A comparison of models including possibility of cure for survival data.

In the long term follow-up study of clinical survival data, we often encounter situations where some patients survive for many years following treatment, and some of them even die of other causes apparently unrelated to their previous disease. Features of this kind of data set include a high percentage of censoring and deaths due to causes other than the disease. The issue considered is to provide a measurement of long term survival. Many statisticians use the 5-year survival probability as such a measurement. Under the assumption that a proportion of patients are cured and have approximately the same hazard function as that of people without the disease, a general cure model is presented. This model provides a predictive probability of cure, given survival for a specified period of time, which is more realistic in predicting the long term survival than the 5-year survival probability. The goal is to provide such probabilities and develop methods to compare submodels of the general cure model. These are illustrated with two particular data sets. The first objective of my dissertation is to test if the probability of cure is zero. The second objective is to select the best submodel based on the Bayes factor, scoring rules, and residual analysis. These are illustrated with the malignant melanoma data as presented by Andersen, Borgan, Gill, and Keiding (1993). For this data set, our results show that models including the possibility of cure perform significantly better than those without it and the probability of cure by the surgery is about 44 percent. The third objective is to compare marginal posterior distributions derived from the Gibbs sampler and the Laplace approximation. The fourth objective is to extend the general cure model to the competing risks framework. These are illustrated with the bone marrow transplant data. In this data set, the time to relapse and the time to non-relapse related death are known to be dependent, since a subject with graft-versus-host-disease, the major cause of non-relapse related death, has less risk for relapse. A dependent approach, which is a finite mixtures model, is proposed.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104270/1/9513319.pdfDescription of 9513319.pdf : Restricted to UM users only