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Accuracy and Errors in Hypothesis Testing

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Increasing the sample size at interim for a two-sample experiment without Type I error inflation.

Keith Dunnigan1, Dennis W King

  • 1STATKING Consulting, Cincinnati, OH, USA. dunnigan_k@yahoo.com

Pharmaceutical Statistics
|September 19, 2009
PubMed
Summary
This summary is machine-generated.

This study confirms that sample size (SS) can be increased at interim analysis in two-sample experiments if conditional power is at least 50% and early stopping for futility is not permitted. This approach eliminates Type I error risk but forfeits early stopping for efficacy.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design

Background:

  • Interim analysis allows for sample size (SS) adjustments in clinical trials.
  • Previous work established conditions for increasing SS in one-sample experiments with known variance.

Purpose of the Study:

  • To extend the principle of sample size re-estimation to two-sample experiments with proportional sample sizes and arbitrary common variance.
  • To derive formulas for conditional power (CP) at interim analysis for both one-sided and two-sided hypothesis tests in this context.

Main Methods:

  • Verification of existing sample size adjustment principles for a two-sample experiment.
  • Derivation of conditional power formulas for proportional, unequal sample sizes in treatment groups.
  • Development of an SAS macro for practical application and illustration with a hypothetical example.

Main Results:

  • The study confirms that sample size can be arbitrarily increased in two-sample experiments under specific conditions (CP ≥ 50%, no early stopping for futility).
  • New formulas for conditional power are derived for one-sided superiority and two-sided hypothesis tests with proportional sample sizes.
  • An SAS macro and example are provided for implementing these calculations.

Conclusions:

  • This trial design strategy sacrifices the ability to stop early for efficacy in exchange for controlling Type I error.
  • Implementation requires a data monitoring committee, blinded sponsors, and a pre-defined interim analysis plan detailing SS adjustments.