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Using negative controls to adjust for unmeasured confounding bias in time series studies

Nature Reviews Methods Primers volume 3, Article number: 66 (2023) Cite this article

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Abstract

Unmeasured confounding threatens the validity of observational studies. Negative control variables (NCs) are variables that either do not cause the outcome of interest or are not caused by the exposure of interest and are increasingly available from emerging sensing technologies and digitized health records. Under appropriate assumptions, NCs can be used to adjust for unmeasured confounding bias. This Primer explains the assumptions and implementation of NCs for unmeasured confounding bias adjustment. Among the method’s broad applications in public health research, time series studies of environmental exposures — air pollution, wildfires and heat — and health outcomes are focused on. Three types of unmeasured confounding in time series studies are considered: time-invariant confounders with time-invariant confounding effects; time-invariant confounders with time-modified confounding effects; and time-varying confounders with immediate and/or lagged confounding effects. For each type of confounding, guidance is provided on how to select NCs using several case studies. Finally, challenges and opportunities are described, to help catalyse additional methodological developments.

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Fig. 1: Daily PM2.5 levels and daily maximum temperature in Napa County, California, during the 2020 wildfire season.
Fig. 2: Diagram of a confounder.
Fig. 3: Illustration of negative control exposures and negative control outcomes.
Fig. 4: Considering an instrumental variable Z as a negative control exposure.
Fig. 5: Illustration of negative control exposures and negative control outcomes to adjust for an unmeasured type I confounder.
Fig. 6: Illustration of negative control exposures and negative control outcomes to adjust for an unmeasured type II confounder.
Fig. 7: Illustration of negative control exposures and negative control outcomes to adjust for an unmeasured type III confounder.

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Acknowledgements

J.K.H. thanks the National Institute of Environmental Health Sciences (T32 ES 7069), Sloan Foundation (G-2020-13946) and Environmental Protection Agency (CR-83467701) for financial support. E.J.T.T. thanks the National Institutes of Health (NIH) (R01AG065276), National Cancer Institute (NCI) (R01CA222147), General Medical Sciences (R01GM139926) and National Institute of Allergy and Infectious Diseases (R01AI27271) for financial support. F.D. thanks the NIH (R01ES026217, R01MD012769, R01ES028033, 5R01AG060232-03, 1R01ES030616, 1R01AG066793, 1R01ES029950, 1R01ES 034373-01) and Sloan Foundation (G-2020-13946) for financial support.

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Authors and Affiliations

  1. Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA

    Jie Kate Hu & Francesca Dominici

  2. Department of Statistics and Data Science, Wharton School, University of Pennsylvania, Philadelphia, PA, USA

    Eric J. Tchetgen Tchetgen

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Contributions

Introduction (J.K.H. and F.D.); Experimentation (J.K.H., E.J.T.T. and F.D.); Results (J.K.H. and E.J.T.T.); Applications (J.K.H. and F.D.); Reproducibility and data deposition (J.K.H. and F.D.); Limitations and optimizations (J.K.H. and E.J.T.T.); Outlook (J.K.H., E.J.T.T. and F.D.); Overview of the Primer (all authors).

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Correspondence to Jie Kate Hu.

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Nature Reviews Methods Primers thanks Sara Levintow; W. Dana Flanders; and William Henley, who co-reviewed with Sharlene Alauddin, for their contribution to the peer review of this work.

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Related links

AirNow: https://gispub.epa.gov/airnow

GRIDMET: https://developers.google.com/earth-engine/datasets/catalog/IDAHO_EPSCOR_GRIDMET

Highest September temperatures in Napa: https://www.extremeweatherwatch.com/cities/napa/month-september/highest-temperatures

NASA: https://data.nasa.gov/

National Center of Health Statistics: https://data.cdc.gov/

NOAA: https://data.noaa.gov/

Supplementary information

Glossary

Asymptotically unbiased

An estimator for a parameter is asymptotically unbiased if its expectation converges to the true value of the parameter when the sample size is large enough.

Backdoor criterion

A graphic test in which a set of variables U satisfies the backdoor criterion relative to an ordered pair of variables (A, Y) in a directed acyclic graph (DAG) if no node in U is a descendant of A; and U blocks every path between A and Y that contains an arrow into A.

Categorical variable

A characteristic that cannot be quantifiable. Categorical variables can be either nominal or ordinal.

Causal inference

The process of using data for uncovering causal relationships between variables.

Directed acyclic graph

(DAG). A graph contains a set of vertices (nodes) and a set of edges that connect some pairs of vertices. If every edge in a graph is an arrow that points from the first to the second vertex, we have a directed graph. A DAG is a graph that is directed and without directed cycles.

Negative control exposure

(NCE). A variable Z is an NCE if it is known a priori not to cause outcome Y, and the association between Z and Y is subject to the same unmeasured confounding mechanism as between exposure A and outcome Y.

Negative control outcome

(NCO). A variable W is an NCO if it is known a priori not to be caused by exposure A and the association between A and W is subject to the same unmeasured confounding mechanism as between exposure A and outcome Y.

Non-differential error

The measurement error of a confounder is said to be non-differential if the measured confounder is conditionally independent of the exposure and outcome, given the true confounder.

Statistical inference

The process of using a sample to make inferences about a population.

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Hu, J.K., Tchetgen Tchetgen, E.J. & Dominici, F. Using negative controls to adjust for unmeasured confounding bias in time series studies. Nat Rev Methods Primers 3, 66 (2023). https://doi.org/10.1038/s43586-023-00249-4

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