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.
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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).
Babanezhad M, Vansteelandt S, Goetghebeur E (2010) Comparison of causal effect estimators under exposure misclassification. J Stat Plan Inference 140:1306–1319MathSciNetCrossRefzbMATHGoogle Scholar
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
Blakely T, McKenzie S, Carter K (2013) Misclassification of the mediator matters when estimating indirect effects. J Epidemiol Commun Health 67:458–466CrossRefGoogle Scholar
Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models: a modern perspective. Chapman & Hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
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
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
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
Pearl J (2009) On measurement bias in causal inference. Technical Report R-357, Department of Computer Science, University of California, Los AngelesGoogle Scholar
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
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
Robins JM, Hernán MA, Brumback B (2000) Marginal structural models and causal inference in epidemiology. Epidemiology 11:550–560CrossRefGoogle Scholar