Development of an exact theory of decomposing population attributable fractions and application to decomposition of Alzheimer’s disease risk

A new mathematically exact method of population attributable fraction (PAF) decomposition free of limitations inherent in existing approaches was developed and compared to existing methods based on the Miettinen, Norton, and Niedhammer-Chastang formulae. The developed approach is applicable for two broadly used study designs involving either a single or multiple data sources to measure the predictors and outcomes of interest. The approach was applied to Medicare data to estimate six disease-specific contributions to the overall PAF of Alzheimer's disease risk: stroke (7.2%), hypertension (6.5%), diabetes (4.4%), renal disease (0.9%), traumatic brain injury (0.9%), and depression (9.6%). We found that the approximation based on the Norton formula was the best approach among the methods utilized prior to the development of our approach. However, the quality of such approximations and the respective biases should be re-estimated on a case-by-case basis. An extension of the approach to health disparities was proposed and discussed.