Asymptotic properties of maximum likelihood estimators with sample size recalculation
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Consider an experiment in which the primary objective is to determine the significance of a treatment effect at a predetermined type I error and statistical power. Assume that the sample size required to maintain these type I error and power will be re-estimated at an interim analysis. A secondary objective is to estimate the treatment effect. Our main finding is that the asymptotic distributions of standardized statistics are random mixtures of distributions, which are non-normal except under certain model choices for sample size re-estimation (SSR). Monte-Carlo simulation studies and an illustrative example highlight the fact that asymptotic distributions of estimators with SSR may differ from the asymptotic distribution of the same estimators without SSR.
KeywordsAdaptive designs Asymptotic distribution theory Interim analysis Local alternatives Maximum likelihood estimation Mixture distributions
Mathematics Subject Classification62K99 62L05 62F05 62E20
We thank Dr. Assaf P. Oron, an unknown referee and the editor for their very valuable feedback on our manuscript.
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