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Robustness of sample size re‐estimation procedure in clinical trials (arbitrary populations)
Author(s) -
Govindarajulu Z.
Publication year - 2003
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1462
Subject(s) - sample size determination , statistics , estimator , null hypothesis , nominal level , mathematics , confidence interval , interval estimation , statistical power , robustness (evolution) , type i and type ii errors , biochemistry , chemistry , gene
In clinical trials, one of the main questions that is being asked is how many additional observations, if any, are needed beyond those originally planned. In a two‐treatment double‐blind clinical experiment, one is interested in testing the null hypothesis of equality of the means against one‐sided alternative when the common variance σ2 is unknown. We wish to determine the required total sample size when the error probabilities αand βare specified at a predetermined alternative. Shih provided a two‐stage procedure which is an extension of Stein's one‐sample procedure, assuming normal response. He estimates σ2 by the method of maximum likelihood via the EM algorithm and carries out a simulation study in order to evaluate the effective level of significance and the power. The author proposed a closed‐form estimator for σ2 and showed analytically that the difference between the effective and nominal levels of significance is negligible and that the power exceeds 1‐β when the initial sample size is large. Here we consider responses from arbitrary distributions in which the mean and the variance are not functionally related and show that when the initial sample size is large, the conclusions drawn previously by the author still hold. The effective coverage probability of a fixed‐width interval is also evaluated. Proofs of certain assertions are deferred to the Appendix. Copyright © 2003 John Wiley & Sons, Ltd.