Bayesian sensitivity analysis to unmeasured confounding for misclassified data
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Bayesian sensitivity analysis to unmeasured confounding for misclassified data Qi Zhou1 · Yoo-Mi Chin2 · James D. Stamey3 · Joon Jin Song3 Received: 3 December 2018 / Accepted: 10 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
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. Keywords Unmeasured confounder · Misclassification · Bayesian inference · Observational study · Intimate partner violence
1 Introduction Many questions of interest for observational studies face the issue that causal inference cannot be made directly due to lack of randomization of the exposure status. The ignorability assumption (Rosenbaum and Rubin 1983b) states that the exposure status and potential outcome are independent conditional on all the possible confounding, which
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Joon Jin Song [email protected]
1
School of Management, Xi’an Jiaotong University, No. 28 Xianning Road, Xi’an 710049, Shaanxi, China
2
Department of Economics, Baylor University, One Bear Place 98003, Waco, TX 76798-7123, USA
3
Department of Statistical Science, Baylor University, P.O. Box 97140, Waco, TX 76798-7140, USA
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Q. Zhou et al.
ensures valid causal inference in observational studies. Dealing with this assumption in application, researchers have attempted to assume that the ignorability assumption is satisfied automatically or to increase the likelihood of meeting the assumption using statistical methods, such as propensity score analysis. Rather than ignorability assumption is met, we posit an unmeasured confounder in our inferential models in this paper, accounting for information not contained in the measured covariates. Another common problem in observational data with binary outcomes is misclassification. Errors in the outcome are often due to either an imperfect diagnostic test or a sensitive question asked in a survey. It is well known that misclassification leads to biased estimates of the covariate effects (Neuhaus 1999). Adjusting for misclassification in the outcome variable has been addressed from both the frequentist (Magder and Hughes 1997) and the Bayesian approac
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