A Test for Differential Response Patterns in 2-Treatment Studies

Abstract

A method is presented for testing whether a pair of pre-treatment by post-treatment data matrices from a drug vs. placebo study can be partitioned into drug-typical and placebo-typical regions. A large sample Chi square test is derived for testing a specific partition posited a priori and a generalized Chi square test over a set of searched partitions is also derived. Some Monte Carlo tests are reported for the generalized test which confirm that the upper tails of the Chi square distribution provide appropriate probability levels for testing the null hypothesis that both samples are drawn from the same population. When the samples are drawn from different populations whose differences are well described by traditional parametric models, ANOCOVA or a test for differences in slope were more powerful in rejecting the null hypothesis. When two populations were chosen whose difference was not well described by these models, the newly derived test was more powerful.