Testing for the existence of a desirable dose combination
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Updated: Aug 18, 2026

Diagonal Method to Measure Synergy Among Any Number of Drugs
Published on: June 21, 2018
H M Hung1, G Y Chi, R J Lipicky
1Statistical Evaluation and Research Branch, Food and Drug Administration, Rockville, Maryland 20857.
Abstract:
We consider the problem of studying several dose combinations of two drugs for a therapeutic endpoint in a multilevel factorial clinical trial. Two test statistics are constructed to test whether there exists at least one dose combination that is more effective than its component doses. Their distributions involve nuisance parameters quantifying the mean differences among the doses of the two component drugs. It is shown that their power functions achieve maxima as all the nuisance parameters approach infinity in absolute value. The significance levels of the two tests are derived and two alpha-level tests are proposed. Tables are given to provide the alpha-level critical values for these tests and to gain insights into their power performances.
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