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A Selective Review of Negative Control Methods in Epidemiology

  • Epidemiologic Methods (P Howards, Section Editor)
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A Correction to this article was published on 08 May 2021

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Abstract

Purpose of Review

Negative controls are a powerful tool to detect and adjust for bias in epidemiological research. This paper introduces negative controls to a broader audience and provides guidance on principled design and causal analysis based on a formal negative control framework.

Recent Findings

We review and summarize causal and statistical assumptions, practical strategies, and validation criteria that can be combined with subject-matter knowledge to perform negative control analyses. We also review existing statistical methodologies for the detection, reduction, and correction of confounding bias, and briefly discuss recent advances towards nonparametric identification of causal effects in a double-negative control design.

Summary

There is great potential for valid and accurate causal inference leveraging contemporary healthcare data in which negative controls are routinely available. Design and analysis of observational data leveraging negative controls is an area of growing interest in health and social sciences. Despite these developments, further effort is needed to disseminate these novel methods to ensure they are adopted by practicing epidemiologists.

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References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. Ioannidis JPA. “Why most published research findings are false”. In: PLOS Medicine 2.8 (2005), pp. 696–701.

  2. Hernán MA, Robins JM. Using big data to emulate a target trial when a randomized trial is not available. In: Am J Epidemiol. 2016;183(8):758–64.

    Google Scholar 

  3. •• Lipsitch M, Tchetgen Tchetgen EJ, Cohen T. Negative controls: a tool for detecting confounding and bias in observational studies. In: Epidemiology. 2010;21.3:383–8 This paper is the first to formally define negative control exposure and outcome with conditions for bias detection as well as examples in epidemiology.

    Google Scholar 

  4. Arnold BF, Ercumen A, Benjamin-Chung J, Colford JM Jr. Brief report: negative controls to detect selection bias and measurement bias in epidemiologic studies. In: Epidemiology. 2016;27.5:637.

    Google Scholar 

  5. Arnold B, Ercumen A. Negative control outcomes: a tool to detect bias in randomized trials. In: J Am Med Assoc. 2016;316(24):2597–8.

    Google Scholar 

  6. Rosenbaum PR. The role of known effects in observational studies. In: Biometrics. 1989;45(2):557–69.

  7. Weiss NS. Can the “specificity” of an association be rehabilitated as a basis for supporting a causal hypothesis? In: Epidemiology. 2002;13(1):6–8.

    Google Scholar 

  8. Glass DJ. Experimental Design for Biologists. Cold Spring Harbor Laboratory Press, 2014.

  9. Cai Z and Kuroki M. “On identifying total effects in the presence of latent variables and selection bias”. In: Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence. 2008, pp. 62–69.

  10. Liu L, Tchetgen Tchetgen EJ. “Regression-based negative control of homophily in dyadic peer effect analysis”. In: arXiv preprint arXiv:2002.06521 (2020).

  11. Egami N. “Identification of Causal Diffusion Effects Under Structural Stationarity”. In: arXiv preprint arXiv:1810.07858 (2018).

  12. • Miao W, Shi X, and Tchetgen Tchetgen EJ. “A Confounding Bridge Approach for Double Negative Control Inference on Causal Effects”. In: (2020). In progress, a prior version can be found at https://arxiv.org/abs/1808.04945. This paper introduces the confounding bridge function that links primary and negative control outcome distributions for identification of the average treatment effect leveraging a negative control exposure.

  13. Sofer T, Richardson DB, Colicino E, Schwartz J, Tchetgen Tchetgen EJ. On negative outcome control of unobserved confounding as a generalization of difference-in-differences. In: Stat Sci. 2016;31(3):348–61.

    Google Scholar 

  14. Jackson LA, Jackson ML, Nelson JC, Neuzil KM, Weiss NS. Evidence of bias in estimates of influenza vaccine effectiveness in seniors. In: Int J Epidemiol. 2006;35(2):337–44.

    Google Scholar 

  15. Splawa-Neyman J, Dabrowska DM, Speed TP. On the application of probability theory to agricultural experiments. Essay on principles. Section 9. In: Stat Sci. 1990:465–72.

  16. Rubin DB. Estimating causal effects of treatments in randomized and nonrandomized studies. In: Journal of Educational Psychology. 1974;66.5:688.

  17. • Shi X, Miao W, Tchetgen Tchetgen EJ. Multiply robust causal inference with double negative control adjustment for categorical unmeasured confounding. In: J Royal Stat Soc: Series B (Statistical Methodology). 2020;82.2:521–40 This paper provides a general semiparametric framework for obtaining inferences about the average treatment effect under categorical unmeasured confounding and negative controls.

    Article  Google Scholar 

  18. Alan Brookhart M, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. In: Pharmacoepidemiology and Drug Safety. 2010;19(6):537–54.

  19. Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables. In: J Am Stat Assoc. 1996;91(434):444–55.

    Google Scholar 

  20. Hernán MA and Robins JM. “Instruments for causal inference: an epidemiologist’s dream?” In: Epidemiology (2006), pp. 360–372.

  21. Robins JM. Correcting for non-compliance in randomized trials using structural nested mean models. In: Commun Stat-Theory and methods. 1994;23(8):2379–412.

    Google Scholar 

  22. Wang L, Tchetgen Tchetgen EJ. Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables. In: J Royal Stat Soc: Series B (Statistical Methodology). 2018;80.3:531–50.

    Article  Google Scholar 

  23. Prasad V, Jena AB. Prespecified falsification end points: can they validate true observational associations? In: J Am Med Assoc. 2013;309(3):241–2.

    CAS  Google Scholar 

  24. Markovitz AA, Hollingsworth JM, Ayanian JZ, Norton EC, Yan PL, Ryan AM. Performance in the Medicare shared savings program after accounting for nonrandom exit: an instrumental variable analysis. In: Ann Int Med. 2019;171(1):27–36.

    Google Scholar 

  25. Bijlsma MJ, Vansteelandt S, Janssen F, Hak E. The effect of adherence to statin therapy on cardiovascular mortality: quantification of unmeasured bias using falsification end-points. In: BMC Public Health. 2016;16.1:303.

    Google Scholar 

  26. Lin C-K, Lin R-T, Chen P-C, Wang P, De Marcellis-Warin N, Zigler C, et al. A global perspective on sulfur oxide controls in coal-fired power plants and cardiovascular disease. In: Sci Rep. 2018;8(1):1–9.

  27. Dusetzina SB, Brookhart MA, Maciejewski ML. Control outcomes and exposures for improving internal validity of nonrandomized studies. In: Health Serv Res. 2015;50(5):1432–51.

    Google Scholar 

  28. Rosenbaum PR. Design of observational studies. New York, NY: Springer-Verlag, 2010.

  29. Munaf̀o MR, Tilling K, Taylor AE, Evans DM, Smith GD. Collider scope: when selection bias can substantially influence observed associations. In: Int J Epidemiol. 2018;47(1):226–35.

    Google Scholar 

  30. Mealli F, Pacini B. Using secondary outcomes to sharpen inference in randomized experiments with noncompliance. In: J Am Stat Assoc. 2013;108(503):1120–31.

    CAS  Google Scholar 

  31. Rosenbaum PR. Detecting bias with confidence in observational studies. In: Biometrika. 1992;79(2):367–74.

    Google Scholar 

  32. Flanders WD, Klein M, Darrow LA, Strickland MJ, Sarnat SE, Sarnat JA, et al. A method for detection of residual confounding in time-series and other observational studies. In: Epidemiology. 2011;22.1:59.

  33. • Flanders WD, Strickland MJ, Klein M. A new method for partial correction of residual confounding in time-series and other observational studies. In: Am J Epidemiol. 2017;185.10:941–9 This paper develops a regression-based method taking future air pollution as a negative control exposure to reduce residual confounding bias in a time-series study on air pollution effects.

  34. de Luna X, Fowler P, Johansson P. Proxy variables and nonparametric identification of causal effects. In: Econ Lett. 2017;150:152–4.

    Google Scholar 

  35. Kuroki M, Pearl J. Measurement bias and effect restoration in causal inference. In: Biometrika. 2014;101(2):423–37.

    Google Scholar 

  36. •• Miao W, Geng Z, Tchetgen Tchetgen EJ. Identifying causal effects with proxy variables of an unmeasured confounder. In: Biometrika. 2018;105.4:987–93 This paper establishes sufficient conditions for nonparametric identification of the average treatment effect using double negative control.

    Google Scholar 

  37. • Madigan D, Stang PE, Berlin JA, Schuemie M, Overhage JM, Suchard MA, et al. A systematic statistical approach to evaluating evidence from observational studies. In: Annu Rev Stat Appl. 2014;1:11–39 This paper provides a systematic review of challenges in observational studies and describes a data-driven approach to calculating calibrated p values leveraging negative controls.

  38. Schuemie MJ, Ryan PB, DuMouchel W, Suchard MA, Madigan D. Interpreting observational studies: why empirical calibration is needed to correct p-values. In: Stat Med. 2014;33(2):209–18.

    Google Scholar 

  39. Schuemie MJ, Hripcsak G, Ryan PB, Madigan D, Suchard MA. Robust empirical calibration of p-values using observational data. In: Statistics in Medicine. 2016;35.22:3883.

  40. Schuemie MJ, Hripcsak G, Ryan PB, Madigan D, Suchard MA. Empirical confidence interval calibration for population-level effect estimation studies in observational healthcare data. In: Proc Natl Acad Sci. 2018;115(11):2571–7.

    CAS  Google Scholar 

  41. Schuemie MJ, Ryan PB, Hripcsak G, Madigan D, Suchard MA. Improving reproducibility by using high-throughput observational studies with empirical calibration. In: Philos Trans Royal Soc A: Math Phys Eng Sci. 2018;376.2128:20170356.

    Article  Google Scholar 

  42. Yerushalmy J. The relationship of parents’ cigarette smoking to outcome of pregnancy– implications as to the problem of inferring causation from observed associations. In: Am J Epidemiol. 1971;93(6):443–56.

    CAS  Google Scholar 

  43. Mitchell EA, Ford RPK, Stewart AW, Taylor BJ, Becroft DMO, Thompson JMD, et al. Smoking and the sudden infant death syndrome. In: Pediatrics. 1993;91(5):893–6.

  44. Howe LD, Matijasevich A, Tilling K, Brion M-J, Leary SD, Smith GD, Lawlor DA. Maternal smoking during pregnancy and off- spring trajectories of height and adiposity: comparing maternal and paternal associations. In: Int J Epidemiol. 2012;41(3):722–32.

  45. Brion M-JA, Leary SD, Smith GD, Ness AR. Similar associations of parental prenatal smoking suggest child blood pressure is not influenced by intrauterine effects. In: Hypertension. 2007;49(6):1422–8.

    CAS  Google Scholar 

  46. Smith GD. Assessing intrauterine influences on offspring health outcomes: can epidemiological studies yield robust findings? In: Basic Clin Pharmacol Toxicol. 2008;102(2):245–56.

    CAS  Google Scholar 

  47. Brew BK, Gong T, Williams DM, Larsson H, Almqvist C. Using fathers as a negative control exposure to test the developmental origins of health and disease hypothesis: a case study on maternal distress and offspring asthma using Swedish register data. In: Scand J Public Health. 2017;45.17(suppl):36–40.

  48. Taylor AE, Smith GD, Bares CB, Edwards AC, Munaf̀o MR. Partner smoking and maternal cotinine during pregnancy: implications for negative control methods. In: Drug Alcohol Depend. 2014;139:159–63.

    CAS  Google Scholar 

  49. Wang M, Tchetgen Tchetgen EJ. Invited commentary: bias attenuation and identification of causal effects with multiple negative controls. In: Am J Epidemiol. 2017;185(10):950–3.

    Google Scholar 

  50. Yu Y, Li H, Sun X, Liu X, Yang F, Hou L, et al. Identification and estimation of causal effects using a negative control exposure in time-series studies with applications to environmental epidemiology. Am J Epidemiol. kwaa172. https://doi.org/10.1093/aje/kwaa172.

  51. Lumley T, Sheppard L. Assessing seasonal confounding and model selection bias in air pollution epidemiology using positive and negative control analyses. In: Environmetrics. 2000;11(6):705–17.

    CAS  Google Scholar 

  52. Selby JV, Friedman GD, Quesenberry CP Jr, Weiss NS. A case–control study of screening sigmoidoscopy and mortality from colorectal cancer. In: N Engl J Med. 1992;326(10):653–7.

    CAS  Google Scholar 

  53. Zauber AG. The impact of screening on colorectal cancer mortality and incidence: has it really made a difference? In: Digest Dis Sci. 2015;60(3):681–91.

    Google Scholar 

  54. • Lousdal ML, Lash TL, Flanders WD, Brookhart MA, Kristiansen IS, Kalager M, et al. Negative controls to detect uncontrolled confounding in observational studies of mammographic screening comparing participants and non-participants. In: Int J Epidemiol. 2020; This paper uses both negative control exposure and negative control outcome to detect residual confounding in an observational study of mammographic screening comparing participants and non-participants.

  55. Sheppard L, Levy D, Norris G, Larson TV, Koenig JQ. Effects of ambient air pollution on nonelderly asthma hospital admissions in Seattle, Washington, 1987–1994. In: Epidemiology. 1999:23–30.

  56. Cuyler Hammond E, Horn D. The relationship between human smoking habits and death rates: a follow-up study of 187,766 men. In: J Am Med Assoc. 1954;155(15):1316–28.

    Google Scholar 

  57. Doll R, Bradford Hill A. The mortality of doctors in relation to their smoking habits. In: Br Med J. 1954;1(4877):1451–5.

    CAS  Google Scholar 

  58. Doll R, Hill BA. Lung cancer and other causes of death in relation to smoking. In: Br Med J. 1956;2(5001):1071–81.

  59. Cornfield J, William H, Hammond EC, Lilienfeld AM, Shimkin MB, Wynder EL. Smoking and lung cancer: recent evidence and a discussion of some questions. In: J Natl Cancer Inst. 1959;22(1):173–203.

  60. Trichopoulos D, Zavitsanos X, Katsouyanni K, Tzonou A, Dalla-Vorgia P. Psychological stress and fatal heart attack: the Athens (1981) earthquake natural experiment. In: Lancet. 1983;321(8322):441–4.

    Google Scholar 

  61. Smith GD. Negative control exposures in epidemiologic studies. Comments on “Negative controls: a tool for detecting confounding and bias in observational studies”. In: Epidemiology. 2012;23(2):350–1.

  62. Weisskopf MG, Tchetgen Tchetgen EJ, Raz R. Commentary: on the use of imperfect negative control exposures in epidemiologic studies. In: Epidemiology. 2016;27(3):365–7.

    Google Scholar 

  63. Richardson DB, Keil A, Tchetgen Tchetgen EJ, Cooper GS. Negative control outcomes and the analysis of standardized mortality ratios. In: Epidemiology. 2015;26(5):727–32.

    Google Scholar 

  64. Richardson DB, Laurier D, Schubauer-Berigan MK, Tchetgen Tchetgen EJ, Cole SR. Assessment and indirect adjustment for confounding by smoking in cohort studies using relative hazards models. In: Am J Epidemiol. 2014;180(9):933–40.

    Google Scholar 

  65. Tchetgen Tchetgen EJ, Sofer T, and Richardson D. “Negative outcome control for unobserved confounding under a Cox proportional hazards model”. In: (2015). Available at https://biostats.bepress.com/harvardbiostat/paper192/.

  66. Glynn A, Ichino N. “Generalized nonlinear difference-in-difference-in-differences”. In: V-Dem Working Paper 90 (2019). Available at https:// papers. ssrn.com/sol3/papers.cfm?abstract_id=3410888.

  67. Tchetgen Tchetgen EJ. The control outcome calibration approach for causal inference with unobserved confounding. In: Am J Epidemiol. 2014;179(5):633–40.

  68. Gagnon-Bartsch JA, Speed TP. Using control genes to correct for unwanted variation in microarray data. In: Biostatistics. 2012;13(3):539–52.

    Google Scholar 

  69. Jacob L, Gagnon-Bartsch JA, Speed TP. Correcting gene expression data when neither the unwanted variation nor the factor of interest are observed. In: Biostatistics. 2016;17(1):16–28.

    Google Scholar 

  70. • Wang J, Zhao Q, Hastie T, Owen AB. Confounder adjustment in multiple hypothesis testing. In: Ann Stat. 2017;45.5:1863–94 This paper unifies unmeasured confounding adjustment methods in multiple hypothesis testing and provides theoretical guarantees for these methods.

  71. Newey WK, Powell JL. Instrumental variable estimation of nonparametric models. In: Econometrica. 2003;71(5):1565–78.

  72. Hansen LP. Large sample properties of generalized method of moments estimators. In: Econometrica. 1982:1029–54.

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Authors and Affiliations

  1. Department of Biostatistics, University of Michigan, Ann Arbor, USA

    Xu Shi

  2. Department of Probability and Statistics, Peking University, Beijing, China

    Wang Miao

  3. Statistics Department, The Wharton School, University of Pennsylvania, Philadelphia, USA

    Eric Tchetgen Tchetgen

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  1. Xu Shi
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  2. Wang Miao
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Correspondence to Xu Shi.

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Appendices

Appendix 1. Examples of invalid negative controls that violates some assumption

Violation 1: no arrow between U and W. There must be an arrow between U and W, because an NCO is a proxy of unmeasured confounder. It recovers the confounding bias by reflecting variation due to U.

Violation 2: no arrow between U and Z and Z↛A. The only scenario that Z does not need to be associated with U is when Z is an instrumental variable (see first cell of Table 3 of the Appendix). In this case, A is a collider between Z and U, such that Z and U are marginally independent. Conditioning on a collider will create collider bias such that Z and U become conditionally dependent. The requirements about Z in Assumptions 5 and 7 are all made conditioning on A. Therefore, an instrumental variable is a valid NCE.

Violation 3: Y → W. If the outcome causes the NCO, then the treatment directly causes the NCO via the path A→Y→W, which violates Assumption 3.

Violation 4: Z→U←W. The direction of the arrow between U and the negative control does not always matter. For example, we can have Z→U, U→Z, W→U, or U→W. However, if both Z and W cause U, then U is a collider in the path Z→U←W. In this case, conditional on U, Z and W will become associated. This violates Assumption 4.

Appendix 2. Example of causal graphs encoding the negative control assumptions

Below, we enumerate the possible relationships among Z, A, U and among Y, W, U in Appendix Table 3. These partial graphs can be combined into a directed acyclic graph that encodes the negative control assumptions. Grey-colored graphs are invalid because of violation of key assumptions.

Table 3 Examples of graphs for Z, A, U relationships and for W, Y, U relationships. The two pieces of graphs can be combined in to a directed acyclic graph that encodes the negative control assumptions. Gray-colored graphs are invalid because of violation of key assumptions
Full size table

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Shi, X., Miao, W. & Tchetgen, E.T. A Selective Review of Negative Control Methods in Epidemiology. Curr Epidemiol Rep 7, 190–202 (2020). https://doi.org/10.1007/s40471-020-00243-4

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