Population attributable fraction: comparison of two mathematical procedures to estimate the annual attributable number of deaths.

Objective: The purpose of this paper was to compare two mathematical procedures to estimate the annual attributable number of deaths (the Allison et al procedure and the Mokdad et al procedure), and derive a new procedure that combines the best aspects of both procedures. The new procedure calculates attributable number of deaths along a continuum (i.e. for each unit of exposure), and allows for one or more neutral (neither exposed nor nonexposed) exposure categories.

Methods: Mathematical derivations and real datasets were used to demonstrate the theoretical relationship and practical differences between the two procedures. Results of the comparison were used to develop a new procedure that combines the best features of both.

Findings: The Allison procedure is complex because it directly estimates the number of attributable deaths. This necessitates calculation of probabilities of death. The Mokdad procedure is simpler because it estimates the number of attributable deaths indirectly through population attributable fractions. The probabilities of death cancel out in the numerator and denominator of the fractions. However, the Mokdad procedure is not applicable when a neutral exposure category exists.

Conclusion: By combining the innovation of the Allison procedure (allowing for a neutral category) and the simplicity of the Mokdad procedure (using population attributable fractions), this paper proposes a new procedure to calculate attributable numbers of death.