Sparse semi-parametric generated effect modifiers

• Activity Number: 270 - Intersection of Econometrics and Biometrics in Making Policy and Treatment Determinations
• Type: Invited
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Hyung Park* and Eva Petkova and Thaddeus Tarpey and R. Todd Ogden
• Companies: Columbia University and New York University School of Medicine and Wright State University and Department of Biostatistics, Columbia University
• Keywords: Precision medicine ; optimal treatment regime ; partially-linear single-index models ; multiple-index models ; projection pursuit regression ; L1 regularization

Abstract

In a linear regression model for the treatment outcome in a randomized experiment, Petkova et. al. identified a linear combination of covariates that results in a single dimensional composite covariate, that is optimal with respect to having the most differential treatment effect modification (i.e., the maximal interaction between the treatment variable and the composite covariate) in L2. In this presentation, this result will be generalized by incorporating a nonlinear effect modification index that relaxes the linearity assumption and consequently is much more flexible. Employing an appropriate regularization procedure, the method will develop a set of sparse basis for a subspace that is useful in modeling the interaction between a treatment variable and a high dimensional vector-valued covariate. We present asymptotic results for some special cases. A set of simulations and an application of treatment selection for depression is presented to illustrate the method.