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Asymptotic properties of maximum likelihood estimators with sample size recalculation

Author

Listed:
  • Sergey Tarima

    (Medical College of Wisconsin)

  • Nancy Flournoy

    (University of Missouri)

Abstract

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.

Suggested Citation

  • Sergey Tarima & Nancy Flournoy, 2019. "Asymptotic properties of maximum likelihood estimators with sample size recalculation," Statistical Papers, Springer, vol. 60(2), pages 373-394, April.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:2:d:10.1007_s00362-019-01095-x
    DOI: 10.1007/s00362-019-01095-x
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    References listed on IDEAS

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    1. HaiYing Wang & Nancy Flournoy & Eloi Kpamegan, 2014. "A new bounded log-linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 695-720, July.
    2. Per Broberg & Frank Miller, 2017. "Conditional estimation in two-stage adaptive designs," Biometrics, The International Biometric Society, vol. 73(3), pages 895-904, September.
    3. Adam Lane & Nancy Flournoy, 2012. "Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size," Journal of Probability and Statistics, Hindawi, vol. 2012, pages 1-15, October.
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    Cited by:

    1. Sergey Tarima & Nancy Flournoy, 2022. "Most powerful test sequences with early stopping options," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 491-513, May.
    2. Nancy Flournoy & Sergey Tarima, 2023. "Discussion on “Adaptive enrichment designs with a continuous biomarker” by Nigel Stallard," Biometrics, The International Biometric Society, vol. 79(1), pages 31-35, March.

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    1. Sergey Tarima & Nancy Flournoy, 2022. "Most powerful test sequences with early stopping options," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 491-513, May.

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