Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing

Dorn, Jacob; Guo, Kevin

doi:10.1080/01621459.2022.2069572

Cited by 15 publications

(8 citation statements)

References 45 publications

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“…The sharp lower bound is given by the solution of (4) with minimization, which takes the same form as (5) but with W − (X) and W + (X) swapped and α * = 1/(1 + Γ). Dorn and Guo [2022] proved the analytical solution (5) using the Neyman-Pearson lemma. To see this connection, rewrite the constraint in 4).…”

Section: Zhaomentioning

confidence: 97%

See 1 more Smart Citation

Bounds and semiparametric inference in $L^\infty$- and $L^2$-sensitivity analysis for observational studies

Zhang¹,

Zhao²

2022

Preprint

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Sensitivity analysis for the unconfoundedness assumption is a crucial component of observational studies. The marginal sensitivity model has become increasingly popular for this purpose due to its interpretability and mathematical properties. After reviewing the original marginal sensitivity model that imposes a L ∞ -constraint on the maximum logit difference between the observed and full data propensity scores, we introduce a more flexible L 2 -analysis framework; sensitivity value is interpreted as the "average" amount of unmeasured confounding in the analysis. We derive analytic solutions to the stochastic optimization problems under the L 2 -model, which can be used to bound the average treatment effect (ATE). We obtain the efficient influence functions for the optimal values and use them to develop efficient one-step estimators. We show that multiplier bootstrap can be applied to construct a simultaneous confidence band of the ATE. Our proposed methods are illustrated by simulation and real-data studies.

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Section: Zhaomentioning

confidence: 97%

“…Soriano et al [2021] extended this idea to a broader class of balancing weights estimators. Interestingly, Dorn and Guo [2022] showed that the bound obtained by Zhao et al [2019] are conservative even asymptotically. They sharpened the bound by adding a moment constraint to the optimization step.…”

Section: Introductionmentioning

confidence: 99%

Bounds and semiparametric inference in $L^\infty$- and $L^2$-sensitivity analysis for observational studies

Zhang¹,

Zhao²

2022

Preprint

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show abstract

“…For example, a video compression treatment might have systematic and stable treatment effects across subpopulations, while a recommendation algorithm may not because of preference heterogeneity that isn't adequately captured by covariates. Sensitivity analyses in the vein of [4,8,12] that assess the magnitude of violations of outcome model stability that overturn transportation conclusions are a fruitful avenue for future research.…”

Section: Selectionmentioning

confidence: 99%

A Framework for Generalization and Transportation of Causal Estimates Under Covariate Shift

Lal¹,

Zheng²,

Ejdemyr³

2023

Preprint

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Randomized experiments are an excellent tool for estimating internally valid causal effects with the sample at hand, but their external validity is frequently questioned. While classical results on the estimation of Population Average Treatment Effects (PATE) implicitly assume random selection into experiments, this is typically far from true in many medical, socialscientific, and industry experiments. When the experimental sample is different from the target sample along observable or unobservable dimensions (termed covariate shift in the causal learning literature), experimental estimates may be of limited use for policy decisions. We cast this as a sample selection problem and propose methods to re-weight the doublyrobust scores from experimental subjects to estimate treatment effects in the overall sample (=: generalization) or in an alternate target sample (=: transportation). We implement these estimators in the open-source package causalTransportR 1 and illustrate its performance in a simulation study and discuss diagnostics to evaluate its performance. MethodsWe observe n iid copies of (X i , S i , S i A i , S i Y i ) n i=1 , where covariates X i ∈ R p , treatment A i ∈ A := {0, . . . , K}, outcome Y i ∈ R, and selection indicator S i ∈ {0, 1} is a function of pre-treatment variables and is not affected by treatment. In other words, we observe (X i , A i , Y i ) N 1 i=1 for observations with S i = 1 (henceforth the study sample S 1 ), and only (X i ) N i=N 1 +1 for observations with S i = 0 (henceforth the external sample S 0 ). The overall sample is S := S 1 ∪ S 0 .Estimands. We write counterfactual means as φ = E Y a,S=1 for generalizability and E [Y a |S = 0] for transportability, and contrasts between such counterfactual means under any two treatment levels a, a represent the average treatment effects (ATE). 'Standard' estimation of effects in the study sample under unconfoundedness is a well-studied and largely resolved problem (see [10] for a review). We study the generalization and transportation problems in the present paper. To this end, we make the following assumptions:(1) Consistency / SUTVA :2) Ignorability of Treatment: Y 0 , . . . , Y a ⊥ ⊥ A|X = x, S = 1 (3) Overlap (a) Treatment overlap: 0 < Pr (A = a|X = x, S = 1) < 1 (b) Selection overlap: 0 < Pr

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“…Similarly, we can benchmark Λ α by computing how much the odds of treatment change when adding a reference covariate into a propensity model which already includes some baseline covariates (see e.g. Kallus and Zhou, 2021;Dorn and Guo, 2022). Here, we can compute the 1 − αth…”

Section: Calibration For Binary Treatmentsmentioning

confidence: 99%

Sensitivity to Unobserved Confounding in Studies with Factor-structured Outcomes

Zheng¹,

Wu²,

D’Amour³

et al. 2022

Preprint

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We propose an approach for assessing sensitivity to unobserved confounding in studies with multiple outcomes. Under a shared confounding assumption, we argue that it is often reasonable to use residual dependence amongst outcomes to infer a proxy distribution for unobserved confounders. We focus on a class of factor models for which we can bound the causal effects for all outcomes conditional on a single sensitivity parameter that represents the fraction of treatment variance explained by unobserved confounders. We further characterize how causal ignorance regions shrink under assumptions about null control outcomes, propose strategies for benchmarking sensitivity parameters, and derive metrics for quantifying the robustness of effect estimates. Finally, we propose a Bayesian inference strategy for quantifying uncertainty and describe a practical sensitivity workflow which we demonstrate in both simulation and in a case study using data from the National Health and Nutrition Examination Survey (NHANES).

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Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing

Cited by 15 publications

References 45 publications

Bounds and semiparametric inference in $L^\infty$- and $L^2$-sensitivity analysis for observational studies

Bounds and semiparametric inference in $L^\infty$- and $L^2$-sensitivity analysis for observational studies

A Framework for Generalization and Transportation of Causal Estimates Under Covariate Shift

Sensitivity to Unobserved Confounding in Studies with Factor-structured Outcomes

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