To the Editor: The objective of the cohort study by Dr Forman and colleagues1 was to estimate the hypothetical fraction of hypertension incidence associated with dietary and lifestyle factors in women. I believe that the wrong formula was used to calculate the population attributable fraction or risk (PAR).
The study by Forman et al used the crude formula for PAR, which is only appropriate when the association between the exposure and the outcome (as represented by the hazard ratio [HR]) is not adjusted for confounding variables.2 However, the authors adjusted their HRs for 8 variables they believed were confounders of the association between dietary and lifestyle factors and hypertension incidence. The use of adjusted HRs in the crude formula for the PAR is a common error in calculating attributable fractions.2 A review of methods to estimate the PAR reported that using adjusted HRs in the crude formula was “ . . . shown to yield inconsistent estimates . . . and, accordingly, severe bias was exhibited in simulations. . . . ”3
Use of adjusted HRs in the crude PAR formula causes bias because the fraction of the outcome that is attributable to the confounding variables themselves is not adequately accounted for, even though the association of the exposure with the outcome (as represented by the HR) has been adjusted for the confounding variables. When the confounding variables are associated with increased incidence of the outcome, the PAR will be underestimated if the confounding variables (eg, age) are also positively correlated with exposure (eg, body mass index). The PAR will be overestimated if the confounding variables (eg, smoking) are negatively correlated with exposure (eg, body mass index). When the confounding variables are associated with decreased incidence of the outcome, the directions of bias will be reversed. Because the HRs estimated in the study by Forman et al were simultaneously adjusted for a large number of confounding variables, it is not possible to predict the direction or magnitude of bias in their PAR estimates.
A simple PAR computing formula for adjusted HRs is available.2 However, a more efficient and flexible method to estimate the adjusted PAR that uses the same underlying statistical model employed by Forman et al is well documented in statistical4 and medical5 journals.
Financial Disclosures: None reported.
Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature
Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal
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