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

The Widmark equation is used forensically for the determination of the amount of ethanol (alcohol) that may have been consumed and also to determine the blood alcohol concentration (BAC) of an individual at a specific time. It is important to be able to estimate the uncertainty associated with Widmark equations. To date, there has been no detailed determination of contribution to the final uncertainty of Widmark calculations of the volume of distribution of ethanol (V_d), using anthropometric equations, or the contribution of an individual’s body mass. Using published data, published literature, and freedom of information data, we determined that the variability (%CV) associated with V_d was ~10% (Watson et al. and Forrest anthropometric equations) and that the %CV associated with estimated body mass was ~15% compared to ~3% when body mass was directly measured. These data allow an estimation of the overall uncertainty of Widmark calculations using general error propagation. The estimated total uncertainty for BAC calculations increased from ~11% (volume consumed) and ~22% (BAC) to ~19% (volume consumed) and ~37% (BAC) when using measured body mass compared to estimated body mass. These results demonstrate that forensic practitioners should be mindful of the increase in estimated uncertainty in calculated Widmark equation results when estimated body mass is used rather than measured body mass. These data further improve the knowledge around the uncertainty of results calculated with the Widmark equation.     

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

Forensic practitioners regularly use the Widmark equation to determine theoretical blood alcohol concentrations for use in cases involving alcohol. It is important with these calculations to determine the uncertainty associated with any result. Previous work has investigated the uncertainty in percent alcohol by volume (%ABV) from beers produced by small independent breweries in the UK but did not study the top selling beers in the UK. The top selling lagers and ales/bitters in the UK were identified by sales volume and the %ABV determined. These 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 depending if the drinks consumed have been from either ‘big’ brewers or small, independent breweries.     

Widmark factors for local Chinese in Hong Kong. A statistical determination on the effects of various physiological factors

The Widmark formula has been widely adopted in forensic applications to drink driving cases for the last 70 years. It is known that the amount of alcohol consumed and the body weight of the drinkers are important information for the estimation of blood alcohol concentration (BAC). However, the direct application of the Widmark factors derived from Caucasian to the calculation of BAC for the Chinese population often encounters serious challenges. Owing to this inherent weakness, a thorough analysis to determine the theoretical Widmark factors for the Chinese population, r(0) at the start of drinking and the practical factors, r(peak), at peak BAC was conducted. In the present study, other factors such as gender, stomach condition and other physiological conditions are taken into account. The determined theoretical Widmark factors, r(0,) for local Chinese male and female are 0.68 and 0.59 (with BAC in the units of weight/volume), respectively, demonstrating the applicability of the Widmark formula to the Chinese population. The practical factors at peak BAC, r(peak), were also determined to serve the forensic purpose of refuting the "hip-flask" defence in drink driving cases. Findings show that gender and stomach condition are the key factors that could statistically explain the variability of both r(0) and r(peak).     

Estimating the uncertainty associated with Widmark's equation as commonly applied in forensic toxicology

No computation is performed more frequently by forensic toxicologists than that involving Widmark's equation. The equation is employed to estimate either the number of drinks consumed or the corresponding blood or breath alcohol concentration. Despite the wide use of Widmark's equation, rarely is an uncertainty estimate also provided. Estimates from Widmark's equation involve at least seven uncertain random variables. Uncertainty estimates are presented that rely on methods of general error propagation compared to a method developed by Widmark. Assuming reasonable variable and uncertainty estimates, the error propagation method yielded for N=10.4 drinks, a combined uncertainty (standard deviation) of 1.3 drinks (CV=12.3%). Similarly, estimating the blood alcohol concentration yielded for 0.120 g/100 ml, an uncertainty of 0.0255 g/100 ml (CV=21.2%). Widmark's uncertainty method yielded 1.6 drinks (CV=15.4%). The derivation of Widmark's uncertainty estimate is also presented, showing that he considered only rho and beta to be uncertain. Widmark estimates for the number of drinks should include a 2CV estimate of approximately 25% while the blood alcohol concentration estimate should include a 2CV estimate of approximately 42%. Including valid estimates of uncertainty should enhance the legal admissibility and confidence for Widmark estimations.     

The influence of alcohol content variation in UK packaged beers on the uncertainty of calculations using the Widmark equation

It is common for forensic practitioners to calculate an individual's likely blood alcohol concentration following the consumption of alcoholic beverage(s) for legal purposes, such as in driving under the influence (DUI) cases. It is important in these cases to be able to give the uncertainty of measurement on any calculated result, for this reason uncertainty data for the variables used for any calculation are required. In order to determine the uncertainty associated with the alcohol concentration of beer in the UK the alcohol concentration (%v/v) of 218 packaged beers (112 with an alcohol concentration of ≤5.5%v/v and 106 with an alcohol concentration of >5.5%v/v) were tested using an industry standard near infra-red (NIR) analyser. The range of labelled beer alcohol by volume (ABV's) tested was 3.4%v/v – 14%v/v. The beers were obtained from a range of outlets throughout the UK over a period of 12?months. The root mean square error (RMSE) was found to be ±0.43%v/v (beers with declared %ABV of ≤5.5%v/v) and ±0.53%v/v (beers with declared %ABV of >5.5%v/v) the RMSE for all beers was ±0.48%v/v. The standard deviation from the declared %ABV is larger than those previously utilised for uncertainty calculations and illustrates the importance of appropriate experimental data for use in the determination of uncertainty in forensic calculations.     

Elimination rates of breath alcohol

Legal driving limits are set coequally with 0.5 g/L blood alcohol concentration (BAC) or 0.25 mg/L breath alcohol concentration (BrAC) in Austria as well as in other European countries. As mostly some time elapses between BrAC measurement and driving offence, a back calculation of alcohol concentrations is often required. The calculation of hourly BrAC elimination rates can thereby help to avoid unnecessary variances. A study with 59 participants was performed under social conditions. BrAC was determined with the legally accredited Alcotest 7110 MK III A every 30 min, and concomitantly venous blood samples were drawn. Five hundred and four BrAC/BAC value pairs were evaluated. The overall mean peak BrAC was calculated with 0.456 mg/L (±0.119 mg/L standard deviation). The mean hourly BrAC elimination rate was overall determined with 0.082 mg/L per h (0.050–0.114, 95% range). Mean rate of females (0.087 mg/L h⁻¹) and the according 95% limits were statistically significantly higher than of males (mean rate 0.078 mg/L h⁻¹, p < 0.04). Our results confirm the possibility to implement hourly BrAC elimination rates, provided that adequate statistical ranges and basic forensic scientific rules that have been set up for alcohol back calculations are observed.     

Simplified estimation of Widmark "r" values by the method of Forrest.

To simplify blood alcohol calculations, tables are presented giving Widmark 'r' values estimated by the method of ARW Forrest (Journal of the Forensic Science Society 1986; 27: 249-252).     

A Theoretical Analysis of Alcohol Regulation and Drinking-Related Economic Crime

Alcohol consumption is widely believed to influence criminal activity, and numerous sociological, criminological, and psychological studies demonstrate an apparent positive correlation between drinking and crime. Using a multiattribute model of offender and victim behavior, this study examines the theoretical effects of changes in the price of alcohol on the incidence of crimes committed for economic gain. It is shown that in the general case price effects do not result in an unambiguous decrease in the rates of crime or victimization even when the models are constructed to impose a bias towards the finding of a causal negative price effect. Using a modified model of the drinking offender that imposes even further structure on the model, it is shown that the realization and magnitude of a negative equilibrium alcohol price effect will likely depend upon the implementation of complementary alcohol control policies. The implications of the theoretical analysis to policy implementation and empirical research are also considered.     

The Role of Perpetrator Alcohol Use in the Injury Outcomes of Intimate Assaults

Little research has been conducted on the role of perpetrator alcohol use in the injury outcomes of intimate assaults, although alcohol use by an intimate partner may be related to more severe assault outcomes (physical injury and need for medical attention) than is no alcohol use. The role of perceived perpetrator alcohol use in the injury outcomes of intimate assaults (N = 909) was analyzed using 1992–1996 National Crime Victimization Survey data. Logistic regression analyses demonstrated that perpetrator alcohol use was associated with increased likelihood of physical injury and marginally associated with more medical attention seeking by the victim when demographic variables and assault characteristics were controlled. Suggestions for future research on the relationship between alcohol and intimate assault outcomes are presented.     

Alcohol metabolism of local Chinese in Hong Kong: a statistical determination on the effects of various physiological factors

A study was designed to examine the elimination rate of alcohol from the body of the local Chinese after consumption of different types of alcoholic drinks. The breath alcohol of 184 healthy volunteers was determined and converted into blood alcohol levels after they finished drinking. Information on the type and volume of alcoholic drinks consumed, age group, sex, drinking habit, and drinking on empty stomach or with/after meal was recorded for each participant. The results show that the elimination rate of an individual can be explained in terms of physiological variables including sex and drinking habit. The determined elimination rates allow forensic toxicologists to back calculate the blood alcohol concentration (BAC) of the drivers at the time of accident in drunk driving cases. The elimination rates of blood alcohol at 95% prediction intervals for male and female are in the range of 9.5-23.8 mg/100 ml/h and 11.1-37.1 mg/100 ml/h, respectively.     

The relationship between alcohol elimination rate and increasing blood alcohol concentration--calculated from two consecutive blood specimens

In the period 1991-2005, a blood-alcohol concentration (BAC) analysis was carried out at the Institute of forensic medicine in Novi Sad including 2023 two consecutive blood specimens using the Headspace Gas Chromatography method. Cases with no alcohol concentration values, as well as cases where blood samples were taken within 1 h after the criminal act, were not taken into consideration. Following this rule, 1198 cases were considered in this study and all samples were grouped in 29 ranges of BAC1 of delta(BAC) = 0.1 g/kg, starting from 0.1-0.19 g/kg to 2.9-2.99 g/kg of absolute alcohol. Gathered results and elimination curve differ from the zero-order model of elimination proposed by Widmark and point to an elimination process similar to a well-known Michaelis-Menten elimination kinetics model and its variants. Results reported in this study show dependence of alcohol elimination rate (beta-slope) and BAC value. The analysis of beta60-slope versus BAC shows that a correlation between beta60 (y) and BAC (x) has a logarithmic trend line. The value of alcohol elimination rate shows a slight increment with increase of BAC alcohol, with the mean value of beta60 = 0.221 +/- 0.075 g/kg. Differences in values of beta60 among consecutive intervals of delta(BAC) = 0.1 g/kg are not significant (p>0.05). When obtained samples were grouped into ranges of 0.5 g/kg each in these intervals beta60 had the following values by range: 0.1-0.49 g/kg = 0.139 g/kg +/- 0.035; 0.5-0.99 g/kg = 0.184 g/kg +/- 0.043; 1-1.49 g/kg = 0.213 g/kg +/- 0.052; 1.5-1.99 g/kg = 0.239 g/kg +/- 0.058; 2-2.49 g/kg = 0.265 g/kg +/- 0.073; 2.5-2.99 g/kg = 0.306 g/kg +/- 0.096. Differences in values of beta slope among consecutive intervals of delta(BAC) = 0.5 g/kg are significant (p<0.01). The elimination curve in the BAC interval 0.5-2.5 g/kg has a linear trend, while beta-slope (y)/BAC (x) correlation is given as beta60 = 0.15 g/kg + (0.05 g/kg x BAC). Retrograde calculation of the blood alcohol concentration in tempore criminis (BAC(tc)) based on the determined alcohol concentration in the blood specimen (BAC(t)) shows a statistically significant difference between BAC(tc) calculated using a standard zero-order model versus corrected methodology. The higher the BAC(t) and the longer the calculation time, the greater and statistically more significant (p<0.01) is the difference between the calculated values of BAC(tc).     

Evaluation of Stature Estimation from the Database for Forensic Anthropology*†

Abstract: Trotter and Gleser’s ( 1 - 3 ) stature equations, conventionally used to estimate stature, are not appropriate to use in the modern forensic context. In this study, stature is assessed with a modern (birth years after 1944) American sample (N = 242) derived from the National Institute of Justice Database for Forensic Anthropology in the United States and the Forensic Anthropology Databank. New stature formulae have been calculated using forensic stature (FSTAT) and a combined dataset of forensic, cadaver, and measured statures referred to as Any Stature (ASTAT). The new FSTAT‐based equations had an improved accuracy in Blacks with little improvement over Ousley’s ( 4 ) equations for Whites. ASTAT‐based equations performed equal to those of FSTAT equations and may be more appropriate, because they reflect both the variation in reported statures and in cadaver statures. It is essential to use not only equations based on forensic statures, but also equations based on modern samples.     

血液乙醇检测内外标法比较研究

目的通过比较内标法和外标法对血液乙醇含量检测结果,探讨外标法在法医学实践中的应用价值。方法通过收集2005年10月~2006年12月间本中心符合检测要求的血液样品263例,每例分别采用内标法和外标法进行血液样品乙醇含量检测,比较其检测结果。结果外标法检测时间短(2.5min),用量0.5ml,而内标法检测时间长(6.5min),样品量1.0ml;外标法检测血乙醇平均浓度为89.30mg/100ml,内标法检测血乙醇平均浓度为92.37mg/100ml,P=0.001。结论外标法检测时间短(2.5min),用量少,节约检材,可作为大量待测血液样本的筛选检查手段。     

Psychometric properties of the Barratt Impulsiveness Scale version 11 among a Portuguese sample of incarcerated juvenile offenders

The aim of the present study was to examine the psychometric properties of the Barratt Impulsiveness Scale version 11 (BIS-11) among a forensic sample of incarcerated male juvenile offenders (N?=?221). Principal Component Analysis with Promax rotation revealed the expected 6-factor structure, but Confirmatory Factor Analysis of the 6-factor first-order and the 3-factor second-order factorial structures did not present sufficiently good fits. Despite that, the Portuguese adaptation of the BIS-11 demonstrated generally acceptable psychometric properties in terms of internal consistency, mean inter-item correlation, convergent validity, discriminant validity, and concurrent validity that justifies its use among the youth forensic population. Statistically significant associations were found with age of crime onset, conduct disorder, crime seriousness, alcohol use and drug use.     

Employing components-of-variance to evaluate forensic breath test instruments

The evaluation of breath alcohol instruments for forensic suitability generally includes the assessment of accuracy, precision, linearity, blood/breath comparisons, etc. Although relevant and important, these methods fail to evaluate other important analytical and biological components related to measurement variability. An experimental design comparing different instruments measuring replicate breath samples from several subjects is presented here. Three volunteers provided n = 10 breath samples into each of six different instruments within an 18 minute time period. Two-way analysis of variance was employed which quantified the between-instrument effect and the subject/instrument interaction. Variance contributions were also determined for the analytical and biological components. Significant between-instrument and subject/instrument interaction were observed. The biological component of total variance ranged from 56% to 98% among all subject instrument combinations. Such a design can help quantify the influence of and optimize breath sampling parameters that will reduce total measurement variability and enhance overall forensic confidence.     

Forensic appraisal of death due to acute alcohol poisoning: three case reports and a literature review

Death due to acute alcohol poisoning lacks specific anatomical characteristics, compared with other deaths due to drug poisoning. We report three forensic cases of death from acute alcohol poisoning due to inhibition of the respiratory centre and eventual asphyxia. Blood alcohol concentrations in the three fatalities were 5.28, 3.33 and 3.78 mg/mL, respectively. Lethal doses and blood alcohol concentrations showed differences between individuals. Detailed auxiliary tests besides autopsy were undertaken. These cases show that forensic scientists should exclude other causes of death, combine the autopsy with auxiliary tests, and then make an appraisal.     

Alcohol content of beer and malt beverages: forensic consideration

Beer consumption is commonly an issue in a medico-legal setting, requiring estimates either of a likely blood alcohol concentration (BAC) for a given pattern of consumption or vice versa. Four hundred and four beers and malt beverages available for sale in the State of Washington were tested by gas chromatography for their alcohol content. Considerable variability in the alcoholic strength was found, even within the same class. Overall the range of concentrations was 2.92%v/v to 15.66%v/v. The mean alcohol concentration for ales was 5.51%v/v (SD 1.23%v/v), and for lagers, 5.32% (SD 1.43%v/v). Some specialty brews had characteristically higher or lower mean concentrations: ice beers 6.07%v/v, malt liquor 7.23%v/v, light beer 4.13%v/v, seasonal ales 6.30%v/v. Six brands of lager and four light beers account for the majority of all beer sales in the United States, and the mean alcohol concentration for these products was measured as 4.73%v/v and 4.10%v/v respectively. Few of the beers (17%) were labeled with respect to alcohol content, and in some cases, there was a significant disparity between the concentration listed on the label, and the measured alcohol concentration. Toxicologists need to exercise caution when performing Widmark type calculations, using all available information to select the most appropriate estimate for alcoholic strength of a beer or malt beverage.     

The Accuracy of Handheld Pre‐Arrest Breath Test Instruments as a Predictor of the Evidential Breath Alcohol Test Results

Drunk driving is a serious threat to public safety. All available and appropriate tools for curbing this threat should be employed to their full extent. The handheld pre‐arrest breath test instrument (PBT) is one tool for identifying the alcohol‐impaired driver and enforcing drunk driving legislation. A set of data was evaluated (n = 1779) where the PBT instrument was employed in drunk driving arrests to develop a multivariate predictive model. When maintained and operated by trained personnel, the PBT provides a reasonable estimate of the evidential test result within the relevant forensic range (95% prediction interval:  ± 0.003 g/210 L). ROC analysis shows that a multivariate model for PBT prediction of the evidentiary alcohol concentration above versus below the legal limit of 0.08 g/210 L has excellent performance with an AUC of 0.96. These results would be of value in evidential hearings seeking to admit the PBT results in drunk driving trials.     

Results of a proposed breath alcohol proficiency test program

Although proficiency test programs have long been used in both clinical and forensic laboratories, they have not found uniform application in forensic breath alcohol programs. An initial effort to develop a proficiency test program appropriate to forensic breath alcohol analysis is described herein. A total of 11 jurisdictions participated in which 27 modern instruments were evaluated. Five wet bath simulator solutions with ethanol vapor concentrations ranging from 0.0254 to 0.2659 g/210 L were sent to participating programs, instructing them to perform n = 10 measurements on each solution using the same instrument. Four of the solutions contained ethanol only and one contained ethanol mixed with acetone. The systematic errors for all instruments ranged from -11.3% to +11.4% while the coefficient of variations ranged from zero to 6.1%. A components-of-variance analysis revealed at least 79% of the total variance as being due to the between-instrument component for all concentrations. Improving proficiency test program development should consider: (1) clear protocol instructions, (2) frequency of proficiency testing, (3) use lower concentrations for determining limits-of-detection and -quantitation, etc. Despite the lack of a biological component, proficiency test participation should enhance the credibility of forensic breath test programs.     

Error and its Meaning in Forensic Science

The discussion of “error” has gained momentum in forensic science in the wake of the Daubert guidelines and has intensified with the National Academy of Sciences' Report. Error has many different meanings, and too often, forensic practitioners themselves as well as the courts misunderstand scientific error and statistical error rates, often confusing them with practitioner error (or mistakes). Here, we present an overview of these concepts as they pertain to forensic science applications, discussing the difference between practitioner error (including mistakes), instrument error, statistical error, and method error. We urge forensic practitioners to ensure that potential sources of error and method limitations are understood and clearly communicated and advocate that the legal community be informed regarding the differences between interobserver errors, uncertainty, variation, and mistakes.