OpenLB
Open Library of Bioscience
Advanced Search
Biometrical journal. Biometrische Zeitschrift
11, 2019;61 (6): 1507-1525.

Inverse-probability-of-treatment weighted estimation of causal parameters in the presence of error-contaminated and time-dependent confounders.

Di Shu, Grace Y Yi
Author Information
  1. Di Shu: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada. ORCID
  2. Grace Y Yi: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada.
PMID: 31449324 DOI: 10.1002/bimj.201600228

Abstract

Inverse-probability-of-treatment weighted (IPTW) estimation has been widely used to consistently estimate the causal parameters in marginal structural models, with time-dependent confounding effects adjusted for. Just like other causal inference methods, the validity of IPTW estimation typically requires the crucial condition that all variables are precisely measured. However, this condition, is often violated in practice due to various reasons. It has been well documented that ignoring measurement error often leads to biased inference results. In this paper, we consider the IPTW estimation of the causal parameters in marginal structural models in the presence of error-contaminated and time-dependent confounders. We explore several methods to correct for the effects of measurement error on the estimation of causal parameters. Numerical studies are reported to assess the finite sample performance of the proposed methods.

Keywords

causal inference inverse-probability-of-treatment weighting logistic regression model marginal structural model measurement error time-dependent confounding

References

  1. Babanezhad, M., Vansteelandt, S., & Goetghebeur, E. (2010). Comparison of causal effect estimators under exposure misclassification. Journal of Statistical Planning and Inference, 140, 1306-1319.
  2. Blakely, T., McKenzie, S., & Carter, K. (2013). Misclassification of the mediator matters when estimating indirect effects. Journal of Epidemiology and Community Health, 67, 1-9.
  3. Braun, D., Gorfine, M., Parmigiani, G., Arvold, N. D., Dominici, F., & Zigler, C. (2017). Propensity scores with misclassified treatment assignment: A likelihood-based adjustment. Biostatistics, 18, 695-710.
  4. Buonaccorsi, J. P. (2010). Measurement error: Models, methods, and applications. Boca Raton: Chapman & Hall/CRC.
  5. Carroll, R. J. (1989). Covariance analysis in generalized linear measurement error models. Statistics in Medicine, 8, 1075-1093.
  6. Carroll, R. J., Gallo, P., & Gleser, L. J. (1985). Comparison of least squares and errors-in-variables regression, with special reference to randomized analysis of covariance. Journal of the American Statistical Association, 80, 929-932.
  7. Carroll, R. J., Küchenhoff, H., Lombard, F., & Stefanski, L. A. (1996). Asymptotics for the SIMEX estimator in nonlinear measurement error models. Journal of the American Statistical Association, 91, 242-250.
  8. Carroll, R. J., Ruppert, D., Stefanski, L. A., & Crainiceanu, C. M. (2006). Measurement error in nonlinear models: A modern perspective (2nd ed.). Boca Raton: Chapman & Hall/CRC.
  9. Cole, S. R., Chu, H., & Greenland, S. (2006). Multiple-imputation for measurement-error correction. International Journal of Epidemiology, 35, 1074-1081.
  10. Cook, J. R., & Stefanski, L. A. (1994). Simulation-extrapolation estimation in parametric measurement error models. Journal of the American Statistical Association, 89, 1314-1328.
  11. Daniel, R. M., Cousens, S. N., De Stavola, B. L., Kenward, M. G., & Sterne, J. A. C. (2013). Methods for dealing with time-dependent confounding. Statistics in Medicine, 32, 1584-1618.
  12. Devanarayan, V., & Stefanski, L. A. (2002). Empirical simulation extrapolation for measurement error models with replicate measurements. Statistics & Probability Letters, 59, 219-225.
  13. Edwards, J. K., Cole, S. R., Westreich, D., Crane, H., Eron, J. J., Mathews, W. C., … CNICS. (2015). Multiple imputation to account for measurement error in marginal structural models. Epidemiology, 26, 645-652.
  14. Efron, B. (1982). The jackknife, the bootstrap and other resampling plans (Vol. 38). Philadelphia: SIAM.
  15. Efron, B., & Tibshirani, R. (1993). An introduction to the bootstrap. London: Chapman & Hall/CRC.
  16. Freedman, L. S., Midthune, D., Dodd, K. W., Carroll, R. J., & Kipnis, V. (2015). A statistical model for measurement error that incorporates variation over time in the target measure, with application to nutritional epidemiology. Statistics in Medicine, 34, 3590-3605.
  17. Fuller, W. A. (1987). Measurement error models. New York: Wiley.
  18. Gravel, C. A., & Platt, R. W. (2018). Weighted estimation for confounded binary outcomes subject to misclassification. Statistics in Medicine, 37, 425-436.
  19. Gustafson, P. (2003). Measurement error and misclassification in statistics and epidemiology: Impacts and Bayesian adjustments. Boca Raton: Chapman & Hall/CRC.
  20. Hernán, M. A., & Cole, S. R. (2009). Invited commentary: Causal diagrams and measurement bias. American Journal of Epidemiology, 170, 959-962.
  21. Hernán, M. A., & Robins, J. M. (2019). Causal inference. Boca Raton: Chapman & Hall/CRC, forthcoming.
  22. Heyde, C. (1997). Quasi-likelihood and its application: A general approach to optimal parameter estimation. New York: Springer.
  23. Imai, K., & Yamamoto, T. (2010). Causal inference with differential measurement error: Nonparametric identification and sensitivity analysis. American Journal of Political Science, 54, 543-560.
  24. Koehler, E., Brown, E., & Haneuse, S. J.-P. (2009). On the assessment of Monte Carlo error in simulation-based statistical analyses. American Statistician, 63, 155-162.
  25. Kuroki, M., & Pearl, J. (2014). Measurement bias and effect restoration in causal inference. Biometrika, 101, 423-437.
  26. Kyle, R. P., Moodie, E. E. M., Klein, M. B., & Abrahamowicz, M. (2016). Correcting for measurement error in time-varying covariates in marginal structural models. American Journal of Epidemiology, 184, 249-258.
  27. Lash, T. L., Fox, M. P., & Fink, A. K. (2009). Applying quantitative bias analysis to epidemiologic data. New York: Springer.
  28. le Cessie, S., Debeij, J., Rosendaal, F. R., Cannegieter, S. C., & Vandenbrouckea, J. P. (2012). Quantification of bias in direct effects estimates due to different types of measurement error in the mediator. Epidemiology, 23, 551-560.
  29. Lenis, D., Ebnesajjad, C. F., & Stuart, E. A. (2017). A doubly robust estimator for the average treatment effect in the context of a mean-reverting measurement error. Biostatistics, 18, 325-337.
  30. Lockwood, J., & McCaffrey, D. F. (2016). Matching and weighting with functions of error-prone covariates for causal inference. Journal of the American Statistical Association, 111, 1831-1839.
  31. McCaffrey, D. F., Lockwood, J., & Setodji, C. M. (2013). Inverse probability weighting with error-prone covariates. Biometrika, 100, 671-680.
  32. Miglioretti, D. L., & Heagerty, P. J. (2004). Marginal modeling of multilevel binary data with time-varying covariates. Biostatistics, 5, 381-398.
  33. Newey, W. K., & McFadden, D. (1994). Large sample estimation and hypothesis testing. In R. Engle & D. McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 2111-2245).
  34. Ogburn, E. L., & VanderWeele, T. J. (2012). Analytic results on the bias due to nondifferential misclassification of a binary mediator. American Journal of Epidemiology, 176, 555-561.
  35. Pearl, J. (2009). On measurement bias in causal inference (Technical Report R-357). Department of Computer Science, University of California, Los Angeles.
  36. Prentice, R. L. (1982). Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika, 69, 331-342.
  37. Regier, M. D., Moodie, E. E. M., & Platt, R. W. (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. International Journal of Biostatistics, 10, 1-15.
  38. Robins, J. M., Hernán, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11, 550-560.
  39. Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41-55.
  40. Rosner, B., Spiegelman, D., & Willett, W. (1990). Correction of logistic regression relative risk estimates and confidence intervals for measurement error: The case of multiple covariates measured with error. American Journal of Epidemiology, 132, 734-745.
  41. Rosner, B., Willett, W., & Spiegelman, D. (1989). Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Statistics in Medicine, 8, 1051-1069.
  42. Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern epidemiology (3rd ed.). Philadelphia: Lippincott Williams & Wilkins.
  43. Shu, D., & Yi, G. Y. (2019a). Causal inference with measurement error in outcomes: Bias analysis and estimation methods. Statistical Methods in Medical Research, 28(7), 2049-2068.
  44. Shu, D., & Yi, G. Y. (2019b). Weighted causal inference methods with mismeasured covariates and misclassified outcomes. Statistics in Medicine, 38(10), 1835-1854.
  45. Stefanski, L. A., & Carroll, R. J. (1987). Conditional scores and optimal scores for generalized linear measurement-error models. Biometrika, 74, 703-716.
  46. 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.
  47. VanderWeele, T. J., & Hernán, M. A. (2012). Results on differential and dependent measurement error of the exposure and the outcome using signed directed acyclic graphs. American Journal of Epidemiology, 175, 1303-1310.
  48. VanderWeele, T. J., Valeri, L., & Ogburn, E. L. (2012). The role of measurement error and misclassification in mediation analysis. Epidemiology, 23, 561-564.
  49. Webb-Vargas, Y., Rudolph, K. E., Lenis, D., Murakami, P., & Stuart, E. A. (2017). An imputation-based solution to using mismeasured covariates in propensity score analysis. Statistical Methods in Medical Research, 26, 1824-1837.
  50. Yi, G. Y. (2008). A simulation-based marginal method for longitudinal data with dropout and mismeasured covariates. Biostatistics, 9, 501-512.
  51. Yi, G. Y. (2017). Statistical analysis with measurement error or misclassification: Strategy, method and application. New York: Springer.
  52. Yi, G. Y., & He, W. (2012). Bias analysis and the simulation-extrapolation method for survival data with covariate measurement error under parametric proportional odds models. Biometrical Journal, 54, 343-360.

Grants

  1. TD3‐137716/CIHR

MeSH Term

Biometry
Multivariate Analysis
Probability
Regression Analysis
Research Design
Time Factors
Journal Article Research Support, Non-U.S. Gov't
Article has an altmetric score of 1

Word Cloud

Created with Highcharts 10.0.0causalestimationparameterstime-dependentIPTWmarginalstructuralinferencemeasurementerrorInverse-probability-of-treatmentweightedmodelsconfoundingeffectsmethodsconditionoftenpresenceerror-contaminatedconfoundersmodelwidelyusedconsistentlyestimateadjustedJustlikevaliditytypicallyrequirescrucialvariablespreciselymeasuredHoweverviolatedpracticeduevariousreasonswelldocumentedignoringleadsbiasedresultspaperconsiderexploreseveralcorrectNumericalstudiesreportedassessfinitesampleperformanceproposed methodsinverse-probability-of-treatmentweightinglogisticregression

Similar Articles

Cited By (2)