Comparison of Hospital Laboratory Serum Alcohol Levels Obtained

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. We have also presented evidence that
the SAC/BAC ratio is not independent of concentration, thus
rendering calculation of prediction limits through the use of
such ratios open to question.
References
I. Y.H. Caplan. Blood, urine, and other fluid and tissue specimens
for alcohol analysis. In Medicolegal Aspects of Alcohol, 3rd ed.,
J.C. Garriott, Ed. Lawyers & Judges, Tucson, AZ, 1996, p 140.
2. A.W. Jones and D.J. Pounder. Measuring blood-alcohol concentration for clinical and forensic purposes. In Drug Abuse Handbook, S.B. Karch, Ed. CRC Press, Boca Raton, FL, 1998, p 329.
3. B.T. Hodgson and N.K. Shajani. Distribution of ethanol: plasma
to whole blood ratios. Can. Soc. Forensic Sci. J. 18(2): 73-77
(1985).
4. R.C. Baselt. Disposition of alcohol in man. In Medicolegal Aspects
of Alcohol, 3rd ed., J.C. Garriott, Ed. Lawyers & Judges, Tucson,
AZ, 1996, p 71.
5. N.K. Shajani, W. Godolphin, and B.A. Image. Blood alcohol
analysis: comparison of whole blood analysis by gas chromatography with serum analysis by enzymatic method. Can. 5oc.
Forensic Sci. J. 22(4): 317-320 (1989).
6. A.W. Jones, R.G. Hahn, and H.P. Stalberg. Pharmacokinetics of
ethanol in plasma and whole blood: estimation of total body
water by the dilution principle. Eur. J. Clin. Pharmacol. 42" 445448 (1992).
7. C.L. Winek and M. Carfagna. Comparison of plasma, serum and
whole blood ethanol concentrations. J. Anal. Toxicol. 11" 267268 (1987).
8. P.M. Rainey. Relation between serum and whole-blood ethanol
concentrations. Clin. Chem. 39(11): 2288-2292 (1993).
9. R.C. Charlebois, M.R. Corbett, and J.G. Wigmore. Comparison of
ethanol concentrations in blood, serum, and blood cells for
forensic application. J. Anal. Toxicol. 20:171-178 (1996).
10. E.A. Hak, B.J. Gerlitz, P.M. Demont and W.D. Bowthorpe. Determination of serum alcohol:blood alcohol ratios. Can. 5oc.
Forensic Sci. J. 28:123-126 (1995).
11. W.J. Frajola. Blood alcohol testing in the clinical laboratory: problems and suggested remedies. Clin. Chem. 39(3)" 377-379 (1993).
12. S.M. Faynor. Alcohol testing in the clinical laboratory: alternative
remedies. Clin. Chem. 39(12): 2539-2540 (1993).
13. AL2-C AACC/CAP serum alcohol/volatiles participant survey.
W.R. Markus, Chair. College of American Pathologists, Northfield,
IL, 2003.
14. D.J.Wells and M.T. Barnhill, Jr. Comparison of hospital laboratory
serum alcohol obtained by an enzymatic method with whole
blood values determined by gas chromatography. Presented at the
Joint Congress of the International Association of Forensic Toxicologists (TIAFT) and the Society of Forensic Toxicologists (SOFT)
on November 3, 1994 in Tampa, FL.
15. A.W. Jones. Salting-out effect of sodium fluoride and its influence
on the analysis of ethanol by headspace gas chromatography.
J. Anal. Toxicol. 18(5): 292-293 (1994).
16. D.G. Kleinbaum, L.L. Kupper, and K.E. Muller. Applied Regression
Analysis and Other Multivariable Methods, 2nd ed. PWS-Kent,
Boston, MA, 1988, chapters 12 and 17.
29
Journal of Analytical Toxicology,Vol. 31, January/February2007
17. P.J.Cornbleet and N. Gochman. Incorrect least-squaresregression
coefficients in method-comparison analysis. Clin. Chem. 25(3):
432-438 (1979).
18. N.R. Draper and H. Smith. Applied Regression Analysis, 3rd ed.
John Wiley & Sons, New York, NY, 1998, chapters 2, 12, and 25.
19. W.S. Cleveland. LOWESS: a program for smoothing scatterplots
by robust locally weighted regression. Am. Star. 35(1)" 54 (1981 ).
20. W.S. Cleveland. Robust locally weighted regression and
smoothing scatterplots. J. Am. Star. Assoc. 74" 829-836 (1979).
21. D.C. Montgomery and E.A. Peck. Introduction to Linear Regression Analysis, 2nd ed. John Wiley & Sons, New York, NY, 1992,
chapters 4, 6, 9, and 10 and appendix C.
22. R.H. Myers. Classical and Modern Regression with Apptications,
2rid ed. PWS-Kent, Boston, MA, 1990, chapters 4 and 7.
23. S. Weisberg. Applied Linear Regression, 2nd ed. John Wiley &
Sons, New York, NY, 1985, chapter 11.
24. E.J.Williams. Regression Analysis. John Wiley & Sons, New York,
NY, 1959, chapter 6.
30
25. A.W. Jones, R.G. Hahn, and H.P. Stalberg. Distribution of ethanol
and water between plasma and whole blood; inter- and intra-individual variations after administration of ethanol by intravenous
infusion. Scand. J. Clin. Lab. Invest. 50:775-780 (1990).
26. L. Kristoffersen, B. Skuterud, B.R. Larssen, S. Skurtveit and
A. Smith-Kielland. Fast quantification of ethanol in whole blood
specimens by the enzymatic alcohol dehydrogenase method.
Optimization by experimental design. J. Anal. Toxicol. 29(1):
66-70 (2005).
27. R.D. Snee. Validation of regression models: methods and examples. Technometrics 19:415-428 (1977).
28. F. Mosteller and J.W. Tukey. Data Analysis and Regression. A
Second Course in Statistics. Addison-Wesley, Reading, MA, 1977,
chapter 15.
Manuscript received June 1, 2005;
revision received June 15, 2006.