School of Statistics, University of Minnesota
Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension
Precision medicine is an innovative practice for disease treatment that takes into account individual variability in genes, environment, and lifestyle for each patient. Substantial efforts have recently been devoted to studying how to estimate the optimal personalized treatment regime given the individual-level information, which aims to yield the best expected outcome if the treatment regime is followed by each individual in the population. In this talk, 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 of the model 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 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. The advantage of honest inference is that it does not require the initial estimator to achieve perfect model selection and does not require the zero and nonzero effects to be well-separated. We also propose an efficient algorithm for estimation. Our simulations suggest satisfactory performance. An example from a diabetes study illustrates the real application.
Coffee to be served 30 minutes prior to the talk in the alcove outside of FO 2.406.
Viswanath Ramakrishna , 972-883-6873
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