Estimating the potential disease rate reduction under varying conditions of combined effects

Our plain-English summary of Estimating the potential disease rate reduction under varying conditions of combined effects, by H. Checkoway, J.L. Hickey (International Journal of Epidemiology, 1988).

The study

• Authors: H. Checkoway, J.L. Hickey
• Journal: International Journal of Epidemiology
• Published: 1988;17(3):666-72
• Cited by: 5 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. 000894).

Abstract

The disease rate difference between people exposed and not exposed to some factor is the familiar estimate of attributable risk. When there are two or more causal exposures which demonstrate joint effects and are independently distributed, partitioning a population's overall rate between factors requires estimates of the marginal distributions of exposures and the independent (unconditional) and combined rate ratios for each exposure factor. The net potential reduction in the overall disease rate resulting from elimination of one of the exposures depends on these parameters and on the model of combined effect assumed, additive, multiplicative or some departure therefrom. In this paper the authors illustrate the extent to which the assumed model of combined effect of exposures determines which parameters need to be specified to estimate disease rate reductions. The concepts presented are demonstrated algebraically and with simulated hypothetical data. An application of the method is given with data from a case-control study of smoking, asbestos exposure and lung cancer.

In plain English

This was a methods paper, not a new study of workers. Using algebra and invented example numbers, the authors showed how to estimate how much a population's disease rate could fall if one of two exposures that act together were removed. In their example tables, the estimated reduction was larger when the two exposures were assumed to multiply each other's effects than when they were assumed to add together, except where one factor had a rate ratio of 1 (no added risk), when both models gave the same estimate. To illustrate the method, they reused data from an earlier case-control study of lung cancer and cigarette smoking among asbestos miners and millers. In those data, the rate ratio was 4.94 for smoking alone and 2.98 for cumulative asbestos exposure of more than 100 versus less than 100 fibers per cubic centimeter-years. For both together it was 8.21, between the additive and multiplicative expectations. With their method, the authors estimated that eliminating smoking alone would reduce lung cancer incidence by 62%. They estimated that removing asbestos exposure above 100 fibers per cubic centimeter-years would reduce it by 28%. They noted that these estimates needed slight adjustment for confounding between the two factors, and that their hypothetical examples were intentionally simplified.

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: methodological paper (algebraic derivation and simulated hypothetical data), with an illustrative application to previously published case-control data
• Who was studied: No new population was studied. The illustration used published case-control data on lung cancer and smoking among asbestos miners and millers, originally reported by Liddell et al. and taken from a paper by Steenland and Thun.
• Exposure: In the application, smoking (yes versus no) and cumulative asbestos exposure in fibers per cubic centimeter-years (more than 100 versus less than 100). In the hypothetical examples, two generic exposure factors, each present or absent.
• Main results:
  • In Table 1 (fixed rate ratios of 2 and 5), the estimated reduction from eliminating factor 1 was greater under the multiplicative model than under the additive model in every instance.
  • In Table 2, the two models gave equal estimates when the remaining factor's rate ratio was 1. For example, both gave 9.1%.
  • In the first hypothetical example, eliminating factor 1 gave an estimated reduction of 16.7% under the multiplicative model (versus 7.1% under the additive model). Eliminating factor 2 gave 57.1% (additive) and 61.5% (multiplicative).
  • In the asbestos miners and millers data, the rate ratio was 4.94 for smoking and 2.98 for asbestos exposure of more than 100 fibers per cubic centimeter-years.
  • The combined rate ratio for smoking plus asbestos exposure was 8.21, between the additive and multiplicative expectations. The interaction parameter K was 0.166.
  • In that group, eliminating smoking alone was estimated to reduce lung cancer incidence by 62%.
  • In that group, removing asbestos exposure above 100 fibers per cubic centimeter-years (factor 2) was estimated to reduce lung cancer incidence by 28%.
• The authors' conclusion: The authors concluded that dividing a population's disease rate between interacting causes requires knowing how the exposures are distributed and their separate and combined rate ratios. Under an exactly multiplicative model, only the proportion exposed to the eliminated factor and its rate ratio are needed.
• Limitations the authors state:
  • The hypothetical examples were intentionally simplified and considered only two factors, each present or absent.
  • Confounding between exposures was not addressed, because independence of exposures was assumed.
  • The asbestos and smoking estimates needed slight adjustment because of confounding between the two factors.
  • Disease rates and rate ratios, especially for interactive effects, are subject to fluctuation, which adds uncertainty to the estimates.
  • Choosing the model of combined effect is often a matter of judgement and debate.
  • Specifying complex patterns of combined effects generally limits the precision of the estimated reductions.

Topics

Medical terms in this study, explained in our Lexicon: Attributable Risk, rate ratio, Case-Control Study, Asbestos Exposure, Lung Cancer.

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