Original Articles
A new way to estimate the contribution of a risk factor in populations avoided nonadditivity

https://doi.org/10.1016/j.jclinepi.2003.10.003Get rights and content

Abstract

Objective

Attributable fraction in the exposed and (population) attributable fraction have been extensively used to determine the proportion of cases of a particular disease that can be attributable to any risk factor. Epidemiologists know that these measurements can add up to more than 100%; nevertheless, in a clinical context or in mass media, this characteristic is sometimes misinterpreted. This article provides a way to estimate the contribution of a risk factor in populations.

Study design and setting

McElduff et al. have suggested a method for estimating the contribution of a risk factor in a person with more than one risk factor. We extend their suggestion to populations where risk factors are mixed in different proportions. We illustrate the usage of this method by enlarging the example provided by them and compare it with the average attributable fraction suggested by Eide and Gefeller.

Results

Population attributable fraction can be modified to obtain additivity; therefore, the contribution of a risk factor in populations can be estimated, which would be of interest, for example, in clinical or in court settings.

Conclusion

The suggested method and the average attributable fraction provide different results, and would be applicable under different assumptions.

Introduction

Attributable fraction in the exposed (AFE) and (population) attributable fraction (AF) have been extensively used to measure how much of the disease burden could be avoided if some causal factors were eliminated. It is well known by epidemiologists that both measurements can add up to more than 100%; this property of nonadditivity of individual attributable fractions has, nevertheless, brought about some misinterpretations. [1] Several authors have dealt with it; for instance, Coughlin et al. [2] advocated the use of additive models without interaction, and Eide and Gefeller [3] and Gefeller et al. [4] proposed both the sequential and the average attributable fractions.

A different point of view has been adopted by McElduff et al. [5] suggesting a method for estimating the contribution of individual risk factors in persons (the emphasis is ours) with more than one risk factor. Their method estimates the proportion of the AFE for each factor via a weighted mean of the excess relative risk in exposed (in fact, they did not use the term “AFE,” but rather the equivalent “rate fraction”; in this article, we prefer “AFE” and “AF” as used in Benichou and Gail's Encyclopedia [6]). Contrary to the usual methods for measuring attributable fractions, this procedure never adds up to more than 100%. Nevertheless, it can only be applied to individual persons (as suggested by McElduff et al. in a court context) or to a population where all people are exposed to all the considered factors.

In a clinical context or in mass media (where the nonadditivity can be easily misinterpreted), however, it will be important to estimate the contribution of individual risk factors in mixed (exposed and nonexposed) populations with different prevalences of exposure to each risk factor. In fact, the court context can also be considered for populations instead of individuals, as occurs when legal authorities act against tobacco manufacturers. This problem deals with the AF instead of the AFE. In this article, we generalize the method suggested by McElduff et al. [5] to the population setting; our formula enables us to estimate the proportion of cases attributable to a particular risk factor. Next, we point out a mistake in the McElduff et al. [5] method when dealing with interaction terms, and suggest a way to solve it. Finally, we compare our proposal with the average attributable fraction.

Section snippets

Notation and background

AFE is usually defined as [7]AFE=Ie−I0Ie=RR−1RRwhere Ie is the incidence in the exposed people, I0 is the incidence in a nonexposed population, and RR is the relative risk. On the other hand, AF is defined as [8]AF=It−I0It=p×RR−1RR=p×AFEwhere It is the incidence in the overall population and p is the proportion of cases that are exposed.

From here on we present several expressions in which a population divided into various subgroups (e.g., levels of exposure) are exposed to a number of risk

Generalizing to populations

This section refers to the generalization of McElduff et al.'s [5] method to populations; the data used are provided in Table 1. To estimate the percentage of cases attributable to factor A, we should work with levels 2 and 4 (the levels where A is present). People in level 2 are exposed only to factor A, so equation (5) changes to: AFE2 × p2 × (RRA − 1)/(RRA − 1) = 0.5 × 0.2143 × (2 − 1)/(2 − 1) = 0.1071. People in level 4 are exposed to both A and B; then equation (5) holds: AFE4 × p4 × (RRA

Discussion

A characteristic of attributable fraction is that it can add up to more than 100%. This feature is well known by epidemiologists but can produce some confusion when it is used in clinical settings or in mass media [1]. In this article, we have suggested a relatively easy way to construct a population measure of AF without this drawback.

Although multivariate analyses have been widely used to estimate AF for risk factors in multivariate settings [2], [10], fewer efforts have been made to allocate

Acknowledgements

Thanks to a pair of reviewers for pointing out the limitations of McElduff et al.'s method for partitioning the attributable fraction in the exposed.

References (13)

There are more references available in the full text version of this article.

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