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Sensitivity analysis for mistakenly adjusting for mediators in estimating total effect in observational studies
  1. Tingting Wang1,2,
  2. Hongkai Li1,2,
  3. Ping Su1,2,
  4. Yuanyuan Yu1,2,
  5. Xiaoru Sun1,2,
  6. Yi Liu1,2,
  7. Zhongshang Yuan1,2,
  8. Fuzhong Xue1,2
  1. 1 Department of Biostatistics, School of Public Health, Shandong University, Jinan, China
  2. 2 Cheeloo Research Center for Biomedical Big Data, Shandong University, Jinan, China
  1. Correspondence to Professor Fuzhong Xue; xuefzh{at}sdu.edu.cn

Abstract

Objectives In observational studies, epidemiologists often attempt to estimate the total effect of an exposure on an outcome of interest. However, when the underlying diagram is unknown and limited knowledge is available, dissecting bias performances is essential to estimating the total effect of an exposure on an outcome when mistakenly adjusting for mediators under logistic regression. Through simulation, we focused on six causal diagrams concerning different roles of mediators. Sensitivity analysis was conducted to assess the bias performances of varying across exposure-mediator effects and mediator-outcome effects when adjusting for the mediator.

Setting Based on the causal relationships in the real world, we compared the biases of varying across the effects of exposure-mediator with those of varying across the effects of mediator-outcome when adjusting for the mediator. The magnitude of the bias was defined by the difference between the estimated effect (using logistic regression) and the total effect of the exposure on the outcome.

Results In four scenarios (a single mediator, two series mediators, two independent parallel mediators or two correlated parallel mediators), the biases of varying across the effects of exposure-mediator were greater than those of varying across the effects of mediator-outcome when adjusting for the mediator. In contrast, in two other scenarios (a single mediator or two independent parallel mediators in the presence of unobserved confounders), the biases of varying across the effects of exposure-mediator were less than those of varying across the effects of mediator-outcome when adjusting for the mediator.

Conclusions The biases were more sensitive to the variation of effects of exposure-mediator than the effects of mediator-outcome when adjusting for the mediator in the absence of unobserved confounders, while the biases were more sensitive to the variation of effects of mediator-outcome than those of exposure-mediator in the presence of an unobserved confounder.

  • epidemiology
  • public health

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http://creativecommons.org/licenses/by/4.0/

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Footnotes

  • TW and HL contributed equally.

  • Contributors TW and HL jointly conceived the idea behind the article and designed the study. TW conducted the literature review, performed the simulation and prepared the draft of the manuscript. PS, YY, XS, YL and ZY participated in the design of the study and the revision of the manuscript. FX advised on critical revision of the manuscript for important intellectual content. All authors read and approved the final manuscript.

  • Funding This work was supported by grants from the National Natural Science Foundation of China (grant numbers 81573259 and 81773547).

  • Competing interests None declared.

  • Ethics approval Ethics Committee of the School of Public Health (20140322), Shandong University. Written informed consent was obtained from all participants.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Data sharing statement No additional data are available.

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