Directed Model Checks for Regression Models from Survival Analysis

Survival analysis is concerned with the analysis of events occuring over time. Many regression models have been suggested to describe the relation of covariates to these events. Model checks can be used to determine whether a certain model is not suitable for a given dataset. However, formal goodness-of-fit tests to check models are only available for a limited numbers of models. In this thesis, goodness-of-fit tests are suggested for a large class of models, which includes many standard regression models. The approach is based on weighted martingale residuals. By choosing the weights suitably, the test can be made particularly powerful against desired alternatives, e.g. another regression model. A unique feature is that the asymptotic distribution of the test statistic does not depend on which estimators for unknown parameters are used. The asymptotic properties of these tests are being derived. Simulation studies and applications to real datasets show that the tests are promising.