The proportion of a disease or outcome that is due to the influence of some external causal factor is called the attributable fraction [

1]. In alcohol epidemiology, this fraction is termed the alcohol-attributable fraction (AAF) and is defined as that proportion of disease that would disappear if alcohol consumption went to zero. In the categorical case [

2], it has been calculated using the formula [

1,

3]:

where P_{i} represents the proportion of the population exposed in group i and RR_{i} is the relative risk of mortality in exposed group i compared with the reference group (in alcohol often non-drinkers or lifetime abstainers). This is computed for as many drinking categories exist, from i = 0 to k, where i = 0 represents the reference group. This framework has been used extensively by the World Health Organization to estimate the burden of disease as a part of its Comparative Quantification of Risk analysis [4–6], and has been used by colleagues in other countries to establish the alcohol-attributable burden of disease [7–9].

However, these calculations have historically been relatively simplistic, with calculations usually being performed for three categories of average consumption only. More recently, a more differentiated consideration of average alcohol consumption has been introduced [10].

The calculation of AAF for injuries is a conceptually different than for chronic disease, since the acute effects of alcohol become very important and reliance on average consumption alone would considerably bias the results towards lower fraction estimates [11, 12].

Recent work by this group has attempted to improve on the calculation of the AAF for injury by trying to account multiple drinking scenarios and by including other alcohol-drinking variables to better assess fatal injury risk [13, 14].

This has meant incorporating 2 different dimensions of alcohol consumption for computing injury AAF: (1) drinking pattern measures such as binge drinking (both number of weekly occasions and the amount consumed per occasion) and (2) by additionally accounting for mean daily consumption of alcohol by modeling the specific distribution of drinkers and their daily drinking habits within a given population. What's more, we have tried to include alcohol metabolism rates in the liver to better assess time at risk of injury during intoxication, and, even more recently, attempting to account for the discrepancy between per capita consumption versus actual consumption in average daily alcohol drinking levels [15, 16].

The end result of these attempts has been the incorporation of data from many different sources, making this AAF calculation a veritable "data melting pot" - it combines survey data, meta-analyses of relative risk, mortality data, and experimental lab data. While this is not problematic for the calculation of the AAF point estimate, it is very complicated for the calculation of the variance around each point estimate, as each source of data has its own distribution and variance, making combining their different errors complex.

This paper attempts a novel method (the distributional approach) developed by our group to more accurately calculate the AAF and its variance for injury mortality. The main objectives of this paper are four-fold:

1. Present the method to calculate alcohol-attributable fractions for fatal injury, its inherent sources and assumptions, and its data sources.

2. Present the point estimate and uncertainty estimates

3. Provide sensitivity analyses to provide context and alternative scenarios for the above

4. Discuss future improvements that will help in more accurate calculation of the AAF for mortality