The population attributable fraction (PAF), also referred to as the excess fraction1 or attributable risk,2 combines exposure prevalence with a causal risk ratio (or rate ratio or odds ratio in the case of rare disease) to quantify the proportion of disease cases in a population that could be prevented by eliminating an exposure of interest. Unlike the conceptually distinct etiologic fraction,1 which additionally includes cases that occur earlier in time due to exposure, the PAF can be estimated using epidemiologic data. This important and arguably underappreciated dimension of the exposure-disease relationship illustrates that large risk ratios can have little impact at a population level if the exposure is rare, and that small risk ratios can translate into large public health burdens if the exposure is common. Unfortunately PAFs reported in the literature are commonly biased due to incorrect methods of calculation. Namely, investigators have frequently applied adjusted risk ratios to the following PAF formula, which is valid only for unadjusted risk ratios (RRs)3:
where pe is the proportion of the population exposed and RR is the causal risk ratio associated with the exposure. When confounding is present such that the unadjusted RR is not the causal RR, as is typically the case in observational studies, other methods must be used.2,3
In this issue of EPIDEMIOLOGY, Flegal4 explores bias in estimated PAFs driven by essentially this same mistake in the context of weight and its effect on mortality. Because smoking is a strong confounder of the overweight-mortality association, adjusted estimators of the PAF must be used. Flegal shows how the incorrect practice of combining an adjusted RR (obtained via stratification by smoking) with the overall population prevalence of overweight in Equation 1 generally leads to overestimation of the PAF for overweight and mortality. The observed overestimation of the PAF in this context is explained by the fact that smokers have a higher risk of disease (death) and lower prevalence of exposure (overweight) compared with the overall population. Inclusion of an RR adjusted for smoking in Equation 1 is not enough to fully adjust the PAF because Equation 1 does not also account for differences in exposure prevalence across smoking strata.
Fortunately, equally straightforward formulas are available to calculate adjusted PAFs when confounding is present.2 The simplest approach (Flegal’s PAF2) combines an adjusted RR (RRadj) with the prevalence of exposure among cases (Pc):
This approach is useful when there is no effect modification by adjustment factors. It requires knowledge of the prevalence of exposure specifically among the diseased, as opposed to in the whole population, as in Equation 1.
A second valid approach estimates the PAF based on a weighted-sum of stratum-specific attributable fractions, weighting by the proportion of cases in each stratum defined by one or more adjustment factors:
where the adjustment factors form i joint strata, pi is the proportion of the population in stratum i who are exposed, and Wi is the proportion of the diseased individuals who are in stratum i. This weighted-sum approach accommodates effect modification and adjusts for confounding via stratification, but implementation can be impractical if there are multiple adjustment factors leading to sparse data or if adjustment factors are not categorical. It requires estimates of exposure prevalence in each stratum and the proportion of diseased individuals in each stratum. In addition to these Equations, there are regression approaches that overcome some of the limitations of stratification and also yield valid adjusted PAF estimates.2,5
The inputs required for these calculations should be readily available to any investigator who wishes to estimate the PAF for an exposure within the same study population used to estimate the risk ratio. For example, an investigator conducting a cohort study of weight and mortality would be able to identify the proportion of decedents in the study population who were overweight (needed for Equation 2), as well as the prevalence of overweight and proportion of disease in each confounder stratum (needed for Equation 3). The availability of data necessary to correctly estimate an adjusted PAF can be more limited in situations where relative risks generated from one or more source populations are used to estimate the PAF for a different target population (e.g., an entire country, a future population). In these circumstances, estimates of exposure prevalence may be available for the overall target population but not among the diseased (Equation 2) or within strata of adjustment factors (Equation 3). Examples include those cited by Flegal in attempting to quantify deaths attributable to overweight and obesity in the U.S. population, as well as the World Health Organization’s Global Burden of Disease initiatives. Calculation of the PAF in these settings also relies on strong assumptions about portability of the RR between populations which may not be justifiable.6
Ironically, the contexts where PAFs are most difficult to validly estimate also offer some of the greatest opportunities for influencing prioritization of public health policy interventions. In these situations, if strong confounding of an exposure-disease relationship is indicated in the source population, it may be worthwhile to expend the additional resources to obtain the additional inputs necessary for valid estimation of an adjusted PAF for the target population. This may involve conducting additional surveys of exposure prevalence among population subgroups (i.e., among disease subgroups or within the major confounder strata), extrapolating existing survey data (e.g., the National Health and Nutrition Examination Survey), or at least considering a range of plausible values for the parameters required for correct PAF computation. As a last resort, when Equation 1 is implemented incorrectly by applying adjusted RRs, in some cases knowledge about the direction and magnitude of confounding in the RR can be used to anticipate the direction and magnitude of expected bias in the estimated PAF.7
Ultimately investigators have a responsibility to ensure that reported estimates of the PAF are calculated correctly and their limitations communicated clearly. While this can be said of any epidemiologic measure, it is particularly important for the PAF in light of its direct relevance to evidence-based public health decision-making at the population level.
REFERENCES
1. Greenland S, Robins JM. Conceptual problems in the definition and interpretation of attributable fractions. Am J Epidemiol. 1988;128:1185–1197
2. Benichou J. A review of adjusted estimators of attributable risk. Stat Methods Med Res. 2001;10:195–216
3. Rockhill B, Newman B, Weinberg C. Use and misuse of population attributable fractions. Am J Public Health. 1998;88:15–19
4. Flegal K. Bias in calculation of attributable fractions using relative risks from non-smokers only. Epidemiology. (concurrent publication)
5. Bruzzi P, Green SB, Byar DP, Brinton LA, Schairer C. Estimating the population attributable risk for multiple risk factors using case-control data. Am J Epidemiol. 1985;122:904–914
6. Steenland K, Armstrong B. An overview of methods for calculating the burden of disease due to specific risk factors. Epidemiology. 2006;17:512–519
7. Darrow LA, Steenland NK. Confounding and bias in the attributable fraction. Epidemiology. 2011;22:53–58
