Estimates of relative risk
type: Item
instance of: scholarly article
title: Estimates of relative risk
zbMATH Open document ID: 0676.62042
DOI: 10.1007/BF02613131
author: J. M. Begun
published in: Metrika
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176099
review text: For the two-sample model with proportional hazard, i.e., for \(\bar G(x)=1-G(x)=[\bar F(x)]^{\theta}=[1-F(x)]^{\theta}\), \(x\in R\), \(\theta >0\), the problem of estimating the relative risk \((\theta)\) is considered for the conventional uncensored data model. This model corresponds to the classical Cox regression model [\textit{D. R. Cox}, J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)] when the concomitant variate can assume only two values, 0 and 1. A two-step estimator of \(\theta\) is considered. \({\tilde \theta}\), an initial estimator of \(\theta\) is based on the identity \(\bar FdG=\bar GdF\), and this is incorporated in the formulation of the final step estimator. This two-step estimator and the Cox partial maximum likelihood estimator of \(\theta\) share the minimum asymptotic variance property within the class of all rank based regular estimators of the relative risk.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 4107946
zbMATH Keywords: estimation of the constant of proportionality
zbMATH Keywords: nonparametric regression model
zbMATH Keywords: two-sample model
zbMATH Keywords: proportional hazard
zbMATH Keywords: relative risk
zbMATH Keywords: uncensored data model
zbMATH Keywords: Cox regression model
zbMATH Keywords: two-step estimator
zbMATH Keywords: Cox partial maximum likelihood estimator
zbMATH Keywords: minimum asymptotic variance property
zbMATH Keywords: rank based regular estimators
MaRDI profile type: Publication
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OpenAlex ID: W2006312638
description: scientific article; zbMATH DE number 4107946