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Cutting Feedback in Bayesian Regression Adjustment for the Propensity Score

Author

Listed:
  • McCandless Lawrence C

    (Simon Fraser University)

  • Douglas Ian J.

    (London School of Hygiene & Tropical Medicine)

  • Evans Stephen J.

    (London School of Hygiene & Tropical Medicine)

  • Smeeth Liam

    (London School of Hygiene & Tropical Medicine)

Abstract

McCandless, Gustafson and Austin (2009) describe a Bayesian approach to regression adjustment for the propensity score to reduce confounding. A unique property of the method is that the treatment and outcome models are combined via Bayes theorem. However, this estimation procedure can be problematic if the outcome model is misspecified. We observe feedback that can bias propensity score estimates. Building on new innovation in Bayesian computation, we propose a technique for cutting feedback in a Bayesian propensity analysis. We use the posterior distribution of the propensity scores as an input in the regression model for the outcome. The method is approximately Bayesian in the sense that it does not use the full likelihood for estimation. Nonetheless, it severs feedback between the treatment and outcome giving propensity score estimates that are free from bias but modeled with uncertainty. We illustrate the method in a matched cohort study investigating the effect of statins on primary stroke prevention.

Suggested Citation

  • McCandless Lawrence C & Douglas Ian J. & Evans Stephen J. & Smeeth Liam, 2010. "Cutting Feedback in Bayesian Regression Adjustment for the Propensity Score," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-24, March.
    • Handle: RePEc:bpj:ijbist:v:6:y:2010:i:2:n:16
    DOI: 10.2202/1557-4679.1205
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    References listed on IDEAS

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    1. Tan, Zhiqiang, 2006. "A Distributional Approach for Causal Inference Using Propensity Scores," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1619-1637, December.
    2. M.‐H. Chen & J. G. Ibrahim & C. Yiannoutsos, 1999. "Prior elicitation, variable selection and Bayesian computation for logistic regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 223-242.
    3. Rice K.M., 2004. "Equivalence Between Conditional and Mixture Approaches to the Rasch Model and Matched Case-Control Studies, With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 510-522, January.
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    Cited by:

    1. Olli Saarela & David A. Stephens & Erica E. M. Moodie & Marina B. Klein, 2015. "Rejoinder “On Bayesian estimation of marginal structural models”," Biometrics, The International Biometric Society, vol. 71(2), pages 299-301, June.
    2. A. Giffin & B. J. Reich & S. Yang & A. G. Rappold, 2023. "Generalized propensity score approach to causal inference with spatial interference," Biometrics, The International Biometric Society, vol. 79(3), pages 2220-2231, September.
    3. Corwin M. Zigler & Krista Watts & Robert W. Yeh & Yun Wang & Brent A. Coull & Francesca Dominici, 2013. "Model Feedback in Bayesian Propensity Score Estimation," Biometrics, The International Biometric Society, vol. 69(1), pages 263-273, March.
    4. Corwin Matthew Zigler, 2016. "The Central Role of Bayes’ Theorem for Joint Estimation of Causal Effects and Propensity Scores," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 47-54, February.
    5. F. Swen Kuh & Grace S. Chiu & Anton H. Westveld, 2019. "Modeling National Latent Socioeconomic Health and Examination of Policy Effects via Causal Inference," Papers 1911.00512, arXiv.org.
    6. Swen Kuh & Grace S. Chiu & Anton H. Westveld, 2020. "Latent Causal Socioeconomic Health Index," Papers 2009.12217, arXiv.org, revised Oct 2023.
    7. O. Saarela & L. R. Belzile & D. A. Stephens, 2016. "A Bayesian view of doubly robust causal inference," Biometrika, Biometrika Trust, vol. 103(3), pages 667-681.
    8. Olli Saarela & David A. Stephens & Erica E. M. Moodie & Marina B. Klein, 2015. "On Bayesian estimation of marginal structural models," Biometrics, The International Biometric Society, vol. 71(2), pages 279-288, June.
    9. Luo, Yu & Graham, Daniel J. & McCoy, Emma J., 2023. "Semiparametric Bayesian doubly robust causal estimation," LSE Research Online Documents on Economics 117944, London School of Economics and Political Science, LSE Library.
    10. Matthew Cefalu & Francesca Dominici & Nils Arvold & Giovanni Parmigiani, 2017. "Model averaged double robust estimation," Biometrics, The International Biometric Society, vol. 73(2), pages 410-421, June.
    11. Qi Zhou & Catherine McNeal & Laurel A. Copeland & Justin P. Zachariah & Joon Jin Song, 2020. "Bayesian propensity score analysis for clustered observational data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 335-355, June.
    12. James M. Robins & Miguel A. Hernán & Larry Wasserman, 2015. "Discussion of “On Bayesian estimation of marginal structural models”," Biometrics, The International Biometric Society, vol. 71(2), pages 296-299, June.
    13. Alexandra M. Schmidt, 2022. "Discussion on “Spatial+: a novel approach to spatial confounding” by Emiko Dupont, Simon N. Wood, and Nicole H. Augustin," Biometrics, The International Biometric Society, vol. 78(4), pages 1300-1304, December.
    14. Brian J. Reich & Shu Yang & Yawen Guan & Andrew B. Giffin & Matthew J. Miller & Ana Rappold, 2021. "A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications," International Statistical Review, International Statistical Institute, vol. 89(3), pages 605-634, December.

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