Overlap in observational studies with high-dimensional covariates

By A. D'Amour, Peng Ding, Avi Feller, Lihua Lei, Jasjeet S. Sekhon. 2017

229 citations recorded by the source corpus.

Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict overlap restricts global discrepancies between the covariate distributions in the treated and control populations. Exploiting results from information theory, we derive explicit bounds on the average imbalance in covariate means under strict overlap and show that these bounds become more restrictive as the dimension grows large. We discuss how these implications interact with assumptions and procedures commonly deployed in observational causal inference, including sparsity and trimming.

Subfields: Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

CausaLM: Causal Model Explanation Through Counterfactual Language Models (2020, background): “The high-dimensional nature of language does not easily fit into the current methods, specifically as the treatment whose effect is being tested is often binary (D’Amour et al. 2017; Athey et al. 2017).”
A Survey on Causal Inference (2020, background): “[38] argues that the positivity assumption is a strong assumption and is more difficult to be satisfied in the high-dimensional datasets.”
Representation Learning for Treatment Effect Estimation from Observational Data (2018, background): “This assumption is also named as population overlapping [9].”
Conformal inference of counterfactuals and individual treatment effects (2020, methodology): “We refer the readers to D’Amour et al. [2017] for an extensive discussion.”
Adjusting for Confounding with Text Matching (2020, methodology): “If topics of documents confound treatment assignment, then methods (5)D’Amour et al. (2017) show that this assumption may fail in high-dimensional data,”
Towards optimal doubly robust estimation of heterogeneous causal effects (2020, background): “…in the causal literature, and in theory could be guaranteed by simply thresholding propensity score estimates; however, extreme propensity values (i.e., positivity violations) are an important issue in practice, especially in the nonparametric and high-dimensional setup [D’Amour et al., 2017].”
Incremental causal effects (2019, background): “This issue can be exacerbated if the covariate vector X is high-dimensional (D’Amour et al., 2017).”
Support and Invertibility in Domain-Invariant Representations (2019, background): “1 Representation-induced adaptation error When features X are high dimensional, they often contain information that is redundant or irrelevant for predicting the label Y but distinguishes the source and target domains; the higher the dimensionality, the less likely overlap is to hold in X (D’Amour e”
The Blessings of Multiple Causes (2018, background): “That said, as the dimensionality of Z i increases, overlap often becomes increasingly limited (D’Amour et al. 2017).”
Text and Causal Inference: A Review of Using Text to Remove Confounding from Causal Estimates (2020, background): “Other work has explored general methods for adjusting for highdimensional confounders (D’Amour et al., 2017; Rassen et al., 2011; Louizos et al., 2017; Li et al., 2016; Athey et al., 2017).”