Testing Equality of Generalized Treatment Effects

Abstract

Recently, the concept of generalized treatment effect, defined as P(X > Y) where X and Y denote continuous outcome variables for treatment arm and control arm, respectively, has been proposed as an appropriate measure of treatment effect in clinical trials with parallel design. Compared to the mean difference, the generalized treatment effect has many advantages; for example, it is a scaleless measure and it does not change under monotonic transformations. This article investigates the problem of testing equality of generalized treatment effects among several clinical trials. The proposed approach follows the same vein as the generalized variable method for testing equality of several log-normal means proposed by Li (2009). Numerical study demonstrates that the proposed test has excellent type I error control for clinical trials with small to medium sample sizes. Robustness study shows that the proposed method performs reasonably for categorical data.

Key Words:

• Clinical trials
• Generalized test variable
• Generalized p-value

Notes

Note. (10; 10) stands for the scenarios with 10 observations in the treatment arm and control arm respectively. ((10, 20); (10,20)) stands for the scenarios with 10 observations in the treatment arm for the first half of the studies and 20 observations in the treatment arm for the second half of the studies, and 10 observations in the control arm for the first half of the studies and 20 observations in the control arm for the second half of the studies.

Note. See Table 1 footnote for the explanations of sample size settings.

Note. See Table 1 footnote for the explanations of sample size settings.

Note. See Table 1 footnote for the explanations of sample size settings.

Note. See Table 1 footnote for the explanations of sample size settings.

See end of section 3 for details on parameter settings.