Smoothed multiple endpoint procedures.

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Classical multiple endpoint testing procedures such as Scheffe, Tukey, Bonferroni etc. are oftentimes too conservative. This is particularly true if the number of endpoints is large as in many recent applications. In an effort to declare significance of endpoints more rapidly than classical multiple comparison methods permit, procedures with stepwise structure were introduced. Most recent procedures have a stepwise structure, that is they are either single-step, step-up or step-down. To evaluate and compare procedures the proposers have studied properties of these stepwise procedures. One very surprising result of considerable practical value is that the popular step-up procedure is inadmissible, even for a vector risk function consisting of average size as one component and average type II error as the other component. The step-up and step-down procedures also have a disturbing practical property; namely a small negative change in one variable accompanied with reasonably sizeable positive changes in other variables can lead from many rejections to many acceptances. The current proposal is to find "smooth" procedures that retain the desirable properties of stepwise procedures while improving on the shortcomings. By representing the step-up procedure as a linear combination of products of indicator functions a smooth competitor to step-up is found and will be evaluated. Another idea proposed is to find a parametric empirical Bayes procedure that will control the average size component of the vector risk used to evaluate procedures. A critical aspect of the proposal is to study the amount of improvement the new methods have over step-up. The investigators study the problem of how to decide which among many possible individual entities are significant. For example, there are thousands of a person's genes examined in a microarray. Which genes are different or expressed differently when one examines cancer patients compared to non-cancer patients. To be able to decide such could provide a valuable diagnostic tool for early detection of cancer. This example, is one of many, that illustrates the problem of multiple testing procedures. Other areas of application include detection of covert communications, detection of bioweapons, comparing several treatments with a control, examination of mutual fund data in an effort to single out successful funds, examining testing methodologies in education and psychology settings. New and efficient statistical methodologies are introduced and analyzed in this research undertaking.