Reducing Bruzzi’s Formula to Remove Instability in the Estimation of Population Attributable Fraction for Health Outcomes

The aim of this study was to reconcile 3 approaches to calculating population attributable fractions and attributable burden percentage: the approach of Bruzzi et al. (Am J Epidemiol. 1985;122(5):904-914.), the maximum-likelihood method of Greenland and Drescher (Biometrics. 1993;49(3):865-872.), and the multivariable method of Tanuseputro et al. (Popul Health Metr. 2015;13:5.). Using data from a statewide point prevalence survey (Western Australian Point Prevalence Survey, 2014) linked to an administrative database, we compared estimates of attributable burden percentage obtained using the contrasting methods in 6 logistic models of health outcomes from the survey, estimating 95% confidence intervals using nonparametric and weighted bootstrap approaches. Our results show that instability can arise from the fundamental algebraic construction of Bruzzi's formula, and that this instability may substantially influence the calculation of attributable burden percentage and associated confidence intervals. These observations were confirmed in a simulation study. The algebraic reduction of Bruzzi's formula to the 2 alternative methods resulted in markedly more stable estimates for population attributable fraction and attributable burden percentage in cross-sectional studies and cohort designs with fixed follow-up time. We advocate the widespread implementation of the maximum-likelihood approach and the multivariable method.