Identifying Treatment Heterogeneity in Complex Experiments: A Linear Mixed Effects Model Approach

• Activity Number: 304
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Troy Richardson*+ and Gary L. Gadbury
• Companies: Kansas State University and Kansas State University
• Keywords: treatment heterogeneity ; potential outcomes ; subject-treatment interaction

Abstract

Using a potential outcomes framework, Gadbury and others have reported on treatment heterogeneity for several simple designs utilizing a finite-population, randomization-based inference. However, as experimental designs become more complicated, the randomization-based approach becomes increasingly intractable. Since linear mixed effects models are useful for modeling data from complex designs, their role in modeling treatment heterogeneity is investigated. A linear mixed effects "potential outcomes" model is developed and an individual treatment effect is conceptualized as a linear combination of fixed and random effects from the model. Although the variance of the individual effect is inestimable since only one of the potential outcomes is actually observable for a given experimental unit, it is demonstrated that estimable bounds of the variance for treatment heterogeneity exist. These bounds arise from linear combinations of the variance components specified in the potential outcomes model. Assumptions required for equating estimable bounds from observable data to estimates of treatment heterogeneity that could be obtained from potential outcomes data will be discussed.