PARAMETRIC AND NON-PARAMETRIC ANALYSIS OF COMPETING RISKS MODELS

Abstract

Competing risks refers to the phenomenon where an object or individual is subject to multiple risks that are competing to destroy the object or individual, where the occurrence of one of these risks precludes the occurrence of any other risk. In this thesis, we use some useful lifetime distributions to model the risks, and parametric methods to estimate the unknown parameters of these risk models. Maximum likelihood method is used to estimate the model parameters. As expected, there were no analytic solutions for the maximum likelihood estimators, therefore numerical methods are implemented. Bayesian method is also used to estimate the model parameters. Since the posterior probability density function of the vector of unknown parameters is not in a standard form of a known distribution, MCMC using the Metropolis-Hastings algorithm is performed to obtain the Bayes estimates. Non-parametric techniques are also used to estimate the main characteristics of the competing risks model. Two competing risks models are studied in this thesis: homogeneous and regression models. Data analysis is done on bone marrow transplant patients in which there were two risks: leukemia relapse and death in remission. The cumulative incidence function estimates the probability of a specific risk in the presence of all other risks. We also estimate the cumulative incidence function for every risk at different times using the parametric and non-parametric methods applied in this thesis. Testing on the significance of covariates, patient's age and donor's age, found that at least one of them were significant for patients with acute lymphoblastic leukemia (ALL) and acute myelocytic leukemia low-risk (AML-LR), but not for patients with acute myelocytic leukemia high-risk (AML-HR). A comparison between the homogenous and regression competing risks models, using the bone marrow data, is performed. Further investigation is needed on modelling the risks where each risk is assumed to follow different lifetime distributions.