Order restricted inference for comparing the cumulative incidence of a competing risk over several populations

TL;DR

This paper introduces a new asymptotically distribution-free test for comparing cumulative incidence functions across multiple populations under a linear order constraint, improving inference when such an order is justified.

Contribution

It proposes a novel test and estimators for ordered cumulative incidence functions, with proven asymptotic properties and enhanced performance under the order restriction.

Findings

The test is asymptotically distribution-free.

Ordered estimators outperform unrestricted ones when the order holds.

The method is applicable in competing risks scenarios with multiple populations.

Abstract

There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this paper we propose an asymptotically distribution-free test when the alternative is that the incidence functions are linearly ordered, but not equal. The motivation stems from the fact that in many examples such a linear ordering seems reasonable intuitively and is borne out generally from empirical observations. These tests are more powerful when the ordering is justified. We also provide estimators of the incidence functions under this ordering constraint, derive their asymptotic properties for statistical inference purposes, and show improvements over the unrestricted estimators when the order restriction holds.