Uncertainty in Widmark calculations: ABV variation in packaged versions of the most popular beers in the UK

Abstract

Forensic practitioners regularly use the Widmark equation to determine theoretical blood alcohol concentrations for use in cases involving alcohol. It is important in these calculations to determine the uncertainty associated with any result. Previous work has investigated the uncertainty in %ABV from beers produced by small independent breweries in the UK but did not study the top selling beers. The top selling lagers and ales/bitters in the UK were identified by sales volume and the alcohol by volume determined. This data was then used to determine the percent coefficient of variation (%CV) that should be used by forensic practitioners when constructing alcohol technical defence reports for use in forensic cases. These samples, from what may be described as 'big' brewers, were determined to have a smaller root mean square error (RMSE) (±0.1 %v/v, n = 35), and %CV than those previously reported for beers produced by small, independent breweries in the UK. The results from this study shows that different RMSE's should be used for %ABV when determining the uncertainty of results from Widmark calculations when drinks have been consumed from either 'big' brewers or small, independent breweries.

Revised equations allowing the estimation of the uncertainty associated with the Total Body Water version of the Widmark equation

“…%CV Reference e v = coefficient of variance of the volume of drink consumed See table 5 of reference for details. Commonly -2.35% [16] e z = coefficient of variance of the alcoholic strength of the drink consumed Depends on ABV needs to be calculated from SD [17] and [18] "Craft" Beer (SD) −± 0.48% v/v "Commercial" Beer (SD) −± 0.1% v/v e d = coefficient of variance of density of alcohol (ethanol) Considered a constant [16] e B = coefficient of variance of the blood alcohol analysis result Determined from the Measurement variability of the analytical method being used commonly 5%. [19] e β = coefficient of variance of alcohol elimination rate 26.3 mg/100 mL/h [20] e t = coefficient of variance of the duration of the drinking session Based on case information n/a e TBW = coefficient of variance of the total body water of the subject 9.09 L [5] e Fwater = coefficient of variance of fraction of blood volume that is water Considered a constant [5,21]…”

The Contribution of Body Mass and Volume of Distribution to the Estimated Uncertainty Associated with the Widmark Equation

“…Recent work has started to investigate and provide improved estimates of the variability associated with the remaining parameters in the Widmark equation. These include the estimated uncertainty that is likely to be found with the mass of ethanol consumed ( A ), the density of ethanol ( d ) (10), volume of pure ethanol ( v ) (10), and also the ethanol concentration (% v/v) of alcoholic beverages ( z ) in both craft (11) and popular beers (12). An estimate of uncertainty was determined in these variables based on relevant legislation or experimental studies.…”