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Adjustment for Missing Confounders Using External Validation Data and Propensity Scores

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  • Lawrence C. McCandless
  • Sylvia Richardson
  • Nicky Best

Abstract

Reducing bias from missing confounders is a challenging problem in the analysis of observational data. Information about missing variables is sometimes available from external validation data, such as surveys or secondary samples drawn from the same source population. In principle, the validation data permit us to recover information about the missing data, but the difficulty is in eliciting a valid model for the nuisance distribution of the missing confounders. Motivated by a British study of the effects of trihalomethane exposure on risk of full-term low birthweight, we describe a flexible Bayesian procedure for adjusting for a vector of missing confounders using external validation data. We summarize the missing confounders with a scalar summary score using the propensity score methodology of Rosenbaum and Rubin. The score has the property that it induces conditional independence between the exposure and the missing confounders, given the measured confounders. It balances the unmeasured confounders across exposure groups, within levels of measured covariates. To adjust for bias, we need only model and adjust for the summary score during Markov chain Monte Carlo computation. Simulation results illustrate that the proposed method reduces bias from several missing confounders over a range of different sample sizes for the validation data. Appendices A--C are available as online supplementary material.

Suggested Citation

  • Lawrence C. McCandless & Sylvia Richardson & Nicky Best, 2012. "Adjustment for Missing Confounders Using External Validation Data and Propensity Scores," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 40-51, March.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:40-51
    DOI: 10.1080/01621459.2011.643739
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    References listed on IDEAS

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    1. Sander Greenland, 2005. "Multiple‐bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306, March.
    2. Chatterjee N. & Chen Y-H. & Breslow N.E., 2003. "A Pseudoscore Estimator for Regression Problems With Two-Phase Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 158-168, January.
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    1. 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.
    2. Tian Gu & Jeremy Michael George Taylor & Bhramar Mukherjee, 2023. "A synthetic data integration framework to leverage external summary‐level information from heterogeneous populations," Biometrics, The International Biometric Society, vol. 79(4), pages 3831-3845, December.
    3. Bernard C Silenou & Marta Avalos & Catherine Helmer & Claudine Berr & Antoine Pariente & Helene Jacqmin-Gadda, 2019. "Health administrative data enrichment using cohort information: Comparative evaluation of methods by simulation and application to real data," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-16, January.
    4. Cao, Yongxiu & Yu, Jichang, 2023. "Adjusting for unmeasured confounding in survival causal effect using validation data," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    5. 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.

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