Sample Size Adaptation in Fixed-Dose Combination Drug Trial

Abstract

Statistical testing in clinical trials can be complex when the statistical distribution of the test statistic involves a nuisance parameter. Some type of nuisance parameters such as standard deviation of a continuous response variable can be handled without too much difficulty. Other type of nuisance parameters, specifically associated with the main parameter under testing, can be difficult to handle. Without knowledge of the possible value of such a nuisance parameter, the maximum type I error associated with testing the main parameter may occur at an extreme value of the nuisance parameter. A well known example is the intersection-union test for comparing a combination drug with its two component drugs where the nuisance parameter is the mean difference between the two components. Knowledge of the possible range of value of this mean difference may help enhance the clinical trial design. For instance, if the interim internal data suggest that this mean difference falls into a possible range of value, then the sample size may be reallocated after the interim look to possibly improve the efficiency of statistical testing. This research sheds some light into possible power advantage from such a sample size reallocation at the interim look.

Key Words:

• Interim analysis
• Min test
• Nuisance parameter
• Sample size reallocation

ACKNOWLEDGMENTS

The research work presented in this paper was supported by the RSR fund 05-02, provided by Center for Drug Evaluation and Research of the U.S. Food and Drug Administration. The authors thank Dr. Qing Liu for providing many constructive comments to enhance this paper. The views expressed in this paper are not necessarily those of the U.S. Food and Drug Administration.

Notes

Note. α* = Φ(−C _δt ). AAA: The testing approach uses an adaptive test, e.g., the weighted Z statistic following Cui et al. (1999) if sample size is reallocated. ANA: The testing approach uses the conventional test statistic as if sample size were not allocated. NON: If sample size reallocation is never considered, i.e., the conventional test strategy.