Statistics in Biosciences

, Volume 10, Issue 1, pp 233–254 | Cite as

Estimation of Causal Effect Measures in the Presence of Measurement Error in Confounders

  • Di Shu
  • Grace Y. YiEmail author


The odds ratio, risk ratio, and the risk difference are important measures for assessing comparative effectiveness of available treatment plans in epidemiological studies. Estimation of these measures, however, is often challenged by the presence of error-contaminated confounders. In this article, by adapting two correction methods for measurement error effects applicable to the noncausal context, we propose valid methods which consistently estimate the causal odds ratio, causal risk ratio, and the causal risk difference for settings with error-prone confounders. Furthermore, we develop a bootstrap-based procedure to construct estimators with improved asymptotic efficiency. Numerical studies are conducted to assess the performance of the proposed methods.


Causal effect measures Causal inference Comparative effectiveness Confounding Measurement error 



The authors would like to thank the reviewers for their comments on the initial version. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and partially supported by a Collaborative Research Team Project of the Canadian Statistical Sciences Institute (CANSSI).


  1. 1.
    Babanezhad M, Vansteelandt S, Goetghebeur E (2010) Comparison of causal effect estimators under exposure misclassification. J Stat Plan Inference 140:1306–1319MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baiocchi M, Small DS, Lorch S, Rosenbaum PR (2010) Building a stronger instrument in an observational study of perinatal care for premature infants. J Am Stat Assoc 105:1285–1296MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Blakely T, McKenzie S, Carter K (2013) Misclassification of the mediator matters when estimating indirect effects. J Epidemiol Commun Health 67:458–466CrossRefGoogle Scholar
  4. 4.
    Buonaccorsi JP (2010) Measurement error: models, methods, and applications. Chapman & Hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
  5. 5.
    Carroll RJ, Spiegelman CH, Lan KG, Bailey KT, Abbott RD (1984) On errors-in-variables for binary regression models. Biometrika 71:19–25MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models: a modern perspective. Chapman & Hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
  7. 7.
    Cornfield J (1962) Joint dependence of risk of coronary heart disease on serum cholesterol and systolic blood pressure: a discriminant function analysis. Fed Proc 21:59–61Google Scholar
  8. 8.
    Edwards JK, Cole SR, Westreich D (2015) All your data are always missing: incorporating bias due to measurement error into the potential outcomes framework. Int J Epidemiol 44:1452–1459CrossRefGoogle Scholar
  9. 9.
    Efron B (1982) The jackknife, the bootstrap and other resampling plans, vol 38. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  10. 10.
    Fuller WA (1987) Measurement error models, vol 305. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  11. 11.
    Gustafson P (2003) Measurement error and misclassification in statistics and epidemiology: impacts and Bayesian adjustments. Chapman & Hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
  12. 12.
    Hernán MA, Cole SR (2009) Invited commentary: causal diagrams and measurement bias. Am J Epidemiol 170:959–962CrossRefGoogle Scholar
  13. 13.
    Hernán MA, Robins JM (2016) Causal inference. Chapman & Hall/CRC, Boca Raton forthcomingGoogle Scholar
  14. 14.
    Huang Y, Wang C (2001) Consistent functional methods for logistic regression with errors in covariates. J Am Stat Assoc 96:1469–1482MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Imai K, Yamamoto T (2010) Causal inference with differential measurement error: nonparametric identification and sensitivity analysis. Am J Polit Sci 54:543–560CrossRefGoogle Scholar
  16. 16.
    Kyle RP, Moodie EE, Klein MB, Abrahamowicz M (2016) Correcting for measurement error in time-varying covariates in marginal structural models. Am J Epidemiol 184:249–258CrossRefGoogle Scholar
  17. 17.
    Lockwood J, McCaffrey DF (2016) Matching and weighting with functions of error-prone covariates for causal inference. J Am Stat Assoc 111:1831–1839MathSciNetCrossRefGoogle Scholar
  18. 18.
    Lunceford JK, Davidian M (2004) Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Stat Med 23:2937–2960CrossRefGoogle Scholar
  19. 19.
    McCaffrey DF, Lockwood J, Setodji CM (2013) Inverse probability weighting with error-prone covariates. Biometrika 100:671–680MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Ogburn EL, VanderWeele TJ (2012) Analytic results on the bias due to nondifferential misclassification of a binary mediator. Am J Epidemiol 176:555–561CrossRefGoogle Scholar
  21. 21.
    Pearl J (2009) On measurement bias in causal inference. Technical Report R-357, Department of Computer Science, University of California, Los AngelesGoogle Scholar
  22. 22.
    Regier MD, Moodie EE, Platt RW (2014) The effect of error-in-confounders on the estimation of the causal parameter when using marginal structural models and inverse probability-of-treatment weights: a simulation study. Int J Biostat 10:1–15MathSciNetCrossRefGoogle Scholar
  23. 23.
    Robins JM (1999) Marginal structural models versus structural nested models as tools for causal inference. In Statistical models in epidemiology: the environment and clinical trials, pp 95–134. Springer, New YorkGoogle Scholar
  24. 24.
    Robins JM, Hernán MA, Brumback B (2000) Marginal structural models and causal inference in epidemiology. Epidemiology 11:550–560CrossRefGoogle Scholar
  25. 25.
    Rosenbaum PR (1987) Model-based direct adjustment. J Am Stat Assoc 82:387–394CrossRefzbMATHGoogle Scholar
  26. 26.
    Rosenbaum PR (1998) Propensity score. In: Armitage P, Colton T (eds) Encyclopedia of Biostatistics, vol 5. Wiley, Chichester, pp 3551–3555Google Scholar
  27. 27.
    Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70:41–55MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Rosenbaum PR, Rubin DB (1984) Reducing bias in observational studies using subclassification on the propensity score. J Am Stat Assoc 79:516–524CrossRefGoogle Scholar
  29. 29.
    Rothman KJ, Greenland S, Lash TL (2008) Modern Epidemiology. Lippincott Williams & Wilkins, PhiladelphiaGoogle Scholar
  30. 30.
    Small DS, Rosenbaum PR (2008) War and wages: the strength of instrumental variables and their sensitivity to unobserved biases. J Am Stat Assoc 103:924–933MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Stefanski LA, Carroll RJ (1987) Conditional scores and optimal scores for generalized linear measurement-error models. Biometrika 74:703–716MathSciNetzbMATHGoogle Scholar
  32. 32.
    Yi GY (2017) Statistical Analysis with Measurement Error or Misclassification: Strategy, Method and Application. Springer, New YorkCrossRefzbMATHGoogle Scholar
  33. 33.
    Yi GY, He W (2006) Methods for bivariate survival data with mismeasured covariates under an accelerated failure time model. Commun Stat 35:1539–1554MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© International Chinese Statistical Association 2018

Authors and Affiliations

  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations