Predicting the second breath alcohol measurement from the first: an application of regression analysis.
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Biomedical subjects
Publications and source records attributed to R G Gullberg.
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Many jurisdictions have "per se" driving-while-intoxicated (DWI) status expressed in terms of a blood-alcohol concentration (BAC) standard (in grams per 100 mL or the equivalent). Since breath-alcohol (BrAC) analysis is typically employed to determine BAC, there is often challenge to the use of an assumed 2100:1 conversion ratio. This concern may be relevant in light of considerable data that show a low percentage of cases in which BrAC greater than BAC, and this concern increases when the BrAC is used to predict BAC in the context of "per se" legislation. Probability theory provides a basis for estimating the likelihood of an individual having a BrAC greater than or equal to g/210 L with a corresponding BAC less than 0.10 g/100 mL. Actual field data from the state of Wisconsin (n = 404) were evaluated to determine the probability of this occurrence. The probability for this occurrence involves the multiplication law for independent events. The computed probability from the data was 0.018. The actual number of occurrences where BrAC greater than or equal to 0.10 g/210 L and BAC less than 0.10 g/100 mL was 5, resulting in a probability of 0.012. The concern of having BrAC greater than BAC at the critical "per se" level has a very low probability of occurrence, which thus supports the reasonableness of "per se" DWI legislation based upon a blood-alcohol standard determined by breath-alcohol analysis.
Random error is associated with breath alcohol measurements, as with all analytical methods. The total random uncertainty of a group of n measurements is typically determined by computing the standard deviation and requiring it to be less than some appropriate level (i.e., +/- 0.0042 g/210 l). The total random uncertainty has two primary sources; the instrumental method and the sample source. These are typically inseparable values. In breath alcohol testing the two primary sample sources are simulators and human breath. The present study evaluates ten groups of simulator samples consisting of ten measurements each on BAC Verifier Datamaster instruments. The data also includes ten breath alcohol measurements from each of 21 individuals following alcohol consumption. The range of standard deviations for the simulator samples was 0.0003-0.0022 g/210 l. The range of standard deviations for the human breath samples was 0.0015-0.0089 g/210 l. Two statistics that test for homogeneity for variances were applied. The simulator samples resulted in a Cochran's C test of 0.5000 and an Fmax test of 48.9. The human breath samples resulted in a Cochran's C test of 0.1519 and an Fmax test of 27.3. All were significant at P less than 0.001. The statistical tests demonstrated that the intragroup variability among the human subjects was comparable to the intragroup variability among the simulator samples. The data also demonstrates that the sample source (simulator or human) is probably the largest contributor to total random uncertainty. Therefore, when duplicate breath alcohol testing from individuals shows variability in the second decimal place the cause is differences in breath samples provided and not instrumental imprecision.
Duplicate breath alcohol testing from each individual provides confidence in the results when reasonable agreement (i.e. +/- 0.02 g/210 L) is achieved. For this reason many jurisdictions require duplicate testing. The State of Washington has recently implemented an infrared breath testing program and now requires two breath samples from each individual. Statistical analysis of 1847 duplicate breath tests is presented. Three variables are analyzed: first alcohol result (ALC1), the absolute difference between the two breath samples (DIFFA), and the signed difference between the two breath samples (DIFFS). The first breath alcohol result ranged from 0.021 to 0.338 g/210 L with a mean of 0.157 g/210 L. The absolute difference ranged from 0.00 to 0.05 g/210 L. The signed difference ranged from -0.05 g/210 L to 0.05 g/210 L. The absolute difference was regressed upon the first alcohol result and resulted in poor linear correlation of r = 0.212. Duplicate breath test differences do not appear to be a function of subject's alcohol level, but rather of sample provision.
The reporting of breath-alcohol measurements truncated to two decimal places is a form of computational error. The magnitude of the error can range from 0.000 to 0.009 g/210 L. The truncation error will follow a uniform distribution. A total of 500 breath-alcohol test measurements were evaluated to determine the distribution of the third digit. There are 10 possible discrete values for the third digit. The frequency of each third digit was found to range from 44 for the lowest to 57 for the highest. The data closely approximated the uniform distribution. To conform exactly with the uniform distribution, there would have to be 50 of each decimal value. Given that the third digit approximates the uniform distribution, one cannot attach a greater probability to a particular third-digit value as opposed to another.
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A breath alcohol profile is generated as a continuous function of time while a person is providing a breath sample. This paper describes a data acquisition system which samples breath alcohol concentrations at discrete intervals during exhalation. The data are stored on disk for later analysis. It is shown that the area under the profile curve for samples preceded by breath-holding is significantly larger than when breathing is normal prior to sample provision (p less than 0.001). The differences between the breath alcohol concentration measurements are also statistically significant (p less than 0.001) for the two different breathing patterns prior to breath exhalation. These results have physiological implications and suggest another means of evaluating breath alcohol profiles.
The effect of short time interval sampling between replicate breath alcohol samples has been investigated. The results from 10 samples, which were collected approximately one minute apart from eight individuals and approximately 20 seconds apart from one individual, were evaluated by simple linear regression. The regression coefficient (slope) and its standard error were evaluated for the presence of any trend in alcohol depletion. Other statistical analyses were also included in this assessment. All nine subjects had linear regression coefficients for the end-expiratory results that were not significantly different from zero (P > 0.05). In view of the respiratory physiology, there does not appear to be any measurable depletion of breath alcohol concentration due to sampling intervals as short as one minute.
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The mathematical analysis of time domain data provides a useful tool for evaluating biological and instrumental systems. Breath alcohol profile measurements generated during exhalation constitute biological signals that can be subjected to a variety of mathematical treatments. The present paper discusses the application of a variety of mathematical procedures to breath alcohol profiles. These mathematical procedures include model approximation, data smoothing, integration, differentiation, and fourier transformation. The different mathematical procedures provide insight into the physiology of breath alcohol measurement and suggest forensic as well as instrumental applications.
Breath alcohol simulator devices (simulators) containing alcohol and water solutions are used to calibrate and test breath-testing instruments. The manufacturers of simulators design them to contain 500 mL of solution. This study evaluated the variability observed among three different groups of data: one group (experimental) in which the solution volume varied from 400 mL to 600 mL, one group (control) in which the simulator volume remained constant at 500 mL for each aliquot, and finally one group consisting of field simulator measurements collected over time. The infrared breath test instrument employed was a BAC Verifier Datamaster. A one-way analysis of variance and the Cochran's C for equal variances were applied to the data. The results indicated that when the solution volume remained at 500 mL, there was nearly as much or greater within-run variability as when the volumes were varied from 400 mL to 600 mL. Both the experimental and control groups showed statistical significance for the one-way ANOVA and were considered within-run measurements. The high within-run instrumental precision (CV approx. 1%) probably accounts for these results. The field data, considered between-day measurements, had larger within-group variability and resulted in a nonsignificant ANOVA. Small variations from the 500-mL volume in a simulator do not result in a statistically significant difference where between-day measurements are evaluated.
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This study evaluated the stability of cocaine, benzoylecgonine, and cocaethylene in postmortem fluids in cases of cocaine-related death. Femoral and ventricular blood and cisternal cerebrospinal fluid were collected soon after death and again at the time of autopsy. In addition, iliac blood was collected at autopsy. There were no consistent patterns of site-specific differences for any of the analytes, and the central compartment showed both higher and lower concentrations than the peripheral. There was no consistent pattern of direction or magnitude of change in the concentrations with respect to time for any of the analytes. This is consistent with anecdotal reports from other workers and is believed to be a result of competing processes of tissue release and chemical and enzymatic degradation of the analytes. Postmortem cocaine and metabolite concentrations in blood are not necessarily reflective of the perimortem concentrations and should not be the primary consideration in determining the cause of death in suspected cocaine-related deaths.