Conditionally unbiased estimation in the normal setting with unknown variances |
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Authors: | David S Robertson Ekkehard Glimm |
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Institution: | 1. MRC Biostatistics Unit, University of Cambridge, Cambridge, UK;2. Novartis Pharma AG, Novartis Campus, Basel, Switzerland;3. Medical Faculty, Institute for Biometrics and Medical Informatics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany |
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Abstract: | To efficiently and completely correct for selection bias in adaptive two-stage trials, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been derived for trial designs with normally distributed data. However, a common assumption is that the variances are known exactly, which is unlikely to be the case in practice. We extend the work of Cohen and Sackrowitz (Statistics & Probability Letters, 8(3):273-278, 1989), who proposed an UMVCUE for the best performing candidate in the normal setting with a common unknown variance. Our extension allows for multiple selected candidates, as well as unequal stage one and two sample sizes. |
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Keywords: | Selection bias Two-stage sample Uniformly minimum variance conditionally unbiased estimation |
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