Logical Inference of Efficacy in Subgroups and Their Mixtures

Abstract

Measuring treatment efficacy in a mixture population is a fundamental problem in personalized medicine development, in deciding which subgroup or combination of subgroups to treat. Such a development process typically involves comparing a new drug with a control through randomized clinical trials, and treatment efficacy is the relative effect between the new drug and the control. It is now known that hazard ratio and odds ratio are not suitable measures for mixture populations. Over-extension of the use of LSmeans to adjust for imbalance in the data can also be overcome. Going forward, we point out that, intuitively, there are logical relationships among efficacies in the marker positive and negative subgroups and their mixture. For efficacy measures that are Subgroup Mixable (such as ratio of medians and relative response), we show that following what we call the Subgroup Mixable Estimation Principle can ensure such logical relationships be respected.