Finite mixture models in survival data analysis

In the pharmaceutical industry, cost-effectiveness analysis is an important step in the development of new health interventions. It is a method for assessing the gains in health relative to the costs of different health interventions. This assessment helps the regulators, providers, and potential users to make informed decisions. Health gains can be measured in several ways. One of them is the estimated gained life expectancy due to the intervention. Although the randomized controlled trials (RCTs) are considered to be the most reliable sources of the evidence to be used in the cost-effectiveness analysis, data collected from these trials are often incomplete due to censoring and truncation. This requires the extrapolation of the survival probability beyond the time frame of the RCTs. For this purpose, parametric models are necessary to estimate the survival functions. Although there exist several single parametric models (such as the Weibull, Gamma, and lognormal) that can perform this task, they fail to provide accurate estimates when the survival data are heterogeneous. In these situations, the finite mixture models fit the data better and therefore their results are more consistent and reliable. This dissertation studies the implementation of the finite mixture models in survival data analysis. It discusses in detail how to estimate the parameters of a finite mixture models through the expectation and maximization (EM) algorithm. These steps are flexible to account for the effects of covariates. In addition, we propose a new approach via censored quantile regression for finding the initial values of the EM algorithm. This method takes into consideration the special features of survival data and therefore will help improve the efficiency of the EM algorithm. We also demonstrate how to construct the desired confidence intervals of the estimates through bootstrapping. In oncology as well as other therapeutic areas, some patients will not experience the relapse of the disease after being treated. These patients are considered to be cured. It is of interest to know both the cure rate and the survival function of the patients who are not cured by the intervention. We study the mixture cure model in the general framework of finite mixture models as a special case, and provide the modified EM algorithm to estimate both the cure rate and the survival function of the uncured patients. Ph.D.Includes bibliographical reference