J Epidemiol Community Health 55:508-514 doi:10.1136/jech.55.7.508
  • Theory and methods

A heuristic approach to the formulas for population attributable fraction

  1. J A Hanley
  1. Department of Epidemiology and Biostatistics, McGill University, 1020 Pine Avenue West, Montreal, Quebec, Canada H3A 1A2
  1. Dr Hanley (James.Hanley{at}McGill.CA)
  • Accepted 14 January 2001


BACKGROUND As the definitional formula for population attributable fraction is not usually directly usable in applications, separate estimation formulas are required. However, most epidemiology textbooks limit their coverage to Levin's formula, based on the (dichotomous) distribution of the exposure of interest in the population. Few present or explain Miettinen's formula, based on the distribution of the exposure in the cases; and even fewer present the corresponding formulas for situations with more than two levels of exposure. Thus, many health researchers and public health practitioners are unaware of, or are not confident in their use of, these formulas, particularly when they involve several exposure levels, or confounding factors.

METHODS/RESULTS A heuristic approach, coupled with pictorial representations, is offered to help understand and interconnect the structures behind the Levin and Miettinen formulas. The pictorial representation shows how to deal correctly with several exposure levels, and why a commonly used approach is incorrect. Correct and incorrect approaches are also presented for situations where estimates must be aggregated over strata of a confounding factor.


  • Funding: this work was supported by an operating grant from the Natural Sciences and Engineering Research Council of Canada.

  • Conflicts of interest: none.