J Epidemiol Community Health 2001;55:508-514 ( July )

Theory and methods

A heuristic approach to the formulas for population attributable fraction J A Hanley

Department of Epidemiology and Biostatistics, McGill University, 1020 Pine Avenue West, Montreal, Quebec, Canada H3A 1A2

Correspondence to: Dr Hanley (James.Hanley{at}McGill.CA)

Accepted for publication 14 January 2001

BACKGROUNDAs 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/RESULTSA 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.


Keywords: attributable risk epidemiology; regression; case-control study; aetiological fraction; statistics; confounding; matching stratified data

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© 2001 by Journal of Epidemiology and Community Health
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