Journal of Analytical Toxicology,Vol. 31, January/February2007 I Comparisonof Hospital LaboratorySerum Alcohol LevelsObtained by an EnzymaticMethod with Whole Blood LevelsForensicallyDetermined by Gas Chromatography Matthew T. Barnhill, Jr.* 110 Oak Street, Fairhope, Alabama 36532 Donald Herbert University of South Alabama College of Medicine, Department of Radiology, 2451 Fillingim Street, Mobile, Alabama 36617 David J. Wells, Jr. Mission Pharmacal Laboratory, 1325 E. Durango, San Antonio, Texas78210 I Abstract Estimating the equivalent whole blood ethanol level from a serum or plasma determination has been addressed by numerous articles in both the clinical and forensic literature. All previous studies have either involved sample sizes insufficient for adequate statistical evaluation or have utilized gas chromatography for both serum and whole blood analysis. In this study, based on samples from 212 consecutive patients admitted to a hospital trauma center, serum was assayed for ethanol using an enzymatic oxidation method, and the results were compared to whole blood samples taken simultaneously and analyzed by headspace gas chromatography in a forensic toxicology laboratory. Contrary to previously published conclusions, it was found that the serum/whole blood alcohol ratio (SAC/BAC) is concentrationdependent, with average values ranging from around 1.12 to as high as around 1.18, depending on SAC, thus precluding a generally applicable SAC/BAC conversion factor. However, a linear regression model was found to provide adequate prediction intervals at any desired level of confidence for whole blood alcohol from serum alcohol levels up to 300 mg/dL. For example, at a confidence level of 95%, an SAC of 103 mg/dL corresponds to a BAC of at least 0.080 g/dt. Introduction It is well-established that serum alcohol content (SAC) and whole blood alcohol content (BAC)are not equivalent. Ethanol is generally considered to be distributed in blood components * Author to whom correspondence should be addressed. E-mail: [email protected] in proportion to their relative water content (1-3). Because serum contains about 12 to 18% more water than whole blood (1), a serum (or plasma) alcohol level would be expected to be higher than that in the corresponding whole blood sample. Ordinary individual variation in the percentage of whole blood volume occupied by the erythrocytes (hematocrit) has been proposed as a factor likely to preclude the use of a single conversion factor (4-6), and in fact, subject-to-subject differences in SAC/BAC ratios have been observed in all of the studies cited here. Notwithstanding these reports, Winek and Carfagna (7) and Rainey (8) concluded in their studies that the SAC/BAC ratio is independent of the hematocrit. Previously published studies have served to establish the relationship of SAC to the corresponding BAC,along with the uncertainty associated with this relationship. The results of 14 of these studies have been conveniently summarized by Charlebois et al. (9). In most of these studies the data sets were too small to permit a valid statistical evaluation (nine of these involved 25 or fewer test subjects), or Gaussian distributions were assumed to be applicable without sufficient verification. Three recent studies (8-10) recognized these shortcomings and used gas chromatography (GC) to analyze SAC/BAC ratios for large numbers of subjects (211, 235, and 134, respectively). All of these studies were performed under controlled laboratory conditions or they used GC for serum analysis, which is not the methodology commonly encountered in the clinical environment. As pointed out by Shajani et al. (5), the overwhelming majority of hospital laboratories use an enzyme oxidation method for determining serum ethanol levels, whereas most whole blood alcohol levels measured for forensic purposes employ GC with either direct or headspace injection. Few hospital laboratories use an alternative protein- Reproduction(photocopying)of editorialcontentof thisjournalis prohibitedwithoutpublisher'spermission. 23 Journal of Analytical Toxicology, Vol. 31, January/February 2007 free filtrate procedure for analysis of whole blood by the enzymatic method (8,11,12). A recent College of American Pathology (CAP)hospital proficiency survey of volatiles testing results indicated that out of 3170 participants, 2.6% used GC, 18.1% used a dry film enzyme oxidation technology, 74.0% used various other enzyme oxidation methods, and 5.3% used other unspecified methods (13). These percentages have changed little over the past 10 years or so. Clinical testing is generally a one-shot analysis, whereas testing for forensic purposes almost invariably entails replicate analyses. Although previous studies have used replicate testing of both serum and the corresponding whole blood, and therefore provide a quantifiable degree of confidence with regard to uncertainty in their results, no such confidence can be carried over to the solitary SAC test performed under emergency conditions in a clinical laboratory. The present study, incorporating a sufficient sample size to produce statistically valid conclusions, was undertaken in part to address these issues. In the post-Daubert era, the uncertainty in an analytical result used for forensic purposes is as important as the result itself. 'l~o previous large-scale studies have estimated whole blood alcohol content in terms of a specified upper confidence limit of either the SAC/BACratio (9) or the logarithm of this quantity (8). These estimates depended explicitly on the conclusion drawn by the investigators in both studies that the ratios were independent of SAC. The present study employed linear regression to estimate BAC from clinically determined SACvalues at any specified level of confidence. The regression method requires no assumptions regarding the independence of the SAC/BACratio and SAC. In the present study, all samples were obtained from (anonymous) trauma patients at the University of South Alabama Medical Center. All serum testing was by one-shot enzyme oxidation under normal operating conditions in the clinical laboratory, and all whole blood testing was by GC in duplicate at the toxicology laboratory of the Alabama Department of Forensic Sciences (Mobile, ALL Results from a preliminary study by the authors and reported elsewhere (9,14) were obtained by a GC procedure that employed equal volumes of whole blood and aqueous internal standard solution. As Jones (15) has pointed out, this can give rise to various matrix effects. Consequently, the present study was undertaken utilizing methodology assured to eliminate these potential problems. Results from the preliminary study were found to be essentially consistent with those in this study. Experimental Specimen selection and preparation Clinical laboratory computer-generated work reports at the University of South Alabama Medical Center were screened daily for Emergency Department patients for whom there had been concurrent tests for serum ethanol and complete blood count (CBC). This process continued, taking every available sample, until over 200 such cases had been identified. CBC specimens were collected in rubber-stoppered EDTA tubes, 24 and the post-testing residues were stored in a refrigerator at 4~ for no longer than one week after the CBCwas performed. These residues were retrieved and transported to the Alabama Department of Forensic Sciences toxicology laboratory for BAC analysis by headspace GC. Serum ethanol determinations All SAC levels were determined by regular hospital medical technologists using the Dade International (formerly Dupont) ACA IV as part of their routine shift work. All reagents were supplied by the instrument manufacturer. The ACAIVwas operated, maintained, and calibrated as specified by the manufacturer's instructions. The calibration range was 0 through 300 mg/dL. The limit of quantitation for the SAC determination was 10 mg/dL. Standard deviation for the procedure was 2.4 mg/dL within-day and 2.6 mg/dL between-dayat SAC = 160 mg/dL. The laboratory was compliant with the provisions of the Clinical Laboratory Improvement Act of 1986, and certified by the College of American Pathology Laboratory Certification program. A 100 mg/dL whole blood control, required to fall within + 5 mg/dL of target, was run daily. Standard operating procedure required calibration verification and linearity checks every six months, whenever new reagents were introduced, or after any significant instrument maintenance activities. All serum alcohol levels were determined by enzyme oxidation without a preliminary protein precipitation step. Standard procedure specified that a Betadine wipe be used as disinfectant for trauma panel samples. The usual sampling site was the antecubital fossa, although presumably this was not always possible in every trauma case; in any event, medical records do not record collection site. Determination of whole blood ethanol All whole blood alcohol analyses were performed in batches (along with routine forensic case samples) utilizing a GC procedure conforming to rules promulgated under authority of the Implied Consent Act of the State of Alabama. Duplicate 100-1JL aliquots of whole blood were dispensed along with 1.0 mL of aqueous solution containing 0.0005 mL of n-propanol (internal standard) and 0.02 g of sodium fluoride (preservative) into 20-mL headspace vials using a Hamilton Microlab 1000Plus diluter-dispenser (Hamilton, Reno, NV).All analyses were performed on a Perkin-Elmer Sigma 2000 GC equipped with an HS-100 headspace autosampler (Perkin-Elmer, Norwalk, CT) and fitted with a 6-ft x H-in. stainless steel column packed with 5% Carbowax 20M on 60/80 mesh Carbopack B (Supelco, Bellefonte, PA). Linearity over the range 0.010 to 0.500 g/dL for each analytical batch was established simultaneously through the use of a seven-level calibration with correlation coefficient 0.9999. Duplicate calibrators were used at each level. Accuracy in each batch was established through analysis of NISTtraceable aqueous controls [EM 0.5, EM 1.0, EM 3.0: EM Science (now EMD Chemicals, Inc.), Gibbstown, NJ; Setpoint ETH 0.5, ETH 1.0, ETH 1.5, ETH 3.0: NERLDiagnostics, East Providence, RI] at 0.050, 0.100, 0.150, and 0.300 g/dL. Instrumental stability throughout the run was established through the use of duplicate aqueous 0.100 g/dL controls spaced every 10th sample in the batch. The quantitative acceptance criterion Journal of Analytical Toxicology, Vol. 31, January/February2007 for all sample, calibrator and control pairs was agreement within 0.005 g/dL for concentrations s 0.100 g/dL and within 5.00% for concentrations > 0.100 g/dL. The average for each pair of controls had to agree with its corresponding target value to within • 0.005 g/dL for concentrations < 0.100 g/dL and within • 5.00% for concentrations > 0.100 g/dL. Quantitation and reporting utilized software developed in-house which employed a least-squares algorithm. Alcohol concentration reported for each sample (and control) was the mean of the duplicate aliquots, truncated to the third decimal place. Results Ratio results The original set of 212 data points included one false-positive serum alcohol which was necessarily excluded from consideration (indeterminate SAC/BACratio). Examination of the probability plot (Figure 1) of all 211 valid SAC/BACvalues reveals that there are three distinct subpopulations comprising the entire range of the data rather than one homogeneous population. The scatter plot of SAC/BACversus SAC (Figure 2) suggests that there is not a single SAC/BACratio, and also that SAC/BACappears to be a nonlinear function of SAC. If the SAC/BACdata are partitioned into SAC ranges of 50 mg/dL (Figure 3), order begins to emerge. Above SAC = 50 mg/dL, certain points clearly seem to be outliers, all but one of which having SAC/BACvalues less than 1.0. For SAC below 50 mg/dL, there are only 2 apparent outliers, even though 12 of the 28 SAC/BACvalues are less than 1.0. In a study that purports to represent real-world conditions, the decision to exclude data points as outliers cannot be taken lightly. On the other hand, inclusion of obviously faulty data can distort and destroy the usefulness of an idealized model. Consequently,we classified data points as outliers only if 1. they were physiologically impossible (SAC/BAC< 1.0), and 2. statistical analysis revealed that they fell outside the subset median • 3 times the interquartile range (IQR); that is, they were detached (16). The 11 points identified by open triangles in Figure 3 met both of these criteria and were classifiedas outliers and excluded from the ratio analysis. When these points were excluded, those remaining in each subset were approximately normally distributed, as judged by their probability plots and by Kolmogorov-Smirnov tests. Logarithms of the ratios were neither more nor less "normal" than the ratios themselves. SAC/BACmean values and 90% confidence intervals (upper tail a = 0.05) corresponding to the various SAC ranges are shown in Figure 4. The Bonferroni multiple comparison test indicates that the differences between ratio subset mean in SAC range 0-49 mg/dL and those in all other ranges besides 50-99 and 400-429 mg/dL are significant (p = 0.0001, < 0.0001, < 0.0001, < 0.0001, and < 0.0005, respectively). Even if the less-well-determined values from ranges below 50 mg/dL 1.60 ] 1.40 1 ,ooi:-, o.I. . o.eo t 9 @@ 4, i iit. 0.00 ' 0 100 200 SAC 300 (mg/dL) 400 500 Figure 2. Scatterplot of SAC/BAC ratios versus SAC. 1.411- 1.20- $ 'l,!li; ! A e A 0.60- o,4o. /, S' 0.20- ee t 0,00 0 0.0 02 0.4 0.6 0B 10 12 1.4 SAC/BAC~ Figure 1. Normal probability plot of valid SAC/BAC ratio values. 1,6 100 200 300 400 500 SAC (mg/dL) Figure 3. SAC/BAC ratio data partitioned into 50 mg/dL SAC ranges.Open triangles are outliers as defined in the text. 25 Journal of Analytical Toxicology, Vol. 31, January/February2007 (relatively large experimental error) and above 350 mg/dL (paucity of data points) are excluded from consideration, the Bonferroni test indicates that differences between SAC/BAC subset means in SAC range 150-199 mg/dL and those in SAC ranges 50-99 mg/dL and 300-349 mg/dL are still significant (p = 0.004 and p = 0.014, respectively). Regression results All SAC results > 300 mg/dL involved a dilution step to bring them within the calibration range of the enzyme oxidation method, thereby introducing a source of variation not present in the rest of the data. Even without this complicating factor, both the GC method and the enzyme oxidation method would be expected to exhibit greater variation at higher concentra- tions. Therefore, we elected to analyze only data from the (calibrated) range, SAC ~;300 mg/dL. Although it is generally not good practice to reject data points simply because they do not "fit," especially when there is no apparent explanation for the disparity, truly bad data points can introduce serious error into least-squares regression. As pointed out by Cornbleet and Gochman (17), outlying data points can greatly distort the least-squares estimate of parameters because they generate large squared residuals, thereby shifting the calculated regression line toward the of_ fending points. Draper and Smith (18) describe an outlier among residuals as one which is "far greater than the rest in absolute value and perhaps lies three or four standard deviations or further from the mean of the residuals."We performed 120 1,18 1.16 1.14 1.12 e 1.10 1.08 1.06 0 iii 1.04 9 t ~e 9 , .............. i 1.02 2 1.00 t9 0.98 ] 3 0.96 4 094 5 092 0.49 100-149 200-24~q 30D-349 400.449 50~9 150-199 250-2S~ 360-399 6~ . 50 . 100 SAC range (n~l/dL) . 150 . 200 250 3~X) 350 Pro dlcted SAC values (mg/dL) Figure 4. Mean SAC/BACand 90% confidence intervals as a function of 50 mg/dL SAC ranges. Figure 6. Plot of Studentized residualsversuspredictedSAC values for ordinary least-squaresmodel (N = 176). 500" 450A i, 400- /Of" :Z 3.50- ~ 300 9 ** io 250200. t 9 ~' 150 9 100 9 9 ** A A n -2 Z 50. -3 0 100 200 300 400 500 BAC (mgldL) -4 -6 -5 -4 -3 -2 1 0 1 2 3 4 5 6 Stude~UZ~ residual Figure 5. Scatterplotof SAC versus BAC and plot of ordinary least-squares regression analysis (N = 176). Open triangles excluded, as discussed in text. 26 Figure 7. Normal probability plot of Studentized residuals for ordinary least-squaresmodel. Journal of Analytical Toxicology, Vol. 31, January/February 2007 residual diagnostics on the data set with SAC ~ 300 mg/dL, reand pure error (PE) in the data (18). In this case, it appeared jecting as outliers any point with a Studentized residual > 4.5, that the linear model suffered from LOF. In addition, a nine in all. Eight of the nine statistically rejected outliers had LOWESS smooth of the studentized residuals vs. model estiphysiologically impossible SAC/BACratios < 1.0, and one was mates displayed a slight "concave down" pattern, suggesting a false-positive resulting from a known cause (hyperlipidemia). that the linear model had not captured all the information in The resulting data set comprised 176 points as shown in Figure the data. This prompted us to fit the data to a quadratic model. 5 (excluded points shown as open triangles). The model SAC = The quadratic parameter was found to be very small (-0.00040) /~o +/~1 BAC was fitted to these data using the least-squares relative to the linear term (1.263), but all three parameters procedure to estimate the model parameters. were significant, and R 2 was 0.995. However, since there is no We were unable to definitively identify the cause for the outobvious theoretical basis for a quadratic model, and since a liers with SAC/BAC < 1.0, but occasional failure of the instruquadratic regression runs a higher risk of modeling "noise," ment to aspirate an adequate sample (either as a result of and since confidence interval calculation is more involved and intermittent mechanical malfunction, or perhaps operator entails potential ambiguity because of multiple (possibly comerror) seems reasonable. In any event, such cases always proplex) roots, a linear model is still to be preferred if it can be duced a low measured SAC, and therefore a low estimated shown to describe the distribution of the data to an acceptable BAC, so nothing was really lost (forensically) by excluding level. The linear model parameter estimates will be aliased; that them. On the other hand, including these points would is, they will include some fraction of the missing quadratic paincrease the regression slope, thereby giving rise to artificially rameter. The difference in predicted SAC between the linear high BAC estimates. and quadratic models was found to be negligible. For BAC The plot of Studentized residuals (ei* vs. ~i) is shown in levels above about 45 mg/dL and below about 265 mg/dL the Figure 6. The set ofn residuals, e i = (Yi- ~i), i = 1,2 ..... 176, linear and quadratic models predict SAC values within + 1.5%, contain all of the information available on the ways in which well within the experimental uncertainty of either value. Even the fitted model fails to explain the observed variation in the set at BAC = 300 mg/dL (where curvature is becoming more proof (Yi, xi),j = 1,2 ..... 176. The Normal probability plot ofei* is nounced) agreement is still within around 2.6%. shown in Figure 7. A straight line through the points lying beSince the BAC values are presumably determined more actween • 1.0 expected Normal values discloses the presence of curately, they are properly regarded as the independent, or two clusters of points, lying in the respective tails, that deviate predictor, variables in the regression. In effect, this is a calisystematically from the straight line. This plot is characteristic bration in which BAC values serve as the standards and SAC of residuals from a distribution with heavier tails than Normal. values are the measured responses. Whole blood alcohol levels One of the assumptions of the least-squares method is ho(along with prediction intervals) are then estimated from an moscedasticity, and Figure 6 indicates that this condition observed serum alcohol results by means of the calibration might not be met here. However, using computer generated line. This is accomplished through inverse regression (18,24). data, Cornbleet and Gochman (17) demonstrated that, proThe lower and upper limits of the (1 - cz) prediction interval vided the coefficient of variation of the measured y values for the inverse estimate, x0, where does not exceed 20%, ordinary least-squares still calculates the correct regression line even when the variance is proportional x0 = (Y0- fl0)/~l Eq. 1 to x. This limitation is met in the present study, and in addition, a LOWESS smooth of the set of absolute values of the are given by Studentized residuals disclosed no evidence of heteroscedasticity in the data (19,20); however, to be sure, we performed a .~ + dl <.~0 s.~ + d2 Eq. 2 weighted least-squares analysis and found the difference to be where dl and d2 are the roots of negligible. The presence of outlying observations disclosed by the plots in Figures 6 and 7 prompted the deployment of standard rod2[~12_t21-a/2.n-202]_2d~l(yo_~t) + bust methods to the estimation of the model parameters j (18,21,22,23). However, the difference between the respective sets of estimates (/~0,/~1,~2) for the robust methods and those [(Yo-Y)- t21- a/2,n-2~2(I + n-l)] = 0 Eq. 3 obtained by ordinary least-squares was negligible. Thus, the and t21_~/2,. - ~ is the square of Student's t statistic at ( I - a12) evidence of both case and aggregate statistics suggests that the for n - 2 degrees of freedom. The above limits on -~0are often proposed model can provide point and interval estimates of BAC from measures of SAC, using the least-squares parameter estimates of Table I. Linear Model Least-Squares Parameter Estimates Table I. The data set of 176 pairs included 39 Parameter Estimate SE(~j) ~2 R2 Adjusted R2 levels of xi at which there were two or three replicates. The presence of these ~o -0.203 0.945 37.862 0.995 0.995 replicated observations made it possible ~1 I .I 56 0.006 to discriminate between lack of fit (LOF) A A ^ 27 Journal of Analytical Toxicology, Vol. 31, January/February 2007 referred to as inverse tolerance limits or fiducial limits. For example, using parameters derived from this study, a measured SAC of 103 mg/dL can be expected to correspond to a BAC of at least 0.080 g/dL in 95% of all cases. Similarly, SAC = 107 mg/dL would be necessary for a confidence level of 99% should such be required by a court. Stated another way, in only 5 instances out of 100 will an SAC value of 103 mg/dL be expected to correspond to a BAC less than 0.080 g/dL. Discussion In the authors' experience, typically a prosecutor or civil attorney presents a serum alcohol level and requests a simple conversion to whole blood, usually accompanied by a request for comparison to some per se limit. As this and other studies have shown, this situation is fraught with peril. Charlebois et al. (9) and Jones et al. (25) have pointed out that hyperlipidemia is a potential complicating issue, one that is underscored by the false-positive (70 mg/dL) serum result in the present study. Hyperlipidemia causes excessively turbid samples, a situation which will usually become apparent only upon examination of other test results from the same sample. It should be noted that the false positive in question here went unnoticed until it was discovered by the authors. This reflects the fact that alcohol levels measured in a clinical laboratory are usually for immediate medical use and are therefore generally of ephemeral interest. Thus, under ordinary conditions, they are not likely to get a second look. Furthermore, the potential for a systematic error in the single serum can only be assessed through a review of relevant calibration and QA/QC records. Although the authors feel that this and the other studies cited have firmly established the validity of calculating a conversion from SAC to BAC, we are certainly in agreement with Frajola (11), who cautioned that clinical laboratories should not routinely convert serum or plasma alcohol results to whole blood alcohol levels, given the uncertainties that might exist. Prudence demands that an opinion should not be proffered without a complete review of all relevant medical records, not merely the alcohol results. SAC/BAC ratios As Rainey (8) pointed out, in theory it should be the logarithms of the SAC/BAC ratios which are normally distributed rather than the SAC/BACvalues themselves. In his study comparing serum and whole blood alcohol concentrations, both measured by direct injection GC, he found that the logarithms of the SAC/BACratios were normally distributed, whereas the ratios themselves were not. Charlebois et al. (9), however, found the SAC/BAC ratios to be indistinguishable from their log values with regard to distribution. The ratios in the present study were normally distributed (more precisely, the normal distribution hypothesis was not rejected) as indicated by normal probability plots and Kolmogorov-Smirnov tests. Because there was no discernable difference, in the interest of simplicity and in accordance with the time-honored principle 28 of Occam's Razor, we considered the ratios rather than their logarithms. Rainey (8) correctly pointed out that for an SAC-BACconversion factor to exist at all, it is required that the SAC/BAC ratio be independent of SAC. He concluded from an R2 value of 0.005 derived from regression of SAC/BACagainst SAC in his study that the logarithms of the ratios were independent of SAC under his experimental conditions. Charlebois et al. (9) compared ethanol concentrations in serum and whole blood samples using headspace GC for both matrices. They concluded, based on an insignificant slope parameter arising from linear regression, that the mean SAC/BAC ratio was independent of BAC. However, at the same time they noted a variation in the slope of SAC versus BAC between groups of data. But to say that SAC/BACis independent of SAC is equivalent to asserting a linear relationship between SAC and BAC; that is, if SAC/BAC is constant over a range of SAC values then SAC = k x BAC for some constant k. This is inconsistent with the observation of different slopes for different BAC ranges. The present study employing both enzyme oxidation and GC technologies clearly indicated statistically significant dependence of the ratios on SAC and also a slightly nonlinear functional relationship between SAC and BAC. Kristofferson et al. (26) studied the quantification of ethanol in whole blood specimens by the enzyme oxidation method compared to BAC by headspace GC. These authors did not report noticeable nonlinearity in their method comparison, which seems to suggest that the observed nonlinearity in the present study arises from the different sample matrices rather than differences in methodology. The discrepancy between previous studies and the present with regard to concentration dependence of SAC/BACcan perhaps be resolved by pointing out that while a very small R2 value and an insignificant linear regression slope parameter are certainly necessary conditions for independence, they are by no means sufficient. Any symmetric curved data set (i.e., one which has more or less the same value at both ends and has a more or less symmetric slight "hump" or "dip" in the middle), when subjected to straight-line regression, can produce a very small R2value and an insignificant linear regression slope parameter, even though there is obviously some kind of nonlinear functional relationship. If the curvature is subtle enough, or the data set is "noisy" enough, the curvature might be difficult to detect by visual inspection. Also, the use of ratios for either response or predictor variables in regression analyses can give rise to misleading inferences, and therefore the practice is generally to be discouraged (18). Note that dividing the SAC/BAC ratio data into subsets provided a useful construct for examining concentration dependence, but the partition points were arbitrary and the resulting subsets were relatively small. Therefore, no inference regarding prediction limits based on information in Figure 4 should be attempted. Regression In any study such as this one, it is always true that the regression parameters and confidence limit estimates depend Journal of Analytical Toxicology,Vol. 31, January/February2007 on the sample data from which they were derived. Note that in Eq. 3 the inverse prediction (or tolerance) limits are functions of y0, ,~, and ~. Short of a universally accepted reference sample set, there appears to be no way around this problem. As Rainey (8) has pointed out, under ideal conditions each clinical laboratory would determine its own conversion factor relative to the local forensic laboratory; however, this is not generally practical. All that said, the close agreement between the cited studies and the present study suggests that neither the conversion parameters nor the resulting uncertainty in the calculated BAC are likely to change significantly in any future investigation. Therefore, the parameter values based on this data set and listed in Table II can be used with Equations 1-3 to convert SAC to BAC and to calculate the uncertainty in BAC to any desired degree of confidence. A computer spreadsheet which provides the necessary t values (e.g., Microsoft Excel or Lotus 1-2-3) can easily be set up to accomplish this. It is an axiom of good practice that the same set of data cannot be used in both construction and validation of a regression model. In studies in which data are abundant it is common to select separate sets of data for construction and validation. In studies in which data are less abundant it is common to subdivide a single set of data into a construction subset and a validation subset, and there are several algorithms for making such partitions in an optimal manner (27). If the sample size n, is too small for splitting, the PRESS (Prediction Residuals Sum of Squares) procedure may be employed for validation (21,22,28). In this procedure each possible subset of (n - 1) observations is used in turn to form a construction subset for the model, and the corresponding omitted observations form validation subsets. This procedure is consistent with the basic requirement that the same observationyi, I = 1,2 ..... n, is not simultaneously used in both the construction and validation of a model. A PRESS R2 statistic estimated from these residuals may be used to assess the degradation of the fit of the model when it is applied to "new" data. For the linear model in the present study the original and PRESS R2 statistics are 0.9949 and 0.9947, suggesting that there will be no discernable degradation of the predictive performance of the model when it is extrapolated to new data. Table II. Parameter Values for Calculating Inverse Regression Estimates Parameter Value fl0 -0.203258 fl~ 1.155724 ~2 37.861777 n 176 130.613636 150.750000 ~(xi-~) 2 953935.7273 Conclusions We have presented a method by which clinically obtained serum alcohol values may be converted to equivalent whole blood levels as they would have been measured under forensic conditions. This method also allows for calculation of BAC prediction limits throughout the SAC range and at any desired level of confidence. 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