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$ρ$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows

Sourabh Balgi, Jose M. Peña, Adel Daoud

arXiv 15 Sep 2022 · Statistics — Methodology · 1 citations (OpenAlex)

arXiv:2209.07111 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop $\rho$-GNF ($\rho$-graphical normalizing flow), where $\rho{\in}[-1,+1]$ is a bounded sensitivity parameter. This parameter represents the back-door non-causal association due to unobserved confounding, and which is encoded with a Gaussian copula. In other words, the $\rho$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $\rho$, while accounting for various assumed strengths of the unobserved confounding. The output of the $\rho$-GNF is what we denote as the $\rho_{curve}$ that provides the bounds for the ACE given an interval of assumed $\rho$ values. In particular, the $\rho_{curve}$ enables scholars to identify the confounding strength required to nullify the ACE, similar to other sensitivity analysis methods (e.g., the E-value). Leveraging on experiments from simulated and real-world data, we show the benefits of $\rho$-GNF. One benefit is that the $\rho$-GNF uses a Gaussian copula to encode the distribution of the unobserved causes, which is commonly used in many applied settings. This distributional assumption produces narrower ACE bounds compared to other popular sensitivity analysis methods.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1T. J. VanderWeele and P. Ding (2017) https://doi.org/10.7326/M16-2607Sensitivity Analysis in Observational Research: Introducing the E-value1.00083100%
2A. Wehenkel and G. Louppe (2021) http://proceedings.mlr.press/v130/wehenkel21a/wehenkel21a.pdfGraphical Normalizing Flows1.00053100%
3S. Balgi, J. M. Peña, and A. Daoud (2022) https://ojs.aaai.org/index.php/AAAI/article/view/21437Personalized Public Policy Analysis in Social Sciences Using Causal-Graphi…0.92843100%
4C. F. Manski (1990) http://www.jstor.org/stable/2006592Nonparametric Bounds on Treatment Effects0.87472100%
5A. Sjölander (2020) https://doi.org/10.1515/jci-2020-0012A Note on a Sensitivity Analysis for Unmeasured Confounding, and the Related E-value0.87472100%
6J. M. Robins (1989) https://cdn1.sph.harvard.edu/wp-content/uploads/sites/343/2013/03/nchsr.pdfThe Analysis of Randomized and Non-randomized AIDS Tr…0.87462100%
7J. M. Peña (2022) https://doi.org/10.1515/jci-2021-0041Simple Yet Sharp Sensitivity Analysis for Unmeasured Confounding0.87452100%
8A. Sjölander and O. Hössjer (2021) https://doi.org/10.1515/jci-2021-0024Novel Bounds for Causal Effects Based on Sensitivity Parameters on the Risk Difference Scale0.87452100%
9A. Wehenkel and G. Louppe (2019) https://papers.nips.cc/paper/2019/hash/2a084e55c87b1ebcdaad1f62fdbbac8e-Abstract.htmlUnconstrained Monotonic Neural Networks0.81142100%
10C. Cinelli, D. Kumor, B. Chen, J. Pearl, and E. Bareinboim (2019) http://proceedings.mlr.press/v97/cinelli19a/cinelli19a.pdfSensitivity Analysis of Linear Structural Causal Models0.73732100%

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