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Sample size estimation in single-arm clinical trials with multiple testing under frequentist and Bayesian approaches
Boris G Zaslavsky1, John Scott
1Food and Drug Administration, Center for Biologics Evaluation and Research (CBER), Rockville, MD 20852-1448, USA. Boris.Zaslavsky@FDA.HHS.gov
Journal of Biopharmaceutical Statistics
|June 2, 2012
Summary
This study introduces order statistics for one-sided multiple testing in normal and binomial distributions, unifying frequentist and Bayesian approaches. The methods offer adjustments for confidence and credible limits, enhancing clinical trial analysis.
Area of Science:
- Statistical Methods
- Biostatistics
- Hypothesis Testing
Background:
- Multiple testing problems are common in statistical analysis, particularly in clinical trials.
- Existing frequentist and Bayesian methods for multiple testing often lack a unified approach.
- Order statistics offer a potential framework for addressing these challenges.
Purpose of the Study:
- To develop a unified approach for one-sided multiple testing problems using order statistics.
- To adapt confidence and credible limits for both frequentist and Bayesian models.
- To investigate the relationship between sample size and the number of tests in clinical trials.
Main Methods:
- Utilizing order statistics to test the null hypothesis that all individual null hypotheses are true.
- Applying adjusted confidence limits in frequentist models, analogous to Bonferroni adjustments.
- Adjusting Bayesian credible limits to reconcile posterior probabilities with frequentist p-values.
- Investigating asymptotic order statistics for scenarios with a large number of tests, including dependent observations.
Main Results:
- The proposed order statistics method provides a uniform framework for frequentist and Bayesian multiple testing.
- Adjustments to confidence and credible limits ensure valid statistical inference.
- Asymptotic order statistics effectively handle a large number of tests and extend results to dependent data.
- The study quantifies the trade-off between sample size and the number of tests in clinical trials.
Conclusions:
- Order statistics offer a robust and unified methodology for one-sided multiple testing.
- The developed adjustments enhance the applicability of these methods in both frequentist and Bayesian contexts.
- The findings are particularly relevant for optimizing clinical trial design and analysis.
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