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Bayesian Approach for Addressing Differential Covariate Measurement Error in Propensity Score Methods

Published online by Cambridge University Press:  01 January 2025

Hwanhee Hong ,
Kara E. Rudolph  and
Elizabeth A. Stuart
Hwanhee Hong*
Affiliation:
Johns Hopkins Bloomberg School of Public Health
Kara E. Rudolph
Affiliation:
University of California at Berkeley
Elizabeth A. Stuart
Affiliation:
Johns Hopkins Bloomberg School of Public Health
*
Correspondence should be made to Hwanhee Hong, Department of Mental Health, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205 USA. Email: hhong@jhu.edu
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Abstract

Propensity score methods are an important tool to help reduce confounding in non-experimental studies and produce more accurate causal effect estimates. Most propensity score methods assume that covariates are measured without error. However, covariates are often measured with error. Recent work has shown that ignoring such error could lead to bias in treatment effect estimates. In this paper, we consider an additional complication: that of differential measurement error across treatment groups, such as can occur if a covariate is measured differently in the treatment and control groups. We propose two flexible Bayesian approaches for handling differential measurement error when estimating average causal effects using propensity score methods. We consider three scenarios: systematic (i.e., a location shift), heteroscedastic (i.e., different variances), and mixed (both systematic and heteroscedastic) measurement errors. We also explore various prior choices (i.e., weakly informative or point mass) on the sensitivity parameters related to the differential measurement error. We present results from simulation studies evaluating the performance of the proposed methods and apply these approaches to an example estimating the effect of neighborhood disadvantage on adolescent drug use disorders.

Keywords

Bayesian hierarchical modeldifferential measurement errorinverse probability of treatment weightingpropensity score
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017 , pp. 1078 - 1096
Copyright
Copyright © 2016 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-016-9533-x) contains supplementary material, which is available to authorized users.

References

An, W. (2010). Bayesian propensity score estimators: incorporating uncertainties in propensity scores into causal inference. Sociological Methodology 40, 151–189CrossRefGoogle Scholar
Carlin, B. P. & Louis, T. A. (2009). Bayesian methods for data analysis 3Boca Raton, FL: Chapman & Hall/CRCGoogle Scholar
Cole, S. R. Chu, H. & Greenland, S. (2006). Multiple-imputation for measurement-error correction. International Journal of Epidemiology 35, 1074–1081CrossRefGoogle ScholarPubMed
Drake, C. (1993). Effects of misspecification of the propensity score on estimators of treatment effect. Biometrics 49, 1231–1236CrossRefGoogle Scholar
Gössl, C. & Kuechenhoff, H. (2001). Bayesian analysis of logistic regression with an unknown change point and covariate measurement error. Statistics in Medicine 20, 3109–3121CrossRefGoogle ScholarPubMed
Gustafson, P. (2003). Measurement error and misclassification in statistics and epidemiology: impacts and Bayesian adjustments Boca Raton, FL: Chapman & Hall/CRCCrossRefGoogle Scholar
Gustafson, P. McCandless, L. C. Levy, A. R. & Richardson, S. (2010). Simplified Bayesian sensitivity analysis for mismeasured and unobserved confounders. Biometrics 66, 1129–1137CrossRefGoogle ScholarPubMed
Kaplan, D. & Chen, J. (2012). A two-step Bayesian approach for propensity score analysis: simulations and case study. Psychometrika 77, 581–609CrossRefGoogle ScholarPubMed
Kessler, R. C., Avenevoli, S., Costello, E. J., Green, J. G., Gruber, M. J., Heeringa, S., et al. (2009a). National comorbidity survey replication adolescent supplement (NCS-A): II. Overview and design. Journal of the American Academy of Child and Adolescent Psychiatry, 48, 380–385.CrossRefGoogle Scholar
Kessler, R. C. Avenevoli, S. Green, J. Gruber, M. J. Guyer, M. & He, Y. (2009). et al. National comorbidity survey replication adolescent supplement (NCS-A): III. Concordance of DSM-IV/CIDI diagnoses with clinical reassessments. Journal of the American Academy of Child & Adolescent Psychiatry 48, 386–399CrossRefGoogle ScholarPubMed
Lee, B. K. Lessler, J. & Stuart, E. A. (2011). Weight trimming and propensity score weighting. PLoS One 6, e18174CrossRefGoogle ScholarPubMed
Leventhal, T. & Brooks-Gunn, J. (2000). The neighborhoods they live in: the effects of neighborhood residence on child and adolescent outcomes. Psychological Bulletin 126, 309CrossRefGoogle ScholarPubMed
Little, RJA (2004). To model or not to model? Competing modes of inference for finite population sampling. Journal of the American Statistical Association 99, 546–556CrossRefGoogle Scholar
Lockwood, J. R. & McCaffrey, D. F. (2014). Correcting for test score measurement error in ANCOVA models for estimating treatment effects. Journal of Educational and Behavioral Statistics 39, 22–52CrossRefGoogle Scholar
McCaffrey, D.F., Lockwood, J.R., & Setodji, C.M. (2013). Inverse probability weighting with error-prone covariates. Biometrika ast022.CrossRefGoogle Scholar
McCandless, L. C. Gustafson, P. & Austin, P. C. (2009). Bayesian propensity score analysis for observational data. Statistics in Medicine 28, 94–112CrossRefGoogle ScholarPubMed
Merikangas, K. R. Avenevoli, S. Costello, E. J. Koretz, D. & Kessler, R. C. (2009). National comorbidity survey replication adolescent supplement (NCS-A): I. Background and measures. Journal of the American Academy of Child & Adolescent Psychiatry 48, 367–379CrossRefGoogle ScholarPubMed
Pearl, J., & Bareinboim, E. (2011). Transportability of causal and statistical relations: A formal approach. In Data Mining Workshops (ICDMW), 2011 IEEE 11th International Conference on (pp. 540-547). IEEE.CrossRefGoogle Scholar
Raykov, T. (2012). Propensity score analysis with fallible covariates a note on a latent variable modeling approach. Educational and Psychological Measurement 72, 715–733CrossRefGoogle Scholar
Robins, J. Sued, M. Lei-Gomez, Q. & Rotnitzky, A. (2007). Comment: Performance of double-robust estimators when "inverse probability" weights are highly variable. Statistical Science 22, 544–559CrossRefGoogle Scholar
Rosenbaum, P. R. & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55CrossRefGoogle Scholar
Rosenbaum, P. R. (2002). Observational Studies 2New York: SpringerCrossRefGoogle Scholar
Roux, AVD Kiefe, C. I. Jacobs, D. R. Haan, M. Jackson, S. A. Nieto, F. J. Paton, C. C. & Schulz, R. (2001). Area characteristics and individual-level socioeconomic position indicators in three population-based epidemiologic studies. Annals of Epidemiology 11, 395–405CrossRefGoogle Scholar
Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66, 688CrossRefGoogle Scholar
Rubin, D. B. (1980). Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American Statistical Association 75, 591–593Google Scholar
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys New York: WileyCrossRefGoogle Scholar
Rudolph, K. E. Stuart, E. A. Glass, T. A. & Merikangas, K. R. (2004). Neighborhood disadvantage in context: the influence of urbanicity on the association between neighborhood disadvantage and adolescent emotional disorders. Social Psychiatry and Psychiatric Epidemiology 49, 467–475CrossRefGoogle Scholar
Stan Development Team (2014). RStan: the R interface to Stan, Version 2.5.0. http://mc-stan.org/rstan.htmlGoogle Scholar
Steiner, P. M. Cook, T. D. & Shadish, W. R. (2011). On the importance of reliable covariate measurement in selection bias adjustments using propensity scores. Journal of Educational and Behavioral Statistics 36, 213–236CrossRefGoogle Scholar
Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statistical Science 25, 1CrossRefGoogle Scholar
Stürmer, T. Schneeweiss, S. Avorn, J. & Glynn, R. J. (2005). Adjusting effect estimates for unmeasured confounding with validation data using propensity score calibration. American Journal of Epidemiology 162, 279–289CrossRefGoogle ScholarPubMed
Su, Y., & Yajima, M. (2014). R2jags: A Package for Running jags from R. R package version 0.04-03. http://CRAN.R-project.org/package=R2jagsGoogle Scholar
Webb-Vargas, Y., Rudolph, K.E., Lenis, D., Murakami, P., & Stuart, E.A. (2015). Applying multiple imputation for external calibration to propensity score analysis. Statistical Methods in Medical Research In pressGoogle Scholar
Yanez, N. D. Kronmal, R. A. & Shemanski, L. R. (1988). The effects of measurement error in response variables and tests of association of explanatory variables in change models. Statistics in Medicine 17, 2597–26063.0.CO;2-G>CrossRefGoogle Scholar
Zigler, C. M. Watts, K. Yeh, R. W. Wang, Y. Coull, B. A. & Dominici, F. (2013). Model feedback in bayesian propensity score estimation. Biometrics 69, 263–273CrossRefGoogle ScholarPubMed
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