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Robust variance estimation and inference for causal effect estimation

Author

Listed:
  • Tran Linh

    (Department of Statistics, Stanford University, Stanford, California, United States)

  • Petersen Maya

    (Berkeley School of Public Health, University of California, Berkeley, California, United States)

  • Schwab Joshua

    (Berkeley School of Public Health, University of California, Berkeley, California, United States)

  • van der Laan Mark J.

    (Berkeley School of Public Health, University of California, Berkeley, California, United States)

Abstract

We present two novel approaches to variance estimation of semi-parametric efficient point estimators of the treatment-specific mean: (i) a robust approach that directly targets the variance of the influence function (IF) as a counterfactual mean outcome and (ii) a modified non-parametric bootstrap-based approach. The performance of these approaches to variance estimation is compared to variance estimation based on the sample variance of the empirical IF in simulations across different levels of positivity violations and treatment effect sizes. In this article, we focus on estimation of the nuisance parameters using correctly specified parametric models for the treatment mechanism in order to highlight the challenges posed by violation of positivity assumptions (distinct from the challenges posed by non-parametric estimation of the nuisance parameters). Results demonstrate that (1) variance estimation based on the empirical IF may provide highly anti-conservative confidence interval coverage (as reported previously), (2) the proposed robust approach to variance estimation in this setting provides conservative coverage, and (3) the proposed modified bootstrap maintains close to nominal coverage and improves power. In the appendix, we (a) generalize the robust approach of estimating variance to marginal structural working models and (b) provide a proof of the consistency of the targeted minimum loss-based estimation bootstrap.

Suggested Citation

  • Tran Linh & Petersen Maya & Schwab Joshua & van der Laan Mark J., 2023. "Robust variance estimation and inference for causal effect estimation," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-27, January.
    • Handle: RePEc:bpj:causin:v:11:y:2023:i:1:p:27:n:1
    DOI: 10.1515/jci-2021-0067
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    References listed on IDEAS

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    1. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
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