Open Access
VOL. 1 | 2008 Order restricted inference for comparing the cumulative incidence of a competing risk over several populations
Hammou El Barmi, Subhash Kochar, Hari Mukerjee

Editor(s) N. Balakrishnan, Edsel A. Peña, Mervyn J. Silvapulle

Inst. Math. Stat. (IMS) Collect., 2008: 50-61 (2008) DOI: 10.1214/193940307000000040


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.


Published: 1 January 2008
First available in Project Euclid: 1 April 2008

MathSciNet: MR2462196

Digital Object Identifier: 10.1214/193940307000000040

Primary: 60F17 , 62G05
Secondary: 62G30

Keywords: Censoring , confidence bands , Hypothesis testing , stochastic ordering , weak convergence

Rights: Copyright © 2008, Institute of Mathematical Statistics

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