Methods

The underlying experimental datasets were derived from four previously published controlled drinking studies conducted at the Institute of Legal Medicine, Goethe University Frankfurt am Main, whose data were pooled as the primary empirical basis for the original regression-based modelling, Monte Carlo simulation, and derivation of the forensic correction algorithm presented herein. The studies involved healthy adult volunteers who provided written informed consent, and all studies were approved by the responsible ethics committee. Participants consumed alcoholic beverages comprising wheat beer (with and without additional administration of the purported sobering agent “Eezup!”), apple wine (commercially available and self-produced), grappa, and vodka, as described in detail elsewhere [4–7]. Where specified in the original protocols, sobriety was confirmed prior to alcohol administration, and participants received a standardised meal to minimise variability in absorption conditions. Alcohol doses were individually calculated based on sex and body weight using Widmark-based approaches, with adjustment for presystemic elimination/resorption deficit, targeting peak blood alcohol concentrations of approximately 1.0‰ under controlled conditions, and blood sampling was continued until complete ethanol elimination. The original study designs did not include stratification based on individual alcohol tolerance; this reflects a heterogeneous volunteer sample rather than a preselected tolerance group and is compatible with the forensic aim of developing a robust rule applicable to inter-individual variability in practice.

Overall, data from 87 participants were included. As the administration of “Eezup!” showed no statistically significant effect on BAC elimination [4], the corresponding datasets were pooled without modification. For quantitative evaluation of ethanol elimination in the low-concentration range, all individual post-absorptive BAC-time curves were systematically screened for data points ≤ 0.15‰. For each subject, the elimination phase was defined from the last occurrence of the individual peak BAC (cmax) to the end of the measurement series. Within this phase, all measured values ≤ 0.15‰ were included. In total, 459 individual post-peak data points ≤ 0.15‰ were available for analysis.

BAC-time data were analysed using linear regression models to characterise ethanol elimination. For each individual curve, the post-absorptive phase was identified, with the upper limit defined as the maximum measured BAC (cmax) and the lower limit as the first zero or near-zero measurement. Linear regression was applied to the full elimination phase (cmax-0‰) as well as to predefined sub-intervals ([0.9 − 0.6‰], [0.6 − 0.3‰], [0.3-0‰], [cmax-0.6‰], and [cmax-0.9‰]). The resulting slope coefficients represent individual ethanol elimination rates expressed in ‰/h.

All analyses were primarily performed using Python (pandas,_ NumPy_,_ scikit-learn_). To ensure robustness and reproducibility, regression analyses were independently cross-checked using Microsoft Excel (LINEST function).

In a second analytical step, simulation-based retrograde calculations were performed to develop practical back-calculation models for low measured BAC values (< 0.15‰). Three approaches were evaluated: a conservative model, a realistic model, and an extreme model. In all models, back-calculation was based on a standard elimination rate of 0.1‰/h; in the realistic and extreme models, additional time deductions were applied to account for reduced elimination rates in the low-BAC range.

As a reference, the uncorrected linear conservative model for determination of the minimum BAC was used, which back-calculates using a low constant elimination rate of 0.1‰/h over the time interval t between blood sampling and the incident time:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BAC_{retrograde}=BAC_{measured}+0.1\bullet t$$\end{document}

The realistic model was derived from mean elimination rates observed below 0.15‰, incorporating confidence interval-based adjustments to account for inter-individual variability. The extreme model was based on the lowest empirically observed elimination rate to ensure maximal protection against overestimation.

Model robustness was assessed using Monte Carlo simulations (1,000 iterations per BAC range), generating normally distributed elimination rates based on the observed mean and standard deviation. Resulting distributions of back-calculation time deductions were evaluated to quantify uncertainty and validate model stability.