Revisiting the Cumulative Incidence Function With Competing Risks Data

TL;DR

This paper evaluates three methods for estimating the cumulative incidence function in competing risks data, introducing a new method that ensures the total CIF sums to 1 at the last observed time without sacrificing performance.

Contribution

A novel estimator for the CIF in competing risks models that guarantees the sum of all CIFs equals 1 at the end, maintaining comparable statistical performance.

Findings

Method 3 performs similarly to existing methods in bias and variance.

The new method ensures the total CIF sums to 1 at the last event time.

Performance metrics show no loss in accuracy with the new estimator.

Abstract

We consider estimation of the cumulative incidence function (CIF) in the competing risks Cox model. We study three methods. Methods 1 and 2 are existing methods while Method 3 is a newly-proposed method. Method 3 is constructed so that the sum of the CIF's across all event types at the last observed event time is guaranteed, assuming no ties, to be equal to 1. The performance of the methods is examined in a simulation study, and the methods are illustrated on a data example from the field of computer code comprehension. The newly-proposed Method 3 exhibits performance comparable to that of Methods 1 and 2 in terms of bias, variance, and confidence interval coverage rates. Thus, with our newly-proposed estimator, the advantage of having the end-of-study total CIF equal to 1 is achieved with no price to be paid in terms of performance.