Applying k-sample tests to conditional probabilities for competing risks in a clinical trial.

In the presence of competing risks, a full picture of the data can be developed considering the cumulative incidence function for each risk. If one risk type is of particular interest, the conditional probability of failure due to that risk, conditional on no failure due to the remaining competing risks, can be used to compare any number of samples. Kappa-sample tests of significance are derived and extended to stratified test statistics, allowing adjustment to be made for important prognostic factors. The methods are applied to a clinical trial involving patients with advanced breast cancer, where interest focused on progression of disease at old and new sites. They show that estrogen receptor status positive is an important prognostic factor in terms of time to progressive disease at a current tumour site, even when stratified for a potentially confounding measure of spread of disease, whereas progesterone receptor status positive is important with regard to disease progression at new sites only.