title: Why population attributable fractions can sum to more than one.
abstract: BACKGROUND
  Population attributable fractions (PAFs) are useful for estimating the proportion of disease cases that could be prevented if risk factors were reduced or eliminated. For diseases with multiple risk factors, PAFs of individual risk factors can sum to more than 1, a result suggesting the impossible situation in which more than 100% of cases are preventable.
  
  
  METHODS
  A hypothetical example in which risk factors for a disease were eliminated in different sequences was analyzed to show why PAFs can sum to more than 1.
  
  
  RESULTS
  PAF estimates assume each risk factor is the first to be eliminated, thereby describing mutually exclusive scenarios that are illogical to sum, except under special circumstances. PAFs can sum to more than 1 because some individuals with more than one risk factor can have disease prevented in more than one way, and the prevented cases of these individuals could be counted more than once. Upper and lower limits of sequential attributable fractions (SAFs) can be calculated to describe the maximum and minimum proportions of the original number of disease cases that would be prevented if a particular risk factor were eliminated.
  
  
  CONCLUSIONS
  Improved descriptions of the assumptions that underlie the PAF calculations, use of SAF limits, or multivariable PAFs would help avoid unrealistic estimates of the disease burden that would be prevented after resources are expended to reduce or eliminate multiple risk factors.
authors.affiliation: Division of Adult and Community Health, National Center for Chronic Disease Prevention and Health Promotion, Centers for Disease Control and Prevention, Atlanta, Georgia 30341-3724, USA. axr9@cdc.gov
authors.forename: Alexander K
authors.initials: AK
authors.lastname: Rowe
authors.forename: Kenneth E
authors.initials: KE
authors.lastname: Powell
authors.forename: W Dana
authors.initials: WD
authors.lastname: Flanders
mesh_terms: D002908:Chronic Disease; D004812:Epidemiologic Methods; D005260:Female; D006304:Health Status; D006801:Humans; D017053:Infection Control; D008297:Male; D015233:Models, Statistical; D010349:Patient Compliance; D011322:Primary Prevention / Q000379:methods*; D011634:Public Health; D018570:Risk Assessment; D012307:Risk Factors; D012680:Sensitivity and Specificity