A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods
Abstract
In observational cohort mortality studies with prolonged periods of exposure to the agent under study, independent risk factors for death commonly determine subsequent exposure to the study agent. For example, in occupational mortality studies, date of termination of employment is both a determinant of subsequent exposure to the chemical agent under study (since terminated individuals receive no further exposure) and an independent risk factor for death (since disabled individuals tend to leave employment). When a risk factor determines subsequent exposure and is determined by previous exposure, standard analyses that estimate age-specific mortality rates as a function of cumulative exposure can underestimate the true effect of exposure on mortality, whether or not one adjusts for the risk factor in the analysis. This observation raises the question, "Which, if any, empirical population parameter can be causally interpreted as the true effect of exposure in observational mortality studies?" In answer, we offer a graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods. We reanalyze the mortality experience of a cohort of arsenic-exposed copper smelter workers using our approach and compare our results with those obtained using standard methods. We find an adverse effect of arsenic exposure on all cause and lung cancer mortality, which standard methods failed to detect. The analytic approach introduced in this paper may be necessary to control bias in any epidemiologic study in which there exists a risk factor which both determines subsequent exposure and is determined by previous exposure to the agent under study.
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The expression for the sequential-intervention causal effect coincides with Robins' (1987) G-computation formula, which was derived from a more complicated set of counterfactual assumptions.
“This expression coincides with Robins' (1987) G -computation formula, which was derived from a more complicated set of (counterfactual) assumptions.”
From Causal inference in statistics: An overview (2009) · cites this paper as Robins, 1987
The expression for the causal effect of a treatment sequence do(X=x), do(Z2=z2) coincides with Robins' (1987) G-computation formula.
“This expression coincides with Robins' (1987) G-computation formula, which was derived from a more complicated set of (counterfactual) assumptions.”
From An Introduction to Causal Inference (2010) · cites this paper as Robins' (1987)
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- Authors
- Robins, J.
- Affiliations
- Harvard University (US)
- Corresponding author
- Robins, James
- ORCID
- Robins, James
- Venue
- Journal of Chronic Diseases
- Publisher
- Elsevier BV
- Published
- 1987-01
- Volume
- 40
- Pages
- 139S-161S
- ISSN
- 0021-9681 (ISSN-L)
- OpenAlex
- W2035142205
- Cited by
- 305
- References
- 9
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 6 · 2023: 7 · 2022: 9 · 2021: 11 · 2020: 12 · 2019: 12 · 2018: 11 · 2017: 10 · 2016: 10 · 2015: 12 · 2014: 20 · 2013: 6 · 2012: 11
- FWCI
- 3.73
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Chronic Diseases (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institutes of Health (5r23es003405-03)
- National Institute of Environmental Health Sciences (5-P30-ES00002, 5-R23-ES03405, P30ES000002)
- National Institute for Occupational Safety and Health (5 R03 OH01867)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Health Sciences › Medicine › Oncology › Global Cancer Incidence and Screening
- Keywords
- causal inference, directed acyclic graphs, mortality, cumulative exposure, confounding by indication, occupational exposure, arsenic, copper smelter workers, lung cancer mortality, all-cause mortality, bias control
- MeSH terms
- Epidemiologic Methods, Humans, Occupational Diseases, Probability, Risk Factors, Statistics as Topic, Time Factors
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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