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

Sarwar Islam Mozumder,Mark Rutherford,Paul Lambert

doi:10.1002/sim.7498

Abstract

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.

Highlights

To understand more about patient prognosis and disease impact, the probability of death due to a particular cause in the presence of other causes is needed and involves the consideration of competing causes of death
Link functions We showed in Equation 12 that we can derive a log-cumulative subdistribution hazard (SDH) model with covariates and through the general link function, g(·), for the cause-specific cumulative incidence function (CIF), Fk(t), are able to apply similar transformations described in Royston and Parmar[24] for the survival function
Since the SDH function for cause k on which we model the plateau needs to be evaluated whilst simultaneously modelling all other causes, the final knot must be specified after the final observed time of death

Summary

Introduction

To understand more about patient prognosis and disease impact, the probability of death due to a particular cause in the presence of other causes is needed and involves the consideration of competing causes of death. This probability is known as the cause-specific cumulative incidence function (CIF). The choice of model on which to make our statistical inference depends on the research question to be answered. For more aetiologicaltype research questions, regression models on the CSH are more important.[2,3,4] In this paper we focus on developing methodology when interest is in prognosis where models have the advantage of maintaining the one-to-one correspondence

Methods

Results

Discussion

Conclusion