Selective inference for effect modification via the lasso

Abstract

Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are tens or 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. We propose a two stage procedure to solve this problem. First, we use Robinson's transformation to decouple the nuisance parameters from the treatment effect of interest and use machine learning algorithms to estimate the nuisance parameters. Next, after plugging in the estimates of the nuisance parameters, we use the Lasso to choose a low-complexity 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 rate assumptions in classical semiparametric regression. Extensive simulation studies are conducted to verify the asymptotic results and an epidemiological application is used to demonstrate the method.

Jump Interval-Learning for Individualized Decision Making

“…Let's assume q I (•) satisfies equation 1 and the partition P 0 is known to us. In order to eliminate the baseline function u 0 (•), we can apply Robinson's transformation (see for example, Robinson, 1988;Zhao et al, 2017;Chernozhukov et al, 2018, and the references therein) and compute q I by minimizing arg min…”

Modeling Treatment Effect Modification in Multidrug-Resistant Tuberculosis in an Individual Patient Data Meta-Analysis

“…The set of potential effect modifiers investigated is a subset of the adjustment set X (k) . [7,9] The random covariate vector is…”

“…[8] One way to model effect modification in a simple binary treatment setting is through a marginal structural model (MSM) for the conditional average treatment effect (CATE). [7,9] This model may be interpreted as the relationship between covariates and the expected treatment effect where the treatment effect is defined through a contrast of counterfactual outcomes. In non-meta-analytical settings, doubly robust estimators have been proposed for the estimation of a parametric MSM for the CATE [7] as well as for nonparametric CATE models.…”

Estimating Treatment Effects with Causal Forests: An Application

“…One promising avenue to heterogeneous treatment effect estimation starts from an early result of Robinson (1988) on inference in the partially linear model (Nie and Wager, 2017;Zhao, Small, and Ertefaie, 2017). Write e(x) = P W i X i = x for the propensity score and m(x) = E Y i X i = x for the expected outcome marginalizing over treatment.…”

“…Thus, we do not need to give the causal forest all features X that may be confounders. Rather, we can focus on features that we believe may be treatment modifiers; seeZhao, Small, and Ertefaie (2017) for a further discussion.…”