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Title: Precision medicine in high dimensional settings Authors:  Qingyuan Zhao - University of Cambridge (United Kingdom)
Dylan Small - University of Pennsylvania (United States)
Ashkan Ertefaie - University of Rochester (United States) [presenting]
Abstract: Effect modification occurs when the effect of the treatment variable on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are hundreds of covariates, it becomes necessary to use the observed data to select a simpler model for effect modification and then make valid statistical inference. A two-stage procedure is proposed to solve this problem. First, we use Robinsons transformation to decouple the nuisance parameter from the treatment effect and propose to estimate the nuisance parameters by machine learning algorithms. Next, after plugging in the estimates of the nuisance parameters, we use the Lasso to choose a sparse model for effect modification. Compared to a full model consisting of all the covariates, the selected model is much more interpretable. Compared to the univariate subgroup analyses, the selected model greatly reduces the number of false discoveries. We show that the conditional selective inference for the selected model is asymptotically valid given the classical rate assumptions in semiparametric regression. Extensive simulation studies are performed to verify the asymptotic results and an epidemiological application is used to demonstrate our method.