Abstract
Bayesian sensitivity analysis of unmeasured confounding is proposed for observational data with misclassified outcome. The approach simultaneously corrects bias from error in the outcome and examines possible change in the exposure effect estimation assuming the presence of a binary unmeasured confounder. We assess the influence of unmeasured confounding on the exposure effect estimation through two sensitivity parameters that characterize the associations of the unmeasured confounder with the exposure status and with the outcome variable. The proposed approach is illustrated in the study of the effect of female employment status on the likelihood of domestic violence. An extensive simulation study is conducted to confirm the efficacy of the proposed approach. The simulation results indicate accounting for misclassification in outcome and unmeasured confounding significantly reduce the bias in exposure effect estimation and improve the coverage probability of credible intervals.
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References
Carnegie, N.B., Harada, M., Hill, J.L.: Assessing sensitivity to unmeasured confounding using a simulated potential confounder. J. Res. Educ. Eff. 9(3), 395–420 (2016). https://doi.org/10.1080/19345747.2015.1078862
Cornfield, J., Haenszel, W., Hammond, E.C., Lilienfeld, A.M., Shimkin, M.B., Wynder, E.L.: Smoking and lung cancer: recent evidence and a discussion of some questions. J. Natl. Cancer Inst. 22(1), 173–203 (1959)
Dorie, V., Harada, M., Carnegie, N.B., Hill, J.: A flexible, interpretable framework for assessing sensitivity to unmeasured confounding. Stat. Med. 35(20), 3453–70 (2016). https://doi.org/10.1002/sim.6973
Faries, D., Peng, X., Pawaskar, M., Price, K., Stamey, J.D., Seaman, J.J.W.: Evaluating the impact of unmeasured confounding with internal validation data: an example cost evaluation in type 2 diabetes. Value Health 16(2), 259–66 (2013). https://doi.org/10.1016/j.jval.2012.10.012
Gastwirth, J.: Dual and simultaneous sensitivity analysis for matched pairs. Biometrika 85(4), 907–920 (1998). https://doi.org/10.1093/biomet/85.4.907
Gelman, A., Rubin, D.B., et al.: Inference from iterative simulation using multiple sequences. Stat. Sci. 7(4), 457–472 (1992)
Greenland, S.: Basic methods for sensitivity analysis of biases. Int. J. Epidemiol. 25(6), 1107–1116 (1996). https://doi.org/10.1093/ije/25.6.1107-a
Greenland, S.: The impact of prior distributions for uncontrolled confounding and response bias: a case study of the relation of wire codes and magnetic fields to childhood leukemia. J. Am. Stat. Assoc. 98(461), 47–54 (2003). https://doi.org/10.1198/01621450338861905
Greenland, S.: Multiple-bias modelling for analysis of observational data. J. R. Stat. Soc. Ser. A Stat. Soc. 168, 267–291 (2005). https://doi.org/10.1111/j.1467-985X.2004.00349.x
Gustafson, P., McCandless, L.C., Levy, A.R., Richardson, S.: Simplified bayesian sensitivity analysis for mismeasured and unobserved confounders. Biometrics 66(4), 1129–1137 (2010). https://doi.org/10.1111/j.1541-0420.2009.01377.x
Lin, D.Y., Psaty, B.M., Kronmal, R.A.: Assessing the sensitivity of regression results to unmeasured confounders in observational studies. Biometrics 54(3), 948–963 (1998). https://doi.org/10.2307/2533848
Magder, L.S., Hughes, J.P.: Logistic regression when the outcome is measured with uncertainty. Am. J. Epidemiol. 146(2), 195–203 (1997)
McCandless, L.C., Gustafson, P., Levy, A.: Bayesian sensitivity analysis for unmeasured confounding in observational studies. Stat. Med. 26(11), 2331–2347 (2007). https://doi.org/10.1002/sim.2711
McInturff, P., Johnson, W.O., Cowling, D., Gardner, I.A.: Modelling risk when binary outcomes are subject to error. Stat. Med. 23(7), 1095–1109 (2004). https://doi.org/10.1002/sim.1656
Neuhaus, J.M.: Bias and efficiency loss due to misclassified responses in binary regression. Biometrika 86(4), 843–855 (1999)
Paulino, C.D., Soares, P., Neuhaus, J.: Binomial regression with misclassification. Biometrics 59(3), 670–5 (2003)
Rabin, R.F., Jennings, J.M., Campbell, J.C., Bair-Merritt, M.H.: Intimate partner violence screening tools: a systematic review. Am. J. Prev. Med. 36(5), 439–445 (2009). https://doi.org/10.1016/j.amepre.2009.01.024. e4
Rosenbaum, P.R.: Sensitivity analysis for certain permutation inferences in matched observational studies. Biometrika 74(1), 13–26 (1987). https://doi.org/10.1093/biomet/74.1.13
Rosenbaum, P.R.: Covariance adjustment in randomized experiments and observational studies. Stat. Sci. 17(3), 286–304 (2002)
Rosenbaum, P.R., Rubin, D.B.: Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. J. R. Stat. Soc. Ser. B Methodol. 45(2), 212–218 (1983a)
Rosenbaum, P.R., Rubin, D.B.: The central role of the propensity score in observational studies for causal effects. Biometrika 70(1), 41–55 (1983b). https://doi.org/10.1093/biomet/70.1.41
Rubin, D.B.: Bayesian-inference for causal effects - role of randomization. Ann. Stat. 6(1), 34–58 (1978). https://doi.org/10.1214/aos/1176344064
Steenland, K., Greenland, S.: Monte Carlo sensitivity analysis and Bayesian analysis of smoking as an unmeasured confounder in a study of silica and lung cancer. Am. J. Epidemiol. 160(4), 384–392 (2004). https://doi.org/10.1093/aje/kwh211
Vander Weele, T.J., Ding, P.: Sensitivity analysis in observational research: introducing the e-value. Ann. Intern. Med. 167(4), 268–274 (2017). https://doi.org/10.7326/M16-2607
Zhou, Q., Chin, Y.M., Stamey, J.D., Song, J.J.: Bayesian misclassification and propensity score methods for clustered observational studies. J. Appl. Stat. 45, 1547–1560 (2017). https://doi.org/10.1080/02664763.2017.1380786
Acknowledgements
The authors thank the referees for their valuable comments and suggestions. The first author was partially supported by National Natural Science Foundation of China (Grant Nos. 71732006, 71572138, 71390331, 71401132, 71371150).
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Zhou, Q., Chin, YM., Stamey, J.D. et al. Bayesian sensitivity analysis to unmeasured confounding for misclassified data. AStA Adv Stat Anal 104, 577–596 (2020). https://doi.org/10.1007/s10182-019-00357-1
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DOI: https://doi.org/10.1007/s10182-019-00357-1