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

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.

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References

  1. An, W. (2010). Bayesian propensity score estimators: incorporating uncertainties in propensity scores into causal inference. Sociological Methodology, 40, 151–189.

    Article  Google Scholar 

  2. Carlin, B. P., & Louis, T. A. (2009). Bayesian methods for data analysis (3rd ed.). Boca Raton, FL: Chapman & Hall/CRC.

    Google Scholar 

  3. Cole, S. R., Chu, H., & Greenland, S. (2006). Multiple-imputation for measurement-error correction. International Journal of Epidemiology, 35, 1074–1081.

    Article  PubMed  Google Scholar 

  4. Drake, C. (1993). Effects of misspecification of the propensity score on estimators of treatment effect. Biometrics, 49, 1231–1236.

    Article  Google Scholar 

  5. Gössl, C., & Kuechenhoff, H. (2001). Bayesian analysis of logistic regression with an unknown change point and covariate measurement error. Statistics in Medicine, 20, 3109–3121.

    Article  PubMed  Google Scholar 

  6. Gustafson, P. (2003). Measurement error and misclassification in statistics and epidemiology: impacts and Bayesian adjustments. Boca Raton, FL: Chapman & Hall/CRC.

    Google Scholar 

  7. Gustafson, P., McCandless, L. C., Levy, A. R., & Richardson, S. (2010). Simplified Bayesian sensitivity analysis for mismeasured and unobserved confounders. Biometrics, 66, 1129–1137.

    Article  PubMed  Google Scholar 

  8. Kaplan, D., & Chen, J. (2012). A two-step Bayesian approach for propensity score analysis: simulations and case study. Psychometrika, 77, 581–609.

    Article  PubMed  Google Scholar 

  9. 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.

  10. Kessler, R. C., Avenevoli, S., Green, J., Gruber, M. J., Guyer, M., He, Y., et al. (2009b). 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, 386–399.

    Article  Google Scholar 

  11. Lee, B. K., Lessler, J., & Stuart, E. A. (2011). Weight trimming and propensity score weighting. PLoS One, 6, e18174.

    Article  PubMed  PubMed Central  Google Scholar 

  12. Leventhal, T., & Brooks-Gunn, J. (2000). The neighborhoods they live in: the effects of neighborhood residence on child and adolescent outcomes. Psychological Bulletin, 126, 309.

    Article  PubMed  Google Scholar 

  13. Little, R. J. A. (2004). To model or not to model? Competing modes of inference for finite population sampling. Journal of the American Statistical Association, 99, 546–556.

    Article  Google Scholar 

  14. 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, 22–52.

    Article  Google Scholar 

  15. McCaffrey, D.F., Lockwood, J.R., & Setodji, C.M. (2013). Inverse probability weighting with error-prone covariates. Biometrika ast022.

  16. McCandless, L. C., Gustafson, P., & Austin, P. C. (2009). Bayesian propensity score analysis for observational data. Statistics in Medicine, 28, 94–112.

    Article  PubMed  Google Scholar 

  17. 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, 367–379.

    Article  Google Scholar 

  18. 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.

  19. Raykov, T. (2012). Propensity score analysis with fallible covariates a note on a latent variable modeling approach. Educational and Psychological Measurement, 72, 715–733.

    Article  Google Scholar 

  20. 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, 544–559.

    Article  Google Scholar 

  21. Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.

    Article  Google Scholar 

  22. Rosenbaum, P. R. (2002). Observational Studies (2nd ed.). New York: Springer.

    Google Scholar 

  23. Roux, A. V. D., Kiefe, C. I., Jacobs, D. R., Haan, M., Jackson, S. A., Nieto, F. J., et al. (2001). Area characteristics and individual-level socioeconomic position indicators in three population-based epidemiologic studies. Annals of Epidemiology, 11, 395–405.

    Article  PubMed  Google Scholar 

  24. Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688.

    Article  Google Scholar 

  25. Rubin, D. B. (1980). Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American Statistical Association, 75, 591–593.

    Google Scholar 

  26. Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.

    Google Scholar 

  27. 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, 467–475.

    Article  Google Scholar 

  28. Stan Development Team (2014). RStan: the R interface to Stan, Version 2.5.0. http://mc-stan.org/rstan.html

  29. 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, 213–236.

    Article  Google Scholar 

  30. Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statistical Science, 25, 1.

    Article  PubMed  PubMed Central  Google Scholar 

  31. 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, 279–289.

    Article  PubMed  PubMed Central  Google Scholar 

  32. 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=R2jags

  33. 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 press

  34. 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, 2597–2606.

    Article  Google Scholar 

  35. 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, 263–273.

    Article  PubMed  PubMed Central  Google Scholar 

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Correspondence to Hwanhee Hong.

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Hong, H., Rudolph, K.E. & Stuart, E.A. Bayesian Approach for Addressing Differential Covariate Measurement Error in Propensity Score Methods. Psychometrika 82, 1078–1096 (2017). https://doi.org/10.1007/s11336-016-9533-x

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Keywords

  • Bayesian hierarchical model
  • differential measurement error
  • inverse probability of treatment weighting
  • propensity score