Statistical Papers

, Volume 60, Issue 2, pp 373–394 | Cite as

Asymptotic properties of maximum likelihood estimators with sample size recalculation

  • Sergey Tarima
  • Nancy FlournoyEmail author
Regular Article


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.


Adaptive designs Asymptotic distribution theory Interim analysis Local alternatives Maximum likelihood estimation Mixture distributions 

Mathematics Subject Classification

62K99 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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Health and EquityMedical College of WisconsinWauwatosaUSA
  2. 2.Department of StatisticsUniversity of MissouriColumbiaUSA

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