Volume 4: No. 1, January 2007
What Does the Population Attributable Fraction Mean?
Beverly Levine, PhD
Suggested citation for this article: Levine B. What does the population attributable fraction mean? Prev Chronic Dis [serial online] 2007
Jan [date cited]. Available from:
Recent controversy over the disagreement of population attributable fraction
estimates for the obesity–total mortality relation has made the concept of
attributable fraction visible in both scientific and popular news. Most of the
attention in writings on the attributable fraction has focused on technical
matters of estimation and on ensuring a causal relationship between exposure and
outcome. Yet some of the most illuminating questions about the attributable
fraction have to do with another causal question and how the measure is to be
interpreted in light of the answer to this question: What interventions are
available to cause the assumed reduction in risk among the exposed and the
consequent estimated reduction in disease burden? In this paper, I discuss the
limitations to the common interpretations of the attributable fraction and argue
that these limitations cannot be overcome merely by better statistical modeling
or by use of better data sets. They must be addressed through discussion of
specific interventions and the hypothesized causal consequences of such
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Recent controversy over the accuracy of population attributable fraction (AF) estimates for the obesity–total mortality relation has made the concept of AF (also called attributable risk) highly visible in both scientific and popular news. Both the Institute of Medicine (1) and the Centers for Disease Control and Prevention (CDC) (2) have sponsored recent workshops on
the topic of how best to estimate the effects of obesity on the risk of mortality in the United States. and how to resolve disagreements over published estimates (3,4).
Many scientific resources have been directed toward this topic, and the discussion has
been published in top medical and scientific journals in the
United States (3-6).
This article will not address the political or scientific aspects of
this controversy. Its purpose is to discuss the general use of the AF
estimate as a practical tool in applied epidemiology and public health.
The AF is formally written as
P(D) – P(D | Ē)
where P(D) is the (unconditional) probability of disease over a specified time period, and
P(D | Ē) is the probability of disease over the same time period conditional on nonexposed status
(not exposed to the risk factor under study). The AF is the difference
between overall average risk of the entire population (both exposed and
unexposed people) and average risk in the unexposed, expressed as a fraction of
the overall average risk.
Depending on the types of data available, there are different formulas used to estimate
the AF. Much of the discussion in epidemiology textbooks, in the section on
AF in the Encyclopedia of Biostatistics (7,8), and in articles on AF in
epidemiologic and biostatistical journals is devoted to the technical topic of choosing the most appropriate formula for estimating
the above fraction, given various constraints, once it can be assumed that
there is a causal relationship between exposure and disease. Yet some of the most interesting questions about the AF have to do with
causal question that cannot be answered through recourse to technical
discussion: What interventions are available to cause the assumed reduction in risk among the exposed and the consequent estimated reduction in disease burden? Such a question is rarely, if ever, discussed in
writings on the AF.
Before addressing the central point — that this other causal question is
critical to the significance of the AF — I first discuss the two most common interpretations of the AF. These interpretations,
although related, are not equivalent. First, the AF is widely interpreted as the proportion of disease burden causally explained by, or attributable to, the risk factor(s) being considered.
Second, the AF is
the proportion of disease risk that would be eliminated from the
population if exposure to the risk factor were eliminated.
The AF as a partitioning of causality
The interpretation of the AF as the proportion of disease burden attributable to a factor (or a set of factors) is commonly used by those who wish to differentiate between the portion of disease risk that is understood and the portion that remains to be understood.
This interpretation has been used in breast cancer. For example, reports of AFs of
about 25% for the major breast cancer risk factors have been used to imply that
75% of the disease of breast cancer is not understood or is not attributable to
known causes (8). This interpretation is also sometimes used by genetic
epidemiologists to estimate what proportion of disease is causally attributable
to genes (9-11). With AFs such as these, no interventions are intended.
The fractions are estimated for the purpose of summarizing and partitioning
causal knowledge — often between known and unknown causes, as has been the case
in breast cancer — or between genetic and nongenetic causes.
Underlying this interpretation is the philosophical question of what we mean when we say that a certain percentage of disease in
the population is caused by, attributable to, or explainable by a given risk factor or set of factors.
Greenland and Robins (12) tackle the issue of what is meant by the phrase attributable to (5) when they draw a distinction between
excess and etiologic cases. They provide a thorough
discussion of the difference between these kinds of cases and show why the AF
will usually greatly underestimate the proportion of disease burden that is
etiologically related to the exposure.
Another concern with the interpretation of the AF as the proportion of
disease caused by an exposure stems from the model of causes that underlies
much of epidemiology. This model of sufficient component causes holds that a
given case of disease could theoretically have been averted over a
considered time period if any one of a sufficient set of causes were
averted. The AF for different exposures considered one at a time will
usually sum to greater than 100% (greater than the total number of cases)
for a given outcome. In the single-factor-at-a-time AF analytic method, a
death or a case of disease (e.g., myocardial infarction) attributable to
exposure X (e.g., hypertension) could also be, and often is, attributable to
exposure Y (e.g., elevated cholesterol levels). Thus, the consideration of
an outcome as attributable to (or caused by) exposure X (rather than Y) is
A third reason to question the use of the AF in causal partitioning is that a large AF may reflect merely a broad exposure definition rather than
any valuable understanding about causality. As an extreme example of this,
consider that one could report an AF of 100% if one were to consider age
›15 years as a risk factor for breast cancer.
This would say nothing about causality. As Wacholder et al (13) demonstrate, the
AF will always increase with a broader definition of exposure provided that the
individuals newly included under the broader definition have a relative risk for
disease greater than 1.0 when compared with the remaining unexposed
group. As an exposure definition is made more sensitive (i.e., broader), the AF will increase, but the absolute risk of disease
in the exposed category will decline as long as there is a monotonic
dose–response relationship between exposure level and risk of disease. For many
scientists, it is a high absolute risk of disease rather than a broad exposure
definition (and high AF) that is key to valuable information about causality.
Interpretation of the AF as a partition delineating what proportion of disease
or mortality risk scientists should consider causally related and causally
unrelated to a given factor is problematic. Kempthorne, in a classic Biometrics
paper (14), argued against any attempt to quantitatively partition causality
when multiple factors or forces
determine the outcome. He stated that the results of such partitioning attempts
are meaningless for understanding causal processes and for considering realistic
effects of intervention.
The AF as proportion of preventable disease
The AF is frequently interpreted as the proportion of disease risk or incidence that could be eliminated from
the population if exposure were eliminated. The expectation is that the AF has a
practical value for those interested in public health prevention policy,
particularly when dealing with an exposure that is modifiable.
When the AF is interpreted as the proportion of disease risk that could
be eliminated from the population if exposure were eliminated, the simple
fraction is interpreted as an answer to the following narrow, precise
What proportion of disease risk could be eliminated if absolute risk in the exposed were to suddenly and sustainably
go to the level of absolute risk in the unexposed, while nothing else,
including absolute risk in the unexposed, were to change?
This question subsumes another more common, narrower question:
proportion of disease risk could be eliminated if exposure were to be
eliminated, while nothing else changed?
Given the algebraic structure of the AF, the modifiability (or
elimination) of exposure is not the key criterion. The key is elimination of
excess risk associated with exposure, which can theoretically happen in
various ways besides actual elimination of exposure.
A rephrasing of the questions in the previous example is helpful
because it points out the severe limitation to the interpretation of the AF as
a proportion of disease risk that can be eliminated. The question,
What proportion of disease risk could be eliminated if the absolute risk in the exposed were to suddenly and sustainably
go to the level of absolute risk in the unexposed, while nothing else,
including absolute risk in the unexposed, were to change?
is an interesting and valuable question only if one can also ask and
answer the following question:
intervention is available to cause the disease risk in the exposed to quickly become that of the unexposed, while simultaneously changing nothing else?
If this second question sounds meaningless in a given situation —
perhaps because no such intervention nor anything close has been proved — I would argue that
the interpretation of the AF as the proportion of disease risk that can be
eliminated is also meaningless
because the fundamental assumption underlying the AF, that disease risk in the exposed
immediately becomes that of the unexposed, is impossible to meet.
It is an irony that in all the discussions about AF, the causality question that has received the most attention is whether or not there is
truly a causal relationship between exposure and outcome. An example is the discussion about AF in the
Encyclopedia of Biostatistics
(7) in which the three conditions that must be met for the AF to be interpreted as
the proportion of disease risk that can be eliminated are the following: 1) the
estimation of the AF is unbiased; 2) the exposure is causal rather than
merely associated with disease; and 3) elimination of the risk factor has
to have no effect on the distribution of other risk factors. If one cannot
assume a causal relationship between exposure and disease, calculation of the AF
has no clear value. It is also true, however, that there is an equally important
question of causality that needs to be addressed if the above interpretation of
the AF is to have any meaning: What intervention is available to cause the
assumed reduction in disease risk? This
question has received scant, if any, attention in the literature on
attributable fraction. Yet we have data available in many situations where an AF is estimated to at
least begin to address this question.
Returning to the specific topic that began this article — AF estimation for
the obesity and mortality association — suppose there were a scientific consensus that the prevalence of obesity could be greatly reduced in the United States. Different interventions to achieve this reduction would have different effects on the burden of mortality. Hernan (15) points out that the notion of
causal effect is not well defined unless one can specify an intervention, even a hypothetical one, to eliminate
the cause. He notes
that the value of the counterfactual outcome (which in the obesity–mortality AF situation is the number of deaths that would be eliminated following the elimination of obesity) depends entirely on the actual intervention used to manipulate exposure. A strategy to eliminate
(or greatly reduce) the prevalence of obesity in the United States. that relied upon successful persuasion of overweight and obese
individuals in the population to adopt eating and activity patterns that led to safe and sustainable weight loss would have very different consequences for public health and mortality than a strategy that relied on widespread use of gene therapy or liposuction to eliminate excess weight. These planned interventions would have different consequences from a catastrophic event that resulted in
a great reduction in prevalence of overweight and obesity. None of these hypothetical interventions necessarily has its causal effect captured in the obesity–mortality AF estimate.
Some have used the AF to rank order exposures in terms of their
hypothetical public health priority even if there is no available or
proposed intervention. For example, if the AF estimate for risk factor X is
higher than that for risk factor Y, a conclusion might be that risk factor X
is the more burdensome exposure and should receive more attention from a
prevention standpoint. But issues of available or potential interventions,
the risks and benefits of such interventions, and the relation of the
exposure to other exposures in the population (i.e., is it feasible to
hypothesize about changing the exposure while holding all other risk factors
unchanged?) must be rigorously addressed before one can assume that an
exposure with a higher AF is more important for policy makers to consider
than another exposure. The topic of how public health priorities should be set is beyond
the scope of this article, but Buchanan presents a thought-provoking discussion
relevant to this complex topic (16).
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As discussed previously in this article and as stated by Kempthorne (14),
attempts to partition causality when multiple forces act together to produce
the outcome are meaningless. With respect to interpretation of an AF as the
proportion of disease risk that could be eliminated if the excess risk
associated with exposure were to be eliminated, there may be valuable
meaning under a specific set of assumptions. In addition to the assumptions
commonly listed in textbooks, there is one more critical assumption: that we can envision a specific intervention that will cause the
estimated reduction in risk in the exposed while changing no other risk
Some might argue that in the absence of this last assumption, the AF
nonetheless allows for an interesting theoretical case study (i.e., what
would happen to the disease burden if we were to find and use such an intervention?). Because such theoretical cases are not subject to
tests of falsifiability, we must ask ourselves rigorously, in
each case, what purpose they serve. For many exposures, it is time for more
complex and specific theoretical case studies than simple AF estimation.
These more complex theoretical experiments would hypothesize about effects of
specific interventions to reduce or eliminate exposure risk in specific
populations and subpopulations by using the diverse data gained from public
health activities. In the work of Berry et al (17), there is elegant precedent for such complex thought
experiments and for the careful use of existing data to draw as precise a
conclusion as possible about the public health consequences of specific
The AF is only a simple fraction derived from the arithmetic manipulation of probabilities.
As with many other measures in public health, how this fraction is interpreted is
key. In some settings it has taken on a life of its own, regardless of its
meaning in reality. The burden is on those providing AF estimates to state what
their value is to public health professionals and policy makers. The rest of us
in the public health community have the responsibility to continually draw the
discussion of AF estimates back to the central question of public health
This paper is not an argument for never computing a population AF. It is
an argument for more clarity, justification, and complex thinking when using
this measure. AFs are only a beginning of the discussion of the public
health consequences of intervening to reduce the prevalence of risk
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Beverly Levine, Department of Public Health Education, 437 HHP Bldg, Walker Ave, PO Box 26170, University of North Carolina at Greensboro, Greensboro, NC 27402-6170. Telephone: 336-334-3244. E-mail: email@example.com.
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