![[PDF]](/pb-assets/Icons/adobe-pdf-icon-1498649896243.png){kind=icon}
Abstract
Inverse probability weighting estimation has been popularly used to consistently estimate the average treatment effect. Its validity, however, is challenged by the presence of error-prone variables. In this paper, we explore the inverse probability weighting estimation with mismeasured outcome variables. We study the impact of measurement error for both continuous and discrete outcome variables and reveal interesting consequences of the naive analysis which ignores measurement error. When a continuous outcome variable is mismeasured under an additive measurement error model, the naive analysis may still yield a consistent estimator; when the outcome is binary, we derive the asymptotic bias in a closed-form. Furthermore, we develop consistent estimation procedures for practical scenarios where either validation data or replicates are available. With validation data, we propose an efficient method for estimation of average treatment effect; the efficiency gain is substantial relative to usual methods of using validation data. To provide protection against model misspecification, we further propose a doubly robust estimator which is consistent even when either the treatment model or the outcome model is misspecified. Simulation studies are reported to assess the performance of the proposed methods. An application to a smoking cessation dataset is presented.
References
| 1. | Rosenbaum, PR, Rubin, DB. The central role of the propensity score in observational studies for causal effects. Biometrika 1983; 70: 41–55. Google Scholar | Crossref | ISI |
| 2. | Rosenbaum, PR, Rubin, DB. Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. Am Stat 1985; 39: 33–38. Google Scholar | ISI |
| 3. | Rosenbaum, PR, Rubin, DB. Reducing bias in observational studies using subclassification on the propensity score. J Am Stat Assoc 1984; 79: 516–524. Google Scholar | Crossref | ISI |
| 4. | Rosenbaum, PR . Model-based direct adjustment. J Am Stat Assoc 1987; 82: 387–394. Google Scholar | Crossref | ISI |
| 5. | Rosenbaum, PR . Propensity score. In: Armitage P and Colton T (eds) Encyclopedia Biostat 1998; 5: 3551–3555. Google Scholar |
| 6. | Robins, JM, Hernán, MA, Brumback, B. Marginal structural models and causal inference in epidemiology. Epidemiology 2000; 11: 550–560. Google Scholar | Crossref | Medline | ISI |
| 7. | Lunceford, JK, Davidian, M. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Stat Med 2004; 23: 2937–2960. Google Scholar | Crossref | Medline | ISI |
| 8. | Robins, JM, Rotnitzky, A, Zhao, LP. Estimation of regression coefficients when some regressors are not always observed. J Am Stat Assoc 1994; 89: 846–866. Google Scholar | Crossref | ISI |
| 9. | Scharfstein, DO, Rotnitzky, A, Robins, JM. Adjusting for nonignorable drop-out using semiparametric nonresponse models. J Am Stat Assoc 1999; 94: 1096–1120. Google Scholar | Crossref | ISI |
| 10. | Bang, H, Robins, JM. Doubly robust estimation in missing data and causal inference models. Biometrics 2005; 61: 962–973. Google Scholar | Crossref | Medline | ISI |
| 11. | Carroll, RJ, Ruppert, D, Stefanski, LA Measurement error in nonlinear models: a modern perspective, Boca Raton: Chapman and Hall/CRC, 2006. Google Scholar | Crossref |
| 12. | Yi, GY . Statistical analysis with measurement error or misclassification: strategy, method and application, New York: Springer, 2017. Google Scholar | Crossref |
| 13. | McCaffrey, DF, Lockwood, J, Setodji, CM. Inverse probability weighting with error-prone covariates. Biometrika 2013; 100: 671–680. Google Scholar | Crossref | Medline | ISI |
| 14. | Babanezhad, M, Vansteelandt, S, Goetghebeur, E. Comparison of causal effect estimators under exposure misclassification. J Stat Plan Inference 2010; 140: 1306–1319. Google Scholar | Crossref |
| 15. | Braun D, Zigler C, Dominici F, et al. Using validation data to adjust the inverse probability weighting estimator for misclassified treatment. Harvard University Biostatistics Working Paper Series Working Paper 201, 2016: 1–19. Google Scholar |
| 16. | Lee, SM, Landry, J, Jones, PM The effectiveness of a perioperative smoking cessation program: a randomized clinical trial. Anesthesia Analgesia 2013; 117: 605–613. Google Scholar | Crossref | Medline |
| 17. | Newey WK and McFadden D. Large sample estimation and hypothesis testing. In: Engle R and McFadden D (eds) Handbook of econometrics. Amsterdam: Elsevier, 1994, 2111–2245. Google Scholar |
| 18. | Heyde, C . Quasi-likelihood and its application: a general approach to optimal parameter estimation, New York: Springer Science & Business Media, 1997. Google Scholar | Crossref |
| 19. | Yi, GY, Reid, N. A note on mis-specified estimating functions. Statistica Sinica 2010; 20: 1749–1769. Google Scholar |
| 20. | Neuhaus, JM . Bias and efficiency loss due to misclassified responses in binary regression. Biometrika 1999; 86: 843–855. Google Scholar | Crossref | ISI |
| 21. | Magder, LS, Hughes, JP. Logistic regression when the outcome is measured with uncertainty. Am J Epidemiol 1997; 146: 195–203. Google Scholar | Crossref | Medline | ISI |
| 22. | SRNT Subcommittee on Biochemical Verification . Biochemical verification of tobacco use and cessation. Nicotine Tobacco Res 2002; 4: 149–159. Google Scholar | Crossref | Medline |
| 23. | Yi, GY, Ma, Y, Spiegelman, D Functional and structural methods with mixed measurement error and misclassification in covariates. J Am Stat Assoc 2015; 110: 681–696. Google Scholar | Crossref | Medline |
| 24. | Spiegelman, D, Rosner, B, Logan, R. Estimation and inference for logistic regression with covariate misclassification and measurement error in main study/validation study designs. J Am Stat Assoc 2000; 95: 51–61. Google Scholar | Crossref | ISI |
| 25. | Yi, GY, He, W. Methods for bivariate survival data with mismeasured covariates under an accelerated failure time model. Commun Stat-Theory Meth 2006; 35: 1539–1554. Google Scholar | Crossref |
| 26. | White, I, Frost, C, Tokunaga, S. Correcting for measurement error in binary and continuous variables using replicates. Stat Med 2001; 20: 3441–3457. Google Scholar | Crossref | Medline |
| 27. | Austin, PC . The performance of different propensity score methods for estimating marginal odds ratios. Stat Med 2007; 26: 3078–3094. Google Scholar | Crossref | Medline | ISI |
| 28. | Efron, B . The jackknife, the bootstrap and other resampling plans 1982; vol. 38, Philadelphia: SIAM. Google Scholar | Crossref |
