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

Hammou El Barmi, Subhash Kochar, and Hari Mukerjee

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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.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 50-61

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058263

Digital Object Identifier
doi:10.1214/193940307000000040

Mathematical Reviews number (MathSciNet)
MR2462196

Subjects
Primary: 62G05: Estimation 60F17: Functional limit theorems; invariance principles
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
censoring confidence bands hypothesis testing stochastic ordering weak convergence

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

El Barmi, Hammou; Kochar, Subhash; Mukerjee, Hari. Order restricted inference for comparing the cumulative incidence of a competing risk over several populations. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 50--61, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000040. https://projecteuclid.org/euclid.imsc/1207058263


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