Prognostic models with competing risks : Methods and Application to Prostate Cancer data

Abstract

Fundamental statistical methods for analyzing competing risks data have been in discussion for decades. However there’s still an uncertainty on how to approach this type of data due to its complexities and thus there exist several gaps in the available methodology particularly in the area of modeling and model validation. Hence, this has become a topic of interest for many researchers. We review competing-risk regression models with a view toward: testing for prognostic factors, testing for treatment effects after adjusting for prognostic factors and model validation. . An example of prostate cancer data from a French study is used to illustrate the methods examined. This includes the application of the Lunn and McNeil regression model for testing prognostic factors and treatments and the adaptation and modification of a goodness-of-fit test, suggested in the literature, to test the hypothesis whether to include the covariates in a multiplicative Cox proportional hazards model, against the hypothesis whether to include the covariates in a more general class of additive-multiplicative model. Serum prostatic acid phosphatase, Combined index of stage and histological grade, Size of primary tumor, Serum hemoglobin level, Performance rating and age were identified as the more vital factors for the survival of patients from death by prostate cancer. Furthermore, the active treatments (estrogen) significantly effects time to death by prostate cancer, where the survival experience of patients showed improvement for higher doses of estrogen treatment. The goodness of fit test indicated that the model fit was adequate and that all prognostic factors in the model had a multiplicative effect on hazard.