demonstrated by carrying out a comprehensive Monte Carlo simulation study. The flexibilities of the COM-Poisson and generalised gamma families are utilised to carry out a two-way model discrimination using the likelihood-and information-based methods. The proposed estimation technique is then applied to a real melanoma data for illustrative purpose. The results show that both the COM-Poisson and generalised gamma distributions provide additional flexibility in modelling survival data with surviving fraction. We have also shown how covariates can influence the cure rate. Most importantly, the model fits the data better when the destructive mechanism is taken into account.