Indirect corrections for confounding under multiplicative and additive risk models

Our plain-English summary of Indirect corrections for confounding under multiplicative and additive risk models, by M.H. Gail, S. Wacholder, J.H. Lubin (American Journal of Industrial Medicine, 1988).

The study

• Authors: M.H. Gail, S. Wacholder, J.H. Lubin
• Journal: American Journal of Industrial Medicine
• Published: 1988;13(1):119-30
• Cited by: 40 articles, as counted by NIH iCite
• Read it: PubMed · Publisher
• In J-M's library: Johns-Manville's company medical library held a copy (J-M no. 000221).

Abstract

We define a multiplicative model and an additive model for the hazards associated jointly with exposure and with the presence of a confounder like smoking. Under the multiplicative model, the crude relative risk may be adjusted indirectly, by means of a factor proposed by Axelson [1978], and implicitly by Cornfield et al. [1959] and Schlesselman [1978]. We present corresponding indirect correction formulas under the additive risk model for the risk difference and for the excess relative risk. Conditions are established under which these corrections may be applied to age-adjusted rates from composite study populations. We demonstrate that indirect corrections may be no better than crude measures of risk if one assumes the wrong model for the joint action of the exposure and confounding factors. These results are illustrated on an example of occupational exposure to vermiculite. The limitations of the techniques are discussed.

In plain English

This was a statistical methods paper, not a new study of workers. The authors described formulas for indirectly correcting risk estimates for a confounder such as smoking when smoking data for individual workers are not available. They did this under two models of how exposure and smoking combine: a multiplicative model and an additive model. They illustrated the formulas with previously published data from Amandus and Wheeler (1987) on a cohort of vermiculite miners. That cohort had 20 lung cancer cases against 8.96 lung cancer deaths expected from U.S. age-specific death rates, a standardized mortality ratio of 2.23 that was crude because it did not account for smoking. Using that study's smoking assumptions, the corrected relative risk was 1.82 under the multiplicative model. Under the additive model it was 1.70 for smokers and 10.7 for nonsmokers, and the excess relative risk rose from a crude 1.23 to 9.75. The authors warned that corrections based on the wrong model can be misleading, and that without individual smoking data the models cannot be checked. The authors concluded that smoking corrections should be examined routinely, but with care, in occupational studies that lack smoking information.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Statistical methods paper deriving indirect correction formulas for confounding under multiplicative and additive risk models, with a worked example using previously published cohort data
• Who was studied: No new population was studied. The worked example used published data from Amandus and Wheeler (1987): a cohort of vermiculite miners with 20 lung cancer cases over 13,502 person-years of follow-up. These were compared with 8.96 lung cancer deaths expected from general U.S. age-specific lung cancer death rates.
• Exposure: Occupational exposure to vermiculite (example data), with smoking as the confounder. The example used the smoking assumptions of Amandus and Wheeler: a relative risk of 14 for smoking, 84% of miners smoking, and 67% of the general U.S. population smoking.
• Main results:
  • For the vermiculite miners, the standardized mortality ratio for lung cancer was 2.23: 20 observed cases divided by 8.96 deaths expected from U.S. age-specific death rates. The authors called this a crude estimate because smoking was not taken into account.
  • Under the multiplicative model, the smoking-corrected relative risk for the miners was 1.82 for both smokers and nonsmokers. Under the additive model it was 1.70 for smokers and 10.7 for nonsmokers.
  • Under the additive model, the corrected risk difference (66.6 per 100,000 person-years) and the corrected excess relative risk (9.75) were the same for smokers and nonsmokers. Under the multiplicative model, the risk difference was 78.5 for smokers and 5.59 for nonsmokers, and the excess relative risk was 11.5 for smokers and 0.817 for nonsmokers.
  • Correction lowered the relative risk by 18% under the multiplicative model and lowered the risk difference by 18% under the additive model, but raised the excess relative risk by 693% (from a crude 1.23 to 9.75).
  • Indirect adjustments based on the wrong model for how exposure and confounder act together can be misleading.
• The authors' conclusion: The authors concluded that correction for smoking should be examined routinely, but with care, in occupational studies that do not collect smoking information. When the literature gives little guidance on the right model, they considered it prudent to carry out corrections under both the multiplicative and the additive model.
• Limitations the authors state:
  • Without smoking data for each study participant, neither risk model can be checked for appropriateness.
  • The simple adjustments require assuming constant effects of exposure and confounder, and constant proportions with the confounder, across all age groups.
  • The methods need outside information on the confounder's effect in the unexposed population and on the proportions with the confounder.
  • For confounders with multiple levels, knowledge of their effects and distributions is often not available.

Topics

Medical terms in this study, explained in our Lexicon: Confounding, Relative Risk, Occupational Exposure, vermiculite.

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