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Valid causal inference: model selection and sensitivity to unobserved confounding in high-dimensional settings
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-5442-9708
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0003-2135-9963
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0003-3187-1987
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Recently, various methods have been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data generating processes, when high-dimensional nuisance models are estimated by post-model selection or machine learning estimators. These methods typically require that all the confounders are observed to ensure identification of the effects. We contribute by showing how valid semiparametric inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We propose uncertainty intervals which allow for unobserved confounding, and show that the resulting inference is valid when the amount of unobserved confounding is small relative to the sample size; the latter is formalized in terms of convergence rates. Simulation experiments illustrate the finite sample properties of the proposed intervals and investigate an alternative procedure that improves the empirical coverage of the intervals when the amount of unobserved confounding is large.

Keywords [en]
Average treatment effect, Inverse probability weighting, Double robust estimator
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-199233OAI: oai:DiVA.org:umu-199233DiVA, id: diva2:1693994
Funder
Marianne and Marcus Wallenberg FoundationAvailable from: 2022-09-08 Created: 2022-09-08 Last updated: 2024-06-05
In thesis
1. Valid causal inference in high-dimensional and complex settings
Open this publication in new window or tab >>Valid causal inference in high-dimensional and complex settings
2022 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Giltig kausalinferens med högdimensionella och komplexa data
Abstract [en]

The objective of this thesis is to consider some challenges that arise when conducting causal inference based on observational data. High dimensionality can occur when it is necessary to adjust for many covariates, and flexible models must be used to meet convergence assumptions. The latter may require the use of a novel machine learning estimator. Estimating nonparametrically-defined causal estimands at parametric rates and obtaining good-quality confidence intervals (with near nominal coverage) are the primary goals. Another challenge is providing a sensitivity analysis that can be applied in high-dimensional scenarios as a way of assessing the robustness of the results to missing confounders. 

Four papers are included in the thesis. A common theme in all the papers is covariate selection or nonparametric estimation of nuisance models. To provide insight into the performance of the approaches presented, some theoretical results are provided. Additionally, simulation studies are reported. In paper I, covariate selection is discussed as a method for removing redundant variables. This approach is compared to other strategies for variable selection that ensure reasonable confidence interval coverage. Paper II integrates variable selection into a sensitivity analysis, where the sensitivity parameter is the conditional correlation of the outcome and treatment variables. The validity of the analysis where the sensitivity parameter is small relative to the sample size is shown theoretically. In simulation settings, however, the analysis performs as expected, even for larger values of sensitivity parameters, when using a correction of the estimator of the residual variance for the outcome model. Paper IV extends the applicability of the sensitivity analysis method through the use of a different residual variance estimator and applies it to a real study of the effects of smoking during pregnancy on child birth weight. A real data problem of analysing the effect of early retirement on health outcomes is studied in Paper III. Rather than using variable selection strategies, convolutional neural networks are studied to fit the nuisance models.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2022. p. 14
Series
Statistical studies, ISSN 1100-8989 ; 56
Keywords
Causal inference, high dimension, sensitivity analysis, variable selection, convolutional neural network, semiparametric efficiency bound
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-199258 (URN)978-91-7855-881-0 (ISBN)978-91-7855-882-7 (ISBN)
Public defence
2022-10-07, Hörsal NBET.A.101, Norra Beteendevetarhuset, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2022-09-16 Created: 2022-09-09 Last updated: 2024-06-05Bibliographically approved

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Moosavi, NiloofarGorbach, Tetianade Luna, Xavier

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