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Estimation following selection of the largest of two normal means. Journal of Statistical Planning and Inference 138, 1629-1638.

Stallard, Nigel and Todd, Susan and Whitehead, John (2008) Estimation following selection of the largest of two normal means. Journal of Statistical Planning and Inference 138, 1629-1638. Journal of Statistical Planning and Inference, 138 (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.

Item Type: Article
Journal or Publication Title: Journal of Statistical Planning and Inference
Uncontrolled Keywords: Clinical trial analysis ; Select and test designs ; Treatment selection
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 33512
Deposited By: Mr Richard Ingham
Deposited On: 25 May 2010 11:46
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 14:50
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/33512

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