A Permutation Test for Assessing the Presence of Individual Differences in Treatment Effects

Abstract: One size fits all approaches to medicine have become a thing of the past as the understanding of individual differences grows. The paper introduces a test for the presence of heterogeneity in treatment effects in a clinical trial. Heterogeneity is assessed on the basis of the predicted individual treatment effects (PITE) framework and a permutation test is utilized to establish if significant heterogeneity is present. We first use the novel test to show that heterogeneity in the effects of interventions exists in the Amyotrophic Lateral Sclerosis Clinical Trials. We then show, using two different predictive models (linear regression model and Random Forests) that the test has adequate type I error control. Next, we use the ALS data as the basis for simulations to demonstrate the ability of the permutation test to find heterogeneity in treatment effects as a function of both effect size and sample size. We find that the proposed test has good power to detected heterogeneity in treatment effects when the heterogeneity was due primarily to a single predictor, or when it was spread across the predictors. The predictive model, on the other hand is of secondary importance to detect heterogeneity. The non-parametric property of the permutation test can be applied with any predictive method and requires no additional assumptions to obtain PITEs.