Likelihood based inference for cause specific hazard rates under order restrictions
type: Item
instance of: scholarly article
title: Likelihood based inference for cause specific hazard rates under order restrictions
zbMATH Open document ID: 0844.62033
author: Subhash Kochar
author: Tim Robertson
author: Richard Dykstra
published in: Journal of Multivariate Analysis
publication date: 1996-09-01T00:00:00Z
review text: We consider the competing risks model with grouped data or with discrete failure times where a unit is exposed to several risks, but its eventual failure is due to exactly one of the causes. We assume a discrete-time framework and allow for independent random censoring on the right. We obtain maximum likelihood estimates (MLEs) of the cause specific hazard rates under the various alternatives. The restricted maximum likelihood estimators of the cause specific hazard rates under \(H_1\) can be computed by finding the isotonic regression of the usual estimates across risks. This will be discussed in Section 2. In Section 3 we derive a likelihood ratio test for testing \(H_0\) versus \(H_1 - H_0\) and obtain the asymptotic null distribution of the test statistic. This asymptotic test is distribution-free and its null distribution is found to be of the chi-bar squared type. Finally, in the last section, the procedures are illustrated with the help of a data set involving survival rates for mice exposed to radiation.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 797147
zbMATH Keywords: delta method
zbMATH Keywords: multinomial distribution
zbMATH Keywords: competing risks model
zbMATH Keywords: discrete time framework
zbMATH Keywords: independent random censoring
zbMATH Keywords: maximum likelihood estimates
zbMATH Keywords: cause specific hazard rates
zbMATH Keywords: restricted maximum likelihood estimators
zbMATH Keywords: isotonic regression
zbMATH Keywords: likelihood ratio test
zbMATH Keywords: asymptotic null distribution
zbMATH Keywords: distribution-free
zbMATH Keywords: survival rates
MaRDI profile type: Publication
full work available at URL: jmva.1995.1050
OpenAlex ID: W1967634500
DOI: 10.1006/JMVA.1995.1050
description: scientific article; zbMATH DE number 797147