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Type I error in sample size re-estimations based on observed treatment difference.

Z Shun1, W Yuan, W E Brady

  • 1Bristol-Myers Squibb, Organon Inc. and ACRO Inc. 2902 Johnson Cricle, Bridgewater, NJ 08807, USA. shunz@bms.com

Statistics in Medicine
|February 27, 2001
PubMed
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Sample size re-estimation in clinical trials can maintain study power and save resources. This study quantifies the type I error inflation associated with this method, providing mathematical insights and simulation-based evidence for control strategies.

Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Power

Background:

  • Sample size re-estimation (SSR) is a technique used in clinical trials to adjust sample size based on observed data, aiming to maintain adequate statistical power.
  • A primary concern with SSR is the potential inflation of the type I error rate, which has not been rigorously quantified mathematically.
  • Understanding and controlling type I error inflation is crucial for the validity and reliability of clinical trial results.

Purpose of the Study:

  • To mathematically explore and quantify the type I error inflation mechanism in two-sample normal tests when sample size is re-estimated.
  • To derive a conditional type I error function that provides a quantitative measure of inflation.
  • To investigate the impact of decision rules and bounds on type I error control during sample size re-estimation.

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Main Methods:

  • Derivation of a conditional type I error function for normal data under sample size re-estimation.
  • Theoretical analysis of the mathematical mechanisms driving type I error inflation.
  • Computer simulations to validate theoretical findings and assess the effectiveness of different sample size adjustment rules.
  • Exploration of various scenarios with differing error adjustment mechanisms.

Main Results:

  • A mathematical framework was developed to quantify type I error inflation due to sample size re-estimation in two-sample normal tests.
  • The derived conditional type I error function allows for precise visualization and calculation of type I error changes.
  • Without bounds, sample size re-estimation clearly inflates type I error; however, proper adjusting rules can effectively control this inflation.
  • In certain scenarios, type I error can even be reduced by implementing specific sample size adjustment strategies, often involving a trade-off with 'unrealistic power'.

Conclusions:

  • Sample size re-estimation requires careful consideration of type I error control, which can be mathematically quantified and managed.
  • The implementation of well-defined decision rules and bounds is essential for mitigating type I error inflation.
  • The findings suggest that controlled sample size re-estimation can be a valid strategy in clinical trials, potentially improving efficiency without compromising statistical integrity.
  • The principles explored for normal distributions may extend to other data distributions, warranting further investigation.