IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v6y2010i2n16.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1557-4679.1205
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1557-4679.1205?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iván Díaz & Elizabeth Colantuoni & Daniel F. Hanley & Michael Rosenblum, 2019. "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 439-468, July.
    2. Xiaogang Duan & Guosheng Yin, 2017. "Ensemble Approaches to Estimating the Population Mean with Missing Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 899-917, December.
    3. Ming-Hui Chen & Qi-Man Shao, 2002. "Partition-Weighted Monte Carlo Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 338-354, June.
    4. Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Papers 2206.08503, arXiv.org, revised Oct 2022.
    5. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    6. Karel Vermeulen & Stijn Vansteelandt, 2015. "Bias-Reduced Doubly Robust Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1024-1036, September.
    7. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
    8. Guo, Donglin & Xue, Liugen & Hu, Yuqin, 2017. "Covariate-balancing-propensity-score-based inference for linear models with missing responses," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 139-145.
    9. Leonardo Egidi & Ioannis Ntzoufras, 2020. "A Bayesian quest for finding a unified model for predicting volleyball games," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1307-1336, November.
    10. Jie Zhou & Zhiwei Zhang & Zhaohai Li & Jun Zhang, 2015. "Coarsened Propensity Scores and Hybrid Estimators for Missing Data and Causal Inference," International Statistical Review, International Statistical Institute, vol. 83(3), pages 449-471, December.
    11. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    12. Bryan S. Graham & Cristine Campos de Xavier Pinto & Daniel Egel, 2016. "Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 288-301, April.
    13. Chen, Min & Wang, Xinlei, 2011. "Approximate predictive densities and their applications in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1570-1580, April.
    14. Imaduddin Ahmed & Priti Parikh & Parfait Munezero & Graham Sianjase & D’Maris Coffman, 2023. "The impact of power outages on households in Zambia," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 40(3), pages 835-867, October.
    15. Jacob Dorn & Kevin Guo & Nathan Kallus, 2021. "Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding," Papers 2112.11449, arXiv.org, revised Jul 2022.
    16. Min-Hua Jen & Alex Bottle & Graham Kirkwood & Ron Johnston & Paul Aylin, 2011. "The performance of automated case-mix adjustment regression model building methods in a health outcome prediction setting," Health Care Management Science, Springer, vol. 14(3), pages 267-278, September.
    17. Minerva Mukhopadhyay & Sourabh Bhattacharya, 2022. "Bayes factor asymptotics for variable selection in the Gaussian process framework," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 581-613, June.
    18. Sylvie Goetgeluk & Stijn Vansteelandt & Els Goetghebeur, 2008. "Estimation of controlled direct effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 1049-1066, November.
    19. Michal Juraska & Peter B. Gilbert, 2016. "Mark-specific hazard ratio model with missing multivariate marks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 606-625, October.
    20. Evan T.R. Rosenman & Guillaume Basse & Art B. Owen & Mike Baiocchi, 2023. "Combining observational and experimental datasets using shrinkage estimators," Biometrics, The International Biometric Society, vol. 79(4), pages 2961-2973, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:ijbist:v:6:y:2010:i:2:n:16. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.