A Simple Method for Detecting Interactions between a Treatment and a Large Number of Covariates

By Lu Tian, Ash A. Alizadeh, Andrew J. Gentles, Robert Tibshirani. 2012

388 citations recorded by the source corpus.

We consider a setting in which we have a treatment and a large number of covariates for a set of observations, and wish to model their relationship with an outcome of interest. We propose a simple method for modeling interactions between the treatment and covariates. The idea is to modify the covariate in a simple way, and then fit a standard model using the modified covariates and no main effects. We show that coupled with an efficiency augmentation procedure, this method produces valid inferences in a variety of settings. It can be useful for personalized medicine: determining from a large set of biomarkers the subset of patients that can potentially benefit from a treatment. We apply the method to both simulated datasets and gene expression studies of cancer. The modified data can be used for other purposes, for example large scale hypothesis testing for determining which of a set of covariates interact with a treatment variable.

Subfields: Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

Metalearners for estimating heterogeneous treatment effects using machine learning (2017, methodology): “For example, one may transform the outcomes so that any regression method can estimate the CATE directly (SI Appendix, Algorithm SI4) (4, 14, 15).”
The Econometrics of Randomized Experiments (2016, methodology): “Imai and Ratkovic (2013), Signorovitch (2007), Tian et al (2014), and Weisberg and Pontes (2015) develop lasso-like methods for causal inference and treatment effect heterogeneity in a setting where there are potentially a large number of covariates, so that regularization methods to discover which…”
Recursive partitioning for heterogeneous causal effects (2015, methodology): “(23) transform the features rather than the outcomes and then apply LASSO to the model with the original outcome and the transformed features.”
Learning Representations for Counterfactual Inference (2016, methodology): “Tian et al. (2014) presented one of the few methods that achieve balance by transforming or selecting covariates, modeling interactions between treatment and covariates.”
Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes (2015, methodology): “Examples include estimators of the regression of an outcome on covariates, treatment, and their interactions (e.g., Su et al., 2009; Qian and Murphy, 2011; Tian et al., 2014), and estimators of point treatment effects given covariates (e.”
Lasso adjustments of treatment effect estimates in randomized experiments (2015, methodology): “This is pursued in the high-dimensional setting in [19]; this work advocates solving the Lasso on a reduced set of modiﬁed covariates, rather than the full set of covariate × treatment interactions, and includes extensions to binary outcomes and survival data.”
Some methods for heterogeneous treatment effect estimation in high dimensions (2017, methodology): “Tian et al. (2014) introduced a simple linear model based on transformed covariates and show that it is equivalent to transformed outcome regression in the Gaussian case.”
A Survey of Learning Causality with Data (2018, background): “disjoint subsets of features Z u,V u ⊂X u, λ v and λ z are the hyperparameters that control the sparsity of the learned model. Other similar work on learning sparse models for ATE estimation includes [134,140]. Learning Heterogeneous Causal Effects with Ensembles.Ensemble models can provide comparab”
Using Causal Inference to Estimate What-if Outcomes for Targeting Treatments (2016, background): “In comparison, standard approaches for modeling heterogeneous treatment responses rely on defining subpopulations from the data and estimating the average effect for each subpopulation given the covariates [Foster et al., 2010, Imai et al., 2013, Tian et al., 2014, Athey and Imbens, 2015].”
Incorporating Patient Preferences into Estimation of Optimal Individualized Treatment Rules (2017, background): “…2005; Henderson et al., 2010; Qian and Murphy, 2011; Zhao et al., 2011; Goldberg and Kosorok, 2012; Moodie et al., 2012, 2014; Laber et al., 2014; Tian et al., 2014) or policy-search-based (Orellana et al., 2010; Zhang et al., 2012, 2013; Zhao et al., 2012, 2014, 2015; Laber and Zhao, 2015),…”
Machine Learning Methods for Estimating Heterogeneous Causal Eects (2015, methodology): “[29]transform the features rather than the outcomes and then apply LASSO to the model with the original outcome and the transformed features.”
Learning Cost-Effective and Interpretable Treatment Regimes (2017, neutral): “Regression-based methods [27, 31, 28, 32, 43, 27, 25] model the conditional distribution of the outcomes given the treatment and characteristics of patients and choose the treatment resulting in the best possible outcome for each individual.”
A Review of Generalizability and Transportability (2021, background): “These include those that identify variables that qualitatively interact with treatment (i.e., for which the optimal treatment differs by subgroup) (Gunter, Zhu and Murphy, 2011) as well as determine the magnitude of interaction (Chen et al., 2017; Tian et al., 2014).”
Post hoc subgroups in clinical trials: Anathema or analytics? (2015, methodology): “Indeed, the idea of utilizing Z as a dependent variable with (implicitly) c= 0 was suggested independently in a PhD thesis by James Signorovitch.(10,11) However, the variance of Z in the entire study population is minimized when c=m, which follows from the fact that Z is a mixture of two equally wei”
A Survey of Learning Causality with Data: Problems and Methods (2018, background): “Other similar work on learning sparse models for ATE estimation includes [134, 140].”