Expanding Attributable Fraction Applications to Outcomes Wholly Attributable to a Risk Factor

The problem central to this document is the estimation of change in disease attributable to an epidemiological exposure variable that stems from a change in the distribution of that variable. We require that both disease and exposure are quantifiable as real numbers, and then ask how to estimate the fraction of disease attributable to exposure, producing the general attributable fraction methodology. After the mathematical framework is in place, we explore the implications of a disease that is wholly attributable to a given risk factor, demonstrate why standard applications of the attributable fractions do not extend, and present general methodological considerations for this case. Finally, we demonstrate the methodology using the example of alcoholic psychoses.