Elsevier

Annals of Epidemiology

Volume 25, Issue 3, March 2015, Pages 147-154
Annals of Epidemiology

Original article
A history of the population attributable fraction and related measures

https://doi.org/10.1016/j.annepidem.2014.11.015Get rights and content

Abstract

Purpose

Since Doll published the first PAF in 1951, it has been a mainstay. Confusion in terminology abounds with regard to these measures. The ability to estimate all of them in case-control studies as well as in cohort studies is not widely appreciated.

Methods

This article reviews and comments on the historical development of the population attributable fraction (PAF), the exposed attributable fraction (EAF), the rate difference (ID), the population rate (or incidence) difference (PID), and the caseload difference (CD).

Results

The desire for PAFs to sum to no more than 100% and the interpretation of the complement of a PAF as the proportion of a rate that can be attributed to other causes are shown to stem from the same problem: a failure to recognize the pervasiveness of shared etiologic responsibility among causes. A lack of appreciation that “expected” numbers of cases and deaths are not actually the numbers to be expected when an exposure or intervention appreciably affects person-time denominators for rates, as in the case of smoking and nonnormal body mass, makes many CD estimates inflated. A movement may be gaining momentum to shift away from assuming, often unrealistically, the complete elimination of harmful exposures and toward estimating the effects of realistic interventions. This movement could culminate in a merger of the academic concept of transportability with the applied discipline of risk assessment.

Conclusions

A suggestion is offered to pay more attention to absolute measures such as the rate difference, the population rate difference, and the CD, when the latter can be validly estimated and less attention to proportional measures such as the EAF and PAF.

Introduction

The population attributable fraction (PAF) answers the following question: suppose every member of a population who was not in the most favorable level of an exposure or some other condition or event with regard to an adverse outcome had been shifted into that level. By what proportion would the entire population's rate, hazard, risk, prevalence, or caseload have been reduced?

The brief history to follow of the PAF and related measures begins in the early 1950s and ends, not altogether arbitrarily, at the close of the 1980s. The primary focus is on matters of interpretation, with some attention paid to the influence of rather basic features of study design and data analysis. Some statistical issues, such as those pertaining to sampling error and covariate adjustment, are not addressed.

Section snippets

The first PAF

In 1951, Doll [1] estimated what appears to be the first published PAF in the epidemiologic literature. He used the cases from his preliminary (1948–1949) case-control study with Hill [2] to form the numerators for lung cancer incidence rates in Greater London. To obtain the denominators, he apportioned census figures by the smoking distribution in the study's control group. Within each age stratum, he multiplied the total person-time at risk by the rate among the nonsmokers “to estimate the

1954 to 1959

Gefeller wrote that the PAF “fell into oblivion” [15] after 1953. Indeed, the citation to Levin's 1953 article [13] in a 1958 review of statistical methods in cancer research [16] was for another contribution entirely.

Another sign of early indifference to the PAF came in 1954, when the authors of two articles [7], [8] used several case-control studies to break down an external target population's overall lung cancer rate by smoking as Cornfield [6] and Doll [3] had done. Although the

The ID, EAF, PID, and PAF in an early textbook

In their 1960 textbook, Epidemiologic Methods [17], MacMahon, Pugh, and Ipsen described all four measures of primary interest here. They called the ID the “attributable risk” and the PID the “attributable community risk” but gave no names to the EAF or the PAF. The authors wrote, “The concept of attributable community risk is useful in that it provides an estimate of the maximum reduction of a particular disease rate that might be expected if the specified exposure were removed” [17].

With lung

Lilienfeld's praise for the PAF

The PAF received a big boost in 1973 when Lilienfeld, an early adopter, praised its utility in the publication of the American Public Health Association's first Wade Hampton Frost Lecture [26], which he had given the year before. He stated that the PAF is “important to the public health administrator,” but did not elaborate on that use of the measure. His main focus was on what he saw as its implications for setting research priorities.

As Lilienfeld described it, the higher the PAF for a given

An early PAF generalization in theory

In articles in 1975 [33] and 1976 [34], Walter continued with the assumption that attributable fraction of incidence rates are equivalent with attributable fractions of incident caseloads. In the longer article [34], he examined all the measures under consideration here except the PID. He called the ID “Berkson's simple difference” and, following Lilienfeld, called the PAF “the attributable risk” and the EAF “the attributable risk among the exposed.”

Walter [34] stated that exposure-specific

More PAF theory and generalized PAF practice

In 1986, Rothman [44] criticized Doll and Peto [37] for ignoring shared causal responsibility and thereby forcing the sum of their PAFs for causes of cancer not to exceed 100%. In an update, Peto raised the ceiling to 200% [45].

The 1980s also saw other researchers begin to follow in the footsteps of Ouellet et al. [35] and estimate attributable proportions for shifts in exposure distributions more realistic than moving everyone to the exposure level with the lowest rate. In one article,

Comment

Although by the 1990s, the basic elements of the points emphasized here were in place in the literature on the PAF and related measures, that literature has continued to blossom. Particularly, notable contributions have been made by Greenland [50], [51], [52], [53], [54], [55], [56], Rockhill et al. [57], [58].

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