Statistical Issues On Objective, Design, And Analysis Of Noninferiority Active-controlled Clinical Trial

Abstract

In practice, “noninferiority” active-controlled trials have been designed for three different objectives: establishing evidence of efficacy over placebo, preserving a specific percentage of the effect size of the active control, or demonstrating the test treatment is “not much inferior” to the active control. All three objectives can be represented by the same set of statistical hypotheses with the parameters defined differently. The various designs and statistical analysis procedures for active-controlled trials proposed in the literature can be group into two basic types: the historical-controlled trial approach and the cross-study comparison approach. These approaches require some unverifiable constancy assumptions. Under the constancy assumptions, the cross-study comparison uses the estimate effect of active-control treatment as the unbiased estimate of the active/placebo difference in the current noninferiority trial. A normalized Z-statistic is used to test the hypotheses. On the other hand, the historical controlled trial approach uses a conservative confidence limit as if it were a constant to replace the active/placebo difference in the current trial. The two approaches may lead to consistent conclusions only when the constancy assumptions can be supported by a large number of historical studies giving a consistent active-control treatment effect over placebo and that the active-control effect does not change over time.

# This paper does not represent the official position of the Food and Drug Administration nor of Aventis Pharmaceuticals Inc.

Keywords:

• Cross-study comparison
• Historical control
• Constancy assumption
• Unbiased estimate

Acknowledgments

This research was supported by RSR Fund #01–20 of the Center for Drug Evaluation and Research, U.S. Food and Drug Administration. The work was completed when Lu Cui was a member of the Center of Drug Evaluation and Research, FDA.

The authors want to thank the two referees' careful reading and comments that led to the much-improved version of the manuscript.

Notes

# This paper does not represent the official position of the Food and Drug Administration nor of Aventis Pharmaceuticals Inc.