Some statistical methods for the analysis of survival data in cancer clinical trials

Randomised Clinical Trials (RCT) are one of the most powerful tools of medical re- search and provide the basis for changing clinical practice. In oncology, the RCT is of particular importance in searching for new therapies and treatment approaches for patients diagnosed with cancer. Many of these trials have overall survival as a primary endpoint and are often designed with marginal e�ects being of clinical interest. As a result trials are typically large and are expensive in both time and money. Given the substantial cost involved in running clinical trials, it is an ethical imper- ative that statisticians endeavour to make the most e�cient use of any data obtained. A number of methods are explored in this thesis for the analysis of survival data from clinical trials with this e�ciency in mind. Statistical methods of analysis which take account of extreme values of covariates are proposed as well as a method for the analysis of survival data where the assumption of proportionality cannot be assumed. Beyond this, Bayesian theory applied to oncology studies is explored with examples of Bayesian survival models used in a study of pancreatic cancer. Also using a Bayesian approach, methodology for the design and analysis of trial data is proposed whereby trial data are supplemented by the information taken from previous trials. Arguments are made towards unequal allocation ratios for future trials with informative prior distributions.