Stallard, Nigel, Todd, S. (Susan) and Whitehead, John, 1950-. (2008) Estimation following selection of the largest of two normal means. Journal of Statistical Planning and Inference, Vol.138 (No.6). pp. 1629-1638. ISSN 0378-3758

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Abstract

This paper considers the problem of estimation when one of a number of populations, assumed normal with known common variance, is selected on the basis of it having the largest observed mean. Conditional on selection of the population, the observed mean is a biased estimate of the true mean. This problem arises in the analysis of clinical trials in which selection is made between a number of experimental treatments that are compared with each other either with or without an additional control treatment. Attempts to obtain approximately unbiased estimates in this setting have been proposed by Shen [2001. An improved method of evaluating drug effect in a multiple dose clinical trial. Statist. Medicine 20, 1913-1929] and Stallard and Todd [2005. Point estimates and confidence regions for sequential trials involving selection. J. Statist. Plann. Inference 135, 402-419]. This paper explores the problem in the simple setting in which two experimental treatments are compared in a single analysis. It is shown that in this case the estimate of Stallard and Todd is the maximum-likelihood estimate (m.l.e.), and this is compared with the estimate proposed by Shen. In particular, it is shown that the m.l.e. has infinite expectation whatever the true value of the mean being estimated. We show that there is no conditionally unbiased estimator, and propose a new family of approximately conditionally unbiased estimators, comparing these with the estimators suggested by Shen. (c) 2007 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > R Medicine (General)
Divisions:	Faculty of Medicine > Warwick Medical School > Health Sciences Faculty of Medicine > Warwick Medical School
Library of Congress Subject Headings (LCSH):	Clinical trials -- Analysis, Analysis of means, Experimental design, Estimation theory
Journal or Publication Title:	Journal of Statistical Planning and Inference
Publisher:	Elsevier Science BV
ISSN:	0378-3758
Date:	1 July 2008
Volume:	Vol.138
Number:	No.6
Number of Pages:	10
Page Range:	pp. 1629-1638
Identification Number:	10.1016/j.jspi.2007.05.045
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/30263

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