Direct likelihood inference on the cause-specific cumulative incidence function: A flexible parametric regression modelling approach.

In a competing risks analysis, interest lies in the cause-specific cumulative incidence function (CIF) that can be calculated by either (1) transforming on the cause-specific hazard or (2) through its direct relationship with the subdistribution hazard. We expand on current competing risks methodology from within the flexible parametric survival modelling framework (FPM) and focus on approach (2). This models all cause-specific CIFs simultaneously and is more useful when we look to questions on prognosis. We also extend cure models using a similar approach described by Andersson et al for flexible parametric relative survival models. Using SEER public use colorectal data, we compare and contrast our approach with standard methods such as the Fine & Gray model and show that many useful out-of-sample predictions can be made after modelling the cause-specific CIFs using an FPM approach. Alternative link functions may also be incorporated such as the logit link. Models can also be easily extended for time-dependent effects.