The analysis of competing risks data with a focus on estimation of cause-specific and subdistribution hazard ratios from a mixture model

Treatment efficacy in clinical trials is often assessed by time from treatment initiation to occurrence of a certain critical or beneficial event. In most cases the event of interest cannot be observed for all patients, as patients are only followed for a limited time or contact to patients is lost during their follow-up time. Therefore, certain methods were developed in the framework of the so called time-to-event or survival analysis, in order to obtain valid and consistent estimates in the presence of these "censored observations", using all available information. In classical event time analysis only one endpoint exists, as the death of a patient. As patients can die from different causes, in some clinical trials time to one out of two or more mutually exclusive types of event may be of interest. In many oncological studies, for example, time to cancer-specific death is considered as primary endpoint with deaths from other causes acting as so called competing risks. Different methods for data analysis in the competing risks framework were developed in recent years, which either focus on modelling the cause-specific or the subdistribution hazard rate or split the joint distribution of event times and event types into quantities, that can be estimated from observable data. In this work the analysis of event time data in the presence of competing risks is described, including the presentation and discussion of different regression approaches. A major topic of this work is the estimation of cause-specific and subdistribution hazard rates from a mixture model and a new approach using penalized B-splines (P-splines) for estimation of conditional hazard rates in a mixture model is proposed. In order to evaluate the behaviour of the new approach, a simulation study was conducted, using simulation techniques for competing risks data, which are described in detail in this work. The presented regression models were applied to data from a clinical cohort study investigating a risk stratification for cardiac mortality in patients, that survived a myocardial infarction. Finally, the use of the presented methods for event time analysis in the presence of competing risks and results obtained from the simulation study and the data analysis are discussed.