Sample size estimation in single-arm clinical trials with multiple testing under frequentist and Bayesian approaches.
In this paper, we study one-sided multiple testing problems for normal and binomial distributions. We use order statistics to test the null hypothesis {all H ( i0) are true}. This approach allows us to uniformly address frequentist and Bayesian multiple testing models. To calculate order statistics, we use confidence limits. In frequentist models, we apply an adjustment to the confidence limits that is equivalent to the Bonferroni adjustment of p-values. In the Bayesian case, we adjust the credible limits following a concept of reconciliation between the Bayesian posterior probability and the frequentist p-value. We also study the quantitative relationship between the number of tests and the sample size of a clinical trial. If the number of tests is very large, we suggest using asymptotic order statistics. We study the performance of these statistics. The asymptotic order statistics for the normal distribution are used to extend the results for independent observations to dependent observations.
Food and Drug Administration, Center for Biologics Evaluation and Research (CBER), Rockville, MD 20852-1448, USA. Boris.Zaslavsky@FDA.HHS.gov
Boris G
BG
Zaslavsky
John
J
Scott
D000465:Algorithms; D001499:Bayes Theorem; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D018401:Sample Size; D016008:Statistical Distributions; D013223:Statistics as Topic