STATISTICS SEMINAR

SPEAKER:

Ajit C. Tamhane

Department of Industrial Engineering and Management Sciences

Northwestern University.

TITLE:

A Superiority-Equivalence Approach to One-Sided Tests on Multiple Endpoints in Clinical Trials

ABSTRACT:

This paper gives a new formulation of the one-sided multivariate testing problem. This formulation is (i) practically relevant in the context of comparing a new treatment with a control on multiple endpoints, (ii) avoids the anomalies associated with the likelihood ratio test that uses the traditional null hypothesis formulation, and (iii) requires very little multiplicity adjustment. The hypotheses are formulated with the goal of showing that the treatment is equivalent (not inferior) on all endpoints and superior on at least one endpoint compared to the control, where thresholds for equivalence and superiority are specified for each endpoint. The union-intersection (Roy 1953) and intersection-union (Berger 1982) principles are employed to derive the basic test. It is shown that the critical constants required by this test can be sharpened by a careful analysis of its size. The test is illustrated by an example. Some extensions of the test are mentioned.

About the Speaker

Ajit C. Tamhane is professor and chair of the Department of Industrial Engineering and Management Sciences at Northwestern University in Illinois, U.S.A. He is also a professor in the Department of Statistics at Northwestern. He is the co-author of two books. One of his books "Multiple Comparison Procedures" written with Y. Hochberg has become a standard reference on the subject of multiple comparisons. This is one of the areas of Professor Tamhane's research interests particularly in its applications in biostatistics. Other areas of interest include Taguchi-type methods for ordered categorical data, experimental design and quality control. Professor Tamhane received his undergraduate degree in mechanical engineering from the Indian Institute of Technology in Bombay and his M.S. and Ph.D. in statistics and operations research from Cornell University.

References

Here are Adobe pdf files of the transparencies used in the talk and a preprint of the paper on which the talk is based.

Other useful background references are:

• Berger, R. L. (1982). Multiparameter hypothesis testing and acceptance sampling. Technometrics, 24, 295-300.
• Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures, New York: Wiley.
• Lehmacher, W., Wassmer, G. and Reitmeir, P. (1991). Procedures for twosample comparisons with multiple endpoints controlling the experimentwise error rate. Biometrics, 47, 511-521.
• Roy, S. N. (1953). On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematical Statistics, 24, 220-238.
• Silvapulle, M. J. (1997). A curious example involving the likelihood ratio test against one-sided hypotheses. American Statistician, 51, 178-180.
• Tang, D-I, Geller, N. L. and Pocock, S. J. (1993). On the design and analysis of randomized clinical trials with multiple endpoints. Biometrics, 49, 23-30.

Department of Mathematics and Statistics

Graduate Program in Statistics

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Last updated on November 12, 2002