Bayesian and non-Bayesian techniques applied to censored survival data with missing values

This thesis is a comprehensive comparative study of survival analysis methods, in particular the application of the Cox Proportional Hazards (CPH) model to real life data: A data set with 48 right-censored (end of study) patients suffering from multiple myeloma, and the COpenhagen Stroke study (COST) database with 993 right-censored (10 year follow-up) stroke patients. The most frequently applied method, stepwise selection, is a variable selection technique that fits a single model by searching for significant predictors of the survival time in terms of p-values. However, stepwise selection ignores the between-model uncertainty. This leads to biased and overconfident estimates. We compare stepwise selection to a more advanced approach, Bayesian Model Averaging (BMA), to average over all or a subset of models weighted by their posterior model probabilities. We show how to identify a subset of models using Occam's window subset selection with results comparable to an average over all models. We show that BMA has several advantages over stepwise selection. Using an average over models, we can evaluate the model uncertainty and obtain more reliable estimates of the risk factor coefficients. BMA also gives probabilistic evaluations of each risk factor, and we can ask questions such as: " What is the probability that this risk factor coefficient is non-zero, i.e. has an effect? " In stepwise selection, risk factors are either significant or not. We also show how to evaluate and compare the predictive power of competing models using the predictive log-score and a novel evaluation score, the predictive Z-score. We show that BMA improves the predictive power of our models. ii The CPH model is based on an assumption of proportional hazards. We implement two methods for validating this assumption. One can be used before and the other after a model has been fitted. We also show how to implement time-dependent variables and parameters to give a more general Cox regression (CR) model, and how to apply BMA on this model. Most real-life data sets have subjects where all values have not been recorded. Standard survival analysis methods cannot handle missing values, and a lot of valuable information is lost. We present three ways to address this problem: Combining BMA and variable selection, we propose a stepwise BMA method, where variables are removed by evaluating the probability of an effect. When we remove variables with missing values, we reduce the number of subjects with missing values, and significantly increase …