Conservative Sample Size Estimation in Nonparametrics

Abstract

Due to the uncertainty of the results of phase II trials, underpowered phase III trials are often planned. In recent literature the conservative approach for sample size estimation was proposed. Some authors, in the parametric framework, make use of the lower bound of the effect size for conservatively estimating the true power, and so the sample sizes. Here, we present a general bootstrap method for conservatively estimating, on the basis of phase II data, the sample size needed for a phase III trial. The method we propose is based on the use of nonparametric lower bounds for the true power of the test. A wide study is shown for comparing the performances of the new method in estimating the power of the Wilcoxon rank-sum test with those given by standard techniques based on the asymptotic normality of the test statistic. Results indicate that when the phase II sample size is around the ideal sample size for the phase III, the bootstrap provides better results than the other techniques. Since the method is general, it could be used for planning clinical trials for testing superiority, for testing noninferiority, and for more complicated situations, e.g., for testing multiple endpoints.

Key Words:

• Bootstrap
• Lower bounds for the true power
• Sample size estimation
• Uncertainty

ACKNOWLEDGMENTS

Partial support was provided by the Italian Ministry of Research (MIUR) (protocol 2007 AYHZWC Statistical methods for learning in clinical research). Thanks are due to two anonymous reviewers whose comments and suggestions contributed to improve the quality of the article.