Statistical and Causal Robustness for Causal Null Hypothesis Tests

Junhui Yang, Rohit Bhattacharya, Youjin Lee, Ted Westling
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:3956-3978, 2024.

Abstract

Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of $K$ asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of $K$ candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the $K$ proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-yang24b, title = {Statistical and Causal Robustness for Causal Null Hypothesis Tests}, author = {Yang, Junhui and Bhattacharya, Rohit and Lee, Youjin and Westling, Ted}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {3956--3978}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/yang24b/yang24b.pdf}, url = {https://proceedings.mlr.press/v244/yang24b.html}, abstract = {Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of $K$ asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of $K$ candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the $K$ proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study.} }
Endnote
%0 Conference Paper %T Statistical and Causal Robustness for Causal Null Hypothesis Tests %A Junhui Yang %A Rohit Bhattacharya %A Youjin Lee %A Ted Westling %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-yang24b %I PMLR %P 3956--3978 %U https://proceedings.mlr.press/v244/yang24b.html %V 244 %X Prior work applying semiparametric theory to causal inference has primarily focused on deriving estimators that exhibit statistical robustness under a prespecified causal model that permits identification of a desired causal parameter. However, a fundamental challenge is correct specification of such a model, which usually involves making untestable assumptions. Evidence factors is an approach to combining hypothesis tests of a common causal null hypothesis under two or more candidate causal models. Under certain conditions, this yields a test that is valid if at least one of the underlying models is correct, which is a form of causal robustness. We propose a method of combining semiparametric theory with evidence factors. We develop a causal null hypothesis test based on joint asymptotic normality of $K$ asymptotically linear semiparametric estimators, where each estimator is based on a distinct identifying functional derived from each of $K$ candidate causal models. We show that this test provides both statistical and causal robustness in the sense that it is valid if at least one of the $K$ proposed causal models is correct, while also allowing for slower than parametric rates of convergence in estimating nuisance functions. We demonstrate the effectiveness of our method via simulations and applications to the Framingham Heart Study and Wisconsin Longitudinal Study.
APA
Yang, J., Bhattacharya, R., Lee, Y. & Westling, T.. (2024). Statistical and Causal Robustness for Causal Null Hypothesis Tests. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:3956-3978 Available from https://proceedings.mlr.press/v244/yang24b.html.

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