Differential Treatment Effects for Subgroups: 
Pre- and Post-Hoc Statistical Analyses

Investigators: Dei-In Tang, Ph.D. and Eugene Laska, Ph.D.

PROJECT GOALS
Goals for this project are to: 

• (1) develop methods for testing whether the difference in efficacy of two interventions is in the same direction for a set of pre-specified subgroups, and when the answer is negative, for distinguishing those with a positive difference from those with a zero or negative difference; and 
• (2) develop methods that flexibly and validly allow identification of subgroups that were not pre-specified but that show a positive (or negative) difference.

RESEARCH ACTIVITIES AND RESULTS
In the context of pre-specified subgroups, the question of comparing subgroups with an identified control subgroup has been addressed and a likelihood-based test to detect the existence of subgroups which have a better intervention effect than the control subgroup has been constructed. In this study year, the test was extended via the method of closed testing to permit identification of these subgroups with better effects. This test and its extension are reported in a paper in press (Tang and Lin, 1997).

In the context of unpre-specified subgroups, the method of closed testing is also useful because one does not need to know what the subgroups are until one has found a global effect and decides to test for subgroup effects. However, since the method requires that multiple tests be conducted, it can be implemented in many ways depending on what the individual tests are. We have studied the performance of several implementations in each of which a test method in the multiple endpoint literature is used for all the tests. Basically, if a test method is more powerful than another test method, the corresponding implementation of the closed testing method remains more powerful.
 
 

SIGNIFICANCE OF FINDINGS/POLICY IMPLICATIONS
It may well be that the efficacy of an intervention is different in different subgroups of the population. Thus, although conclusions about global costs and benefits of a program have relevance, they may also be misleading and, more importantly, may mistakenly condemn a therapeutic approach that has great merit for the right subgroup of clients. Important differences in efficacy among alternative program initiatives may occur only in some subgroups.

Project completed.

Publications:

Tang, D.-I. and Lin, S. P. (1997). An approximate likelihood ratio test for comparing several treatments to a control. Journal of the American Statistical Association (in press).

Tang, D.-I. and Lin, S. P. (1996). On improving some hypothesis-testing methods for multiple endpoints. Submitted for publication. Under revision.

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