Analysing competing risks data with transformation models

We present a flexible class of marginal models for the cumulative incidence function. The semiparametric transformation model is utilized in a decomposition for the marginal failure probabilities which extends previous work on Farewell's cure model. Novel estimation, inference and prediction procedures are developed, with large sample properties derived from the theory of martingales and U-statistics. A small simulation study demonstrates that the methods are appropriate for practical use. The methods are illustrated with a thorough analysis of a prostate cancer clinical trial. Simple graphical displays are used to check for the goodness of fit.