Statistical methods to study heterogeneity of treatment effects

Abstract

Randomized studies are designed to estimate the average treatment effect (ATE) of an intervention. Individuals may derive quantitatively, or even qualitatively, different effects from the ATE, which is called the heterogeneity of treatment effect. It is important to detect the existence of heterogeneity in the treatment responses, and identify the different sub-populations. Two corresponding statistical methods will be discussed in this talk: a hypothesis testing procedure and a mixture-model based approach. The hypothesis testing procedure was constructed to test for the existence of a treatment effect in sub-populations. The test is nonparametric, and can be applied to all types of outcome measures. A key innovation of this test is to build stochastic search into the test statistic to detect signals that may not be linearly related to the multiple covariates. Simulations were performed to compare the proposed test with existing methods. Power calculation strategy was also developed for the proposed test at the design stage. The mixture-model based approach was developed to identify and study the sub-populations with different treatment effects from an intervention. A latent binary variable was used to indicate whether or not a subject was in a sub-population with average treatment benefit. The mixture-model combines a logistic formulation of the latent variable with proportional hazards models. The parameters in the mixture-model were estimated by the EM algorithm. The properties of the estimators were then studied by the simulations. Finally, all above methods were applied to a real randomized study in a low ejection fraction population that compared the Implantable Cardioverter Defibrillator (ICD) with conventional medical therapy in reducing total mortality.