Clinical useful measures for the study of competing risks in survival analysis

The possible occurrence of multiple events during follow-up is a common situation in several clinical studies. Treatment failure, as the event firstly occurring, may be due to causes having di erent clinical implications in planning therapeutic strategies. The interest is generally focused on some specific causes of failure. Since only one type can be actually observed on each patient, competing risks methodology is appropriate. In this context, the sub-distribution hazard model is applied to infer on the difference among crude cumulative incidences. However, inference on sub-distribution hazards are not directly interpretable from a clinical perspective. To assess treatment or covariate effects, measures of clinical impact based on crude cumulative incidence should be considered. In particular relative risks, excess of risks, relative risk reduction and number of patients needed to be treated are known to be useful to clinical practitioners. The aim of this work is to provide a straightforward approach to obtain point and interval estimates of the above measures, by using transformation models, through suitable link functions in presence of competing risks. In order to make the technique readily applied the proposal of Klein and Andersen, based on pseudo-values, was considered as starting point. The baseline was estimated using regression spline functions with respect to time. Time-varying effects of covariates were tested through interaction with time functions. A published data set from a controlled clinical trial on prostate cancer, using causes of death as end-points, was used for illustration.