Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension

• Activity Number: 234 - New Challenges in Statistical Learning and Inference for Complex Data
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section for Statistical Programmers and Analysts
• Author(s): Yunan Wu* and Lan Wang and Haoda Fu
• Companies: University of Taxas at Dallas and University of Miami and Eli Lilly and Company
• Keywords: confidence interval; inference; optimal treatment regime; precision medicine; high-dimensional data; multiplier bootstrap

Abstract

We develop new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates, but leads to nonconvex estimation in high dimension and imposes significant challenges for inference. We first establish that a local restricted strong convexity condition holds with high probability and that any feasible local sparse solution of the estimation problem can achieve the near-oracle estimation error bound. We further rigorously verify that a wild bootstrap procedure based on a debiased version of the local solution can provide asymptotically honest uniform inference for the effect of a group of variables on optimal decision making. We also propose an efficient algorithm for estimation. Our simulations and real data example suggest satisfactory performance.