1 Metrological approaches to organic chemical purity: primary reference materials for vitamin D metabolites Michael A. Nelson* 1 , Mary Bedner 1 , Brian E. Lang 2 , Blaza Toman 3 , Katrice A. Lippa 1 National Institute of Standards and Technology Material Measurement Laboratory, Chemical Sciences Division 1 and Biosystems and Biomaterials Division 2 Information Technology Laboratory, Statistical Engineering Division 3 Gaithersburg, MD 20899-8392 * Corresponding author contact information: email [email protected]; telephone 301-975-4100; FAX 301-975-0685
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Metrological approaches to organic chemical purity: primary reference materials for vitamin D metabolites
Michael A. Nelson*1, Mary Bedner
1, Brian E. Lang
2, Blaza Toman
3, Katrice A. Lippa
1
National Institute of Standards and Technology
Material Measurement Laboratory, Chemical Sciences Division1 and Biosystems and Biomaterials Division
2
Information Technology Laboratory, Statistical Engineering Division3
Given the critical role of pure, organic compound primary reference standards used to characterize and certify
chemical Certified Reference Materials (CRMs), it is essential that associated mass purity assessments be fit-for-
purpose, represented by an appropriate uncertainty interval, and metrologically sound. The mass fraction purities (%
g/g) of 25-hydroxyvitamin D (25(OH)D) reference standards used to produce and certify values for clinical Vitamin
D metabolite CRMs were investigated by multiple orthogonal quantitative measurement techniques. Quantitative 1H-nuclear magnetic resonance spectroscopy (qNMR) was performed to establish traceability of these materials to
the International System of Units (SI) and to directly assess the principal analyte species. The 25(OH)D standards
contained volatile and water impurities, as well as structurally-related impurities that are difficult to observe by
chromatographic methods or to distinguish from the principal 25(OH)D species by one-dimensional NMR. These
impurities have the potential to introduce significant biases to purity investigations in which a limited number of
measurands are quantified. Combining complementary information from multiple analytical methods, using both
direct and indirect measurement techniques, enabled mitigation of these biases. Purities of 25(OH)D reference
standards and associated uncertainties were determined using frequentist and Bayesian statistical models to combine
data acquired via qNMR, liquid chromatography with UV absorbance and atmospheric pressure-chemical ionization
mass spectrometric detection (LC-UV, LC-ACPI-MS), thermogravimetric analysis (TGA), and Karl Fischer (KF)
๐๐๐ถ = multiplicity (# H/peak) of principal component 25(OH)D analyte peak
๐๐ผ๐ = multiplicity (# H/peak) of internal standard (DMT) peak
๐๐ถ๐ = relative molar mass (molecular weight, g/mol) of the composite 25(OH)D reference standard
material
๐๐ผ๐ = relative molar mass (molecular weight, g/mol) of the internal standard (DMT)
๐ด๐๐๐๐๐ถ = integrated area of 25(OH)D analyte peak
๐ด๐๐๐๐ผ๐ = integrated area of the internal standard peaks
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๐๐ถ๐ = mass (g) of the composite 25(OH)D reference standard material weighed for sample solution
๐๐ผ๐ = mass (g) of the internal standard weighed for sample solution
๐๐ข๐๐๐ก๐ฆ๐ผ๐ = purity (mg/g) of the internal standard
25(OH)D purity values determined via qNMR are traceable to the amount-of-substance of internal standard DMT
(Sigma Aldrich), which is in turn traceable to NIST SRM 350b Benzoic Acid (Acidimetric). The stated purity of
DMT (99.99 % ยฑ 0.16 %) was verified during this investigation by qNMR using SRM 350b and dimethyl sulfone
from the Australian Government National Measurement Institute (NMIA Collection # QNMR002, Batch 06-Q-002)
as internal standards. Purities were determined as the mass percent of principal chemical component 25(OH)D2,
25(OH)D3, or 3-epi-25(OH)D3 in the composite material.
qNMR results were calculated for each sample replicate using three unique sets of integrals extracted from three
different processed regions of the 25(OH)D 1H{
13C} spectra. For each purity calculation, measurement uncertainties
were assessed through the propagation of respective variablesโ absolute uncertainties via a MCM simulation (i
=100,000) of the model defined by Equation 2 [19]. This MCM analysis calculated ๐๐ข๐๐๐ก๐ฆ๐๐ถ for each replicate
using a bespoke Matlab (The MathWorks, Inc., Natick, MA) program, whereby inputs for each Equation 2 variable
were iteratively defined by randomly-generated, normally-distributed values that had a mean equal to the
experimentally-measured value, and a standard deviation equal to the respective uncertainty assignment. These
uncertainties included those of the principal component peak area and composite material mass (๐ด๐๐๐๐๐ถ ,๐๐ถ๐), as
well as those of the internal standard and its respective purity (๐ด๐๐๐๐ผ๐, ๐๐ผ๐, ๐๐ข๐๐๐ก๐ฆ๐ผ๐). The uncertainties associated
with ๐ด๐๐๐๐๐ถ and ๐ด๐๐๐๐ผ๐ of each sample were estimated as the standard deviations of the respective chemical
speciesโ integrated set of 1H peak areas normalized with respect to corresponding proton multiplicities (๐ด๐๐๐/๐).
The proton multiplicity of the principal component and internal standard peaks (๐๐๐ถ, ๐๐ผ๐) and the relative molar
mass of the internal standard were assigned zero uncertainty. The mass purity of a material and its expanded
uncertainty were estimated as the mean and twice the standard deviation of a Gaussian curve fit to the aggregate of
MCM simulation results for all sample replicates (100,000 x 3 samples).
Results and Discussion
The vitamin D metabolite reference standards contained volatile and water impurities not measureable by classical
chromatographic techniques. They also contained isomeric and structurally-related impurities that were either not
resolved via LC-UV and GC-FID or were indistinguishable in one-dimensional proton qNMR (600 MHz) spectra.
DSC was not a viable option owing to the instability of 25(OH)D at temperatures near the melting points. This
investigation demonstrates the complexity and challenges associated with making reliable organic purity
determinations using limited, viable data.
A unit of 25(OH)D2 material was initially acquired as a candidate calibration material for SRM 2972a certification
measurements. Preliminary purity screening measurements were performed to assess the material suitability for use
as a primary reference standard. HPLC-UV (ฮป = 220 nm and 265 nm) analyses were performed using F5 and CN
column methods similar to LC Method 1 and LC Method 2, respectively. Several impurity peaks were observed,
including one that was detected only at 220 nm, and comprised โ 1.2 % of the total chromatogram peak area. The
mean purity determined by detection at both wavelengths and using both LC methods was 98.2 %; however, the
results ranged from 96.7 % to 99.4 % and had a standard deviation of 1.2 %. This variability suggested inconsistent
UV absorbance responses and/or resolution amongst the organic species Therefore, qNMR was implemented to
determine the purity of this material. Results of this screening assessment indicated that the mass purity was only
approximately 65 %. The 1H{
13C} NMR spectra contained several significant peaks from impurity components that
were not observed in the LC chromatograms and not identified during this screening. In light of this, a new, more
pure standard was obtained from the manufacturer and drastic overestimation of the amount of 25(OH)D2 in
subsequent CRM value assignments was prevented. Assessments via qNMR were performed for the other vitamin D
metabolite reference standards and resulting purities were held with a higher degree of confidence than those by the
mass balance. Data from the mass balance approach provided either confirmatory results or information used to
assess observable biases of the qNMR determinations.
The compilation of all analytical results and the purities of each of the four 25(OH)D reference standard materials
are shown in Table 1. The structures of the 25(OH)D analyte species, with pertinent carbon nomenclature to the
qNMRIS analysis, are presented in Figure 1.
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Table 1 Purity assessments of 25-hydroxyvitamin D metabolite reference standards via mass balance method
(including LC-UV, LC-MS/MS, TGA, and Karl Fischer Titration), qNMR analysis, and a combination purity
estimate.
[Table 1]
Fig. 1 Structures of 25-hydroxyvitamin D2, 25-hydroxyvitamin D3, and 3-epi-25-hydroxyvitamin D3 with carbon
nomenclature relevant to identifying quantified protons of qNMR assessment.
[Figure 1]
The mass balance approach was performed with a level of completeness determined to be fit-for-purpose as a
complementary method to qNMR for characterization of reference standards of SRM 2972a 25-hydroxyvitamin D
Calibration Solutions. The โOrganic Analysisโ results in Table 1 are the mean of results determined using the LC
methods, with corresponding expanded uncertainties (Uk=2) that reflect Type A variability associated with the
different LC methods, combined with an estimated 0.5 % Type B uncertainty from peak collation and varying
detector responses. Twelve impurities of 25(OH)D2 were detected via LC-UV, at least nine for 25(OH)D3 Lot 1,
nineteen for 25(OH)D3 Lot 2, and nine for 3-epi-25(OH)D3. Most of the impurities were detected using SIM
detection of m/z = 395 and m/z = 383 for 25(OH)D2 and 25(OH)D3 isomers, respectively, evidencing that the
aggregates of trace-level organic impurities consist primarily of structurally-related species. An analysis of variance
performed for the LC-UV purity results of each material identified the variability to be almost entirely attributable to
that between the two chromatographic methods. Analyses using ฮป= 265 nm detected more impurities than ฮป=220
nm, though both, in addition to MS detection results, determined purity results that were in agreement with respect
to the expanded uncertainty intervals. Individual LC results presented for each method and absorbance wavelength
are estimated as the means of purity values determined via replicate analyses (injections) of sample solutions. The
means from multiple LC separation and detection methods represent reasonable estimates of โOrganic Analysisโ
purity for which the resolution and UV response factors of structurally similar species at a given wavelength are
likely variable. The mean โOrganic Analysis Methodsโ values also included results from LC-MS using SIM mode
detection. Though detecting only structurally-similar species, the LC-MS results were in agreement with
corresponding consensus values and represented significant components of the expanded uncertainty intervals
associated with these approximations.
The combined TGA and KF titration results for the 25(OH)D3 monohydrate reference standards agreed with the
theoretical hydrate mass fraction of 4.3 %, confirming that the hydrate component in these materials is the primary
source of water and volatiles. Though it is recognized that these two methods provide results for measurands of a
different โkindโ, they were equally treated as components of the mass balance approach. This was justified for the
25(OH)D3 Lot 1 material given that all results were well in agreement, suggesting water was the only significant
measured impurity. Although there is disparity between the two results for 25(OH)D3 Lot 2, they were similarly
treated because there was no confirmation of impurity identity or evidence that one or both results were not
influenced by unknown bias. However, the TGA method by principle provides a more comprehensive โVolatiles and
Waterโ assessment. For this investigation, the disparity between the mean result and the TGA result is not
statistically significant. TGA analysis also revealed that the 25(OH)D2 reference standard has a significant volatile
component of 3.74 % ยฑ 0.11 % (Uk=2) and that the 3-epi-25(OH)D3 contains a detectable volatile component
comprising 0.4 % ยฑ 0.1 % (Uk=2) of its total mass.
The mass balance purity estimate (PurityMB, g/g) was calculated according to:
๐๐ข๐๐๐ก๐ฆ๐๐ต = (1 ๐
๐โ ๐ผ๐๐ ) ร ๐๐๐ด (3)
whereby IVW is the mass fraction (g/g) of impurities determined using โWater and Volatiles Methodsโ and POA is the
purity of the principle component species relative to the estimated amount of total organics determined by the
โOrganic Analysis Methodsโ. Uncertainties of these mass balance determinations were estimated from the relative
standard uncertainties of the โOrganic Analysisโ and โVolatiles and Water Methodsโ results combined in
quadrature. This approach was considered fit-for-purpose as part of the purity evaluations of these reference
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standards and may be implemented as part of efforts to exclusively determine the relative mass fraction estimate of a
principal component species. Other more detailed and comprehensive approaches [3] that quantify or estimate
individual impurity components, including inorganic species, may have greater fitness for purpose of specific
applications. Such approaches yield valuable information when comprehensive characterization of all components of
the standard material is desired.
The chemical shifts and coupling constants of 1H spectra were consistent with those of 25(OH)D reported in the
literature [20]. qNMR results were initially quantified with the symmetric, isolated, and well-resolved spectral
signals of 25(OH)D C6 and C7 (Figure 2) olefinic protons. The internal standard was quantified as the average of
the DMT aromatic (singlet, ฮดH = 8.2 ppm, 4 x 1H) and methyl (singlet, ฮดH = 3.9 ppm, 6 x
1H) signals, normalized
torespective proton multiplicities (4 and 6). The certified purity of this material (99.99 % ยฑ 0.16 % [Uk=2]) was
confirmed using qNMR. The proton content of the internal standard was referenced to the aromatic proton content
of SRM 350b Benzoic Acid (Acidimetric) (99.9978 % ยฑ 0.0044 % [Uk=1.96]) via cross-reference with dimethyl
sulfone (NMIA, 100.0 % ยฑ 0.3 % [U95]).
Fig. 2 Overlay of 25-hydroxyvitamin D2, 25-hydroxyvitamin D3, and 3-epi-25-hydroxyvitamin D3 1H{
13C} 600
MHz spectra using 90 degree excitation pulses.
[Figure 2]
Comparison of qNMR results to mass balance estimates indicated that the qNMR assessment via the C6 and C7
olefinic proton peaks were positively biased, as demonstrated by the mean values for 25(OH)D3 Lot 1 and the
25(OH)D2 reference standards. Though these results are not significantly different according to 95 % confidence
intervals, the slightly higher qNMR values were not expected. Given that the DMT internal standard certified purity
was verified, this disparity suggested that the C6 and C7 peaks were positively biased by other species.
Based on LC-UV-MS and NMR assessment, 25(OH)D species isomerize to pre-25-hydroxyvitamin D in solution
[15]. Therefore, qNMR samples were measured immediately after preparation. The spectra indicated no significant
evolution of these species during the 90 min 1H{
13C} NMR analysis. For LC-UV analyses, the area of any detected
thermal isomer peaks (verified by LC-MS) were aggregated with that of the principal 25(OH)D peak. Because of the
transient nature of 25(OH)D species in solution and the relative levels of structurally-related impurities, 2D NMR
experiments only provided confirmation of species identity.
For LC-APCI-MS assessments, the MSD operating in SIM mode analyzed m/z 395 for 25(OH)D2 and m/z 383 for
25(OH)D3 to identify structurally-similar impurities. Seven of the impurities present in the 25(OH)D2 reference
standard were detected, as well as seventeen impurities in the 25(OH)D3 reference standard. This strongly indicated
that several of the organic impurities are structurally related to 25(OH)D species. A major impurity component of
the 3-epi-25(OH)D3 reference standard (โ 1.5 %) was determined to be 25(OH)D3 via LC-UVwith reference the
25(OH)D3 standard. Though 1H-NMR provides structural selectivity, some of the low-level structurally-related and
isomeric impurities have several protons signals that are indiscernible from those of the primary species. This
limited selectivity for certain isomer moieties resulted in some peak overlap of closely structurally-related impurities
and principal component C6 and C7 peaks. Figure 2 presents 1H{
13C} spectra of 25(OH)D2, 25(OH)D3, and 3-epi-
25(OH)D3 samples. For scenarios during which these species are concomitantly present as impurities, the scaled
spectra demonstrate the overlap potential of several quantifiable peaks. A more inclusive spectral analysis using
peaks quantified from multiple chemical shift regions was performed to assess whether the suspected positive bias
was inherent in all peak integrals, or if a more accurate result could be obtained with an alternative 1H signal.
Table 1 shows three separate results for the qNMR analyses, each representing a purity determined using either C6
and C7 olefinic protons (ฮดH = 6.0 ppm to 6.3 ppm); C9, C4, and C1 non-equivalent methylene protons (ฮดH = 2.9
ppm, 2.6 ppm, and 2.4 ppm, respectively); or C18 and/or C21 methyl protons (ฮดH = 0.6 ppm and 1.0 ppm). The
purities are not completely consistent with one another, indicating that the 1H signals were variably influenced by
region-specific signal overlap or difficulties associated with determining peak areas in convoluted regions of the
spectrum. The C18 and C21 methyl proton signals are singlets that have slightly varying chemical shifts amongst the
three vitamin D metabolite species (Figure 3a). This difference causes associated overlapping peaks to be more
discernible as adjustable irregularities of the = 1H peak symmetry, as was observed in most spectra. Also, the upfield
region of 25(OH)D2 1H spectra have additional methyl signals and splitting patterns that are clearly identifiable and
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unique amongst these three metabolites. The integral adjustments had magnitudes of 0.3 % to 0.9 % of the total C18
methyl peak area, which concurs with the average approximate 0.4 % organic impurity component determined via
LC-UV for 25(OH)D2 and both 25(OH)D3 reference standards.
Fig. 3 a) Overlay of 1H{
13C} spectra of 25(OH)D regions (0.7 ppm to 0.5 ppm) containing C18 methyl proton peaks;
25(OH)D3 spectrum scaled to โ1 % intensity of that of 3-epi-25(OH)D3 b) C18 methyl proton peak, c) C6 and C7 proton
peaks and d) C9, C4, and C1 proton peaks.
[Fig. 3]
As shown in Figure 3b, superimposition of the 25(OH)D3 C18 methyl region onto the corresponding 3-epi-
25(OH)D3 (scaled to 1 % relative intensity) spectral region illustrates the discernibility of signal interference when
these species are present as low-level impurities. This was supported by identification of 25(OH)D3 in the 3-epi-
25(OH)D3 reference standard via LC-UV (approximately 1.5 %). Figures 3c and 3d illustrate the ambiguity of these
small isomeric interferences in the two other quantified regions of the spectra, and thus the difficulty in adjusting
associated biases. For these reasons the qNMR purity was assessed exclusively from the C18 (and C21 from
25(OH)D2), methyl 1H peaks. For 25(OH)D3 Lot 1 and 25(OH)D2, the adjusted C18 and C21 methyl integral results
had higher values than those determined via the mass balance approach. Although the respective means of both
methods lie well within the 95 % confidence limits of the other, this suggests that an amount of the underlying peak
bias was not discernible and thus not mitigated. Such a case strengthens the validity of performing a diverse, multi-
method assessment for investigating total mass purity of organic chemical standards [5]. Although qNMR is a direct
and traceable measurement technique, some composite organic materials may contain structurally-similar low-level
impurities that are difficult to distinguish by one-dimensional NMR experiments, but are observable and quantifiable
with LC methods.
Primary reference materials occupy the highest position of a calibration hierarchy, and the uncertainty intervals
associated with respective purity value assignments are propagated through each step of the measurement procedure
These propagate uncertainties are significant components of the total measurement uncertainty budgets.
Cumbersomely large symmetric uncertainty intervals, often derived by combination of uncertainties from multiple
equally-weighted methods that contribute to a combined average [21], may not be fit-for-purpose for primary or
high-level calibrant characterization. Such a case exists when propagated uncertainties are large enough to render
reference materials unsuitable for widespread use within the clinical community. While assessing purity analysis
data, it is useful to develop a heuristic for determining how information from direct methods and mass balance
approaches will contribute to a consensus value. A technically-informed decision process should be implemented
that combines information according to associated degrees of confidence, identifies any need for further
investigation or invalidates inaccurate results from an erroneous measurement system .
When mass balance and direct-method results are nearly equal or have highly-overlapping probability distribution
functions (PDF), complementary results might be combined in an equally-weighted fashion. Such consensus values
are minimally affected by known potential measurement biases. This approach was taken for the qNMR and mass
balance results of most 25(OH)D purity estimates. Different approaches should be taken when the purity result PDFs
have little or no overlap, as was the case for the 3-epi-25(OH)D3 reference standard( mass balance: 98.03 % ยฑ 1.01
% [Uk=2]; qNMR: 94.94 % ยฑ 0.74 % [Uk=2]). Though the source of the disparity was not explicitly characterized, it
is expected that the results of the mass balance method are positively biased from incomplete quantification of all
impurities and non-equivalent UV and MS response factors. The unknown biases [17] associated with these results
give rise to a large assigned uncertainty (3 %) when the significantly different PDFs are combined in an equally-
weighted fashion.
Alternative statistical methods may be employed to infer uncertainties that draw upon expert knowledge of a
measurement system. Scenarios where these approaches might be advantageous are evaluations using pre-defined
constraints of the measurement model (informative priors) that employ analyst expertise or known limits of the
measurement system. Such situations might include observations where direct measurement results, not affected by
a known bias, are significantly different from those determined via a mass balance approach, or when the assessment
of high-purity material yields uncertainty interval bounds that exceed the logistical limit of 100 % mass fraction
purity. The purity evaluation of the 3-epi-25(OH)D3 reference standard is an instance of the former.
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Given the direct mode of measurement via qNMR, a lower chemical mass fraction purity determined by this method
may be justified by the analyst to be closer to the true value than that from the mass balance techniques. It may
therefore be suitable to evaluate the qNMR result and its associated uncertainty as the sole component of the purity
value. Conversely, if the qNMR result is indicative of a higher purity than that of the mass balance then it becomes
ambiguous which methods are significantly biased. For such a situation, value assignment may be based upon the
approach for which the analyst has the greatest confidence.
In addition to these decision-making processes, there are statistical methods implementable for determining
consensus purity values that reflect varying degrees of confidence in the qNMR result. Since the qNMR and mass
balance purity results for 3-epi-25(OH)D3 have no overlap of Gaussian 95 % uncertainty intervals, the
corresponding purity value may be evaluated by a Two-piece normal [22]. The qNMR primary ratio method is
believed to yield results of greater โtruenessโ and this statistical approach may be used to estimate an asymmetric
consensus probability distribution that provides greater weighting to the qNMR result. By this approach, the
consensus distribution has a mode (ฮผ) that is equal to the qNMR result and 2.5th
and 97.5th
percentiles that are
derived from the lower half of the qNMR uncertainty interval and the mean mass balance result, respectively. A
description of this statistical approach and its implementation is described in Online Resource 1. From the binormal
distribution, a mean consensus purity of 95.80 % (u= 0.98 %) and an asymmetric 95 % confidence interval (U95) of
[94.37 %, 98.03 %] was evaluated. Either the two-piece Normal approach or the qNMR result alone is suitable for
purity assignment of 3-epi-25(OH)D3, given the lack of agreement by these methods and the suspected unknown
bias in the mass balance value. The more conservative uncertainty interval of the two-piece Normal is the preferred
evaluation since peak integral adjustments were made during the qNMR analysis to account for observable isomeric
interferences.
Fig. 4 Probability Distribution Functions (PDFs) for 3-epi-25(OH)D3 consensus purity values evaluated using a)
two-piece Normal distribution, b) Markov Chain Monte Carlo Method (MCMC) with a triangular, qNMR-favored
prior distribution and c) MCMC that is constrained only by the mean values of the qNMR and mass balance
methods.
[Fig. 4]
The Bayesian approach to probability assessment provides powerful methodology for evaluating measurement
uncertainty that considers both empirical data and pre-existing knowledge. When there is only partial overlap of the
qNMR and mass balance PDFs, they should be combined according to a prior, expertly-informed characterization of
qNMR โtruenessโ. This predilection should ultimately be based on confidence that qNMR is not influenced by a
significant unknown bias. Figure 4b depicts the PDF of the combined qNMR and mass balance results for 3-epi-
25(OH)D3 evaluated by a Markov Chain Monte Carlo (MCMC) simulation, as described by Possolo and Toman
[23], using OpenBUGS [24]. The consensus purity PDF was evaluated by iterative sampling of a triangular posterior
distribution, constrained to lie between the mean of the two method PDFs, with a mode that has an abscissa equal
1/10 of this interval added to the qNMR mean. The data (results of the qNMR and mass balance methods) were first
transformed into log space by ln (100 โ ๐ฅ), and the respective u were transformed according to ๐ข (100 โ ๐ฅโ ). The
resulting MCMC samples of the consensus value were summarized to obtain a mean 3-epi-25(OH)D3 purity value of
95.97 % with 0.75 % standard uncertainty and an asymmetric U95 of [94.73 %, 97.59 %]. The evaluation of a
consensus PDF in this manner, using an analyst-defined prior, is applicable to this scenario given the expertly-
informed confidence in the โtruthโ of the qNMR measurement.
In a scenario where a direct measurement technique yields purity results that are irreconcilably higher than those
assessed by indirect methods, it is not as clear to the analyst how either or both approaches are biased. In this
instance, the PDF of a consensus result may be obtained via MCMC using a prior distribution that is constrained by
the two method means, but is non-informative in the sense that no further information is provided. The PDF of this
combined value is presented in Figure 4c. With a Bayesian MCMC, the simulated evaluations are in essence
weighted according to the respective qNMR and mass balance input uncertainty intervals. The mean combined
purity value from this evaluation is 96.39 % with a u value of 0.97 % and a U95 of [94.70 %, 98.19 %]. More
detailed description of these Bayesian approaches and their implementation are described in the Electronic
Supplementary Information for this manuscript.
Conclusion
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The aggregate of data acquired by fundamentally-diverse methods was used to assess mass fractions of 25(OH)D
species in vitamin D metabolite reference standards. These investigations were performed to determine the amount
of vitamin D metabolite species present in gravimetrically-prepared calibrant solutions that support NIST's clinical
SRM certifications. The degree of analytical rigor put forth during this purity study was to ensure that biases
inherent in each of the implemented measurement methods were mitigated prior to assigning mass fraction purity
values. Though less-intensive purity investigations are fit for certain analytical purposes, greater confidence is
required for assessments of in-house calibrants and primary reference standards used to provide mass fraction
traceability.
Reliable purity assessments of these materials benefit from both direct and indirect measurement techniques. As
demonstrated in this particular investigation, no single authoritative technique satisfactorily and universally met all
of the measurement challenges. Though the purity via direct methods is often regarded with higher confidence, as
has largely been emphasized here, information from the indirect techniques is critical for assessing potential biases
of the direct methods. This yields valuable insight for performing thorough and proper statistical analyses that
support selective mass fraction purity assessments of reference materials. Extensive, diversified, validated, and well-
coordinated methods must be used to ensure that accurate mass fraction determinations are achieved. Additionally,
analyst-informed approaches to statistical evaluation may be advantageous and appropriate when expert knowledge
of a system is communicated and the results of a particular method are held with a relatively high degree of
confidence. The complexities associated with precisely analyzing and comprehensively evaluating the impurities of
gravimetrically-implemented higher-order 25(OH)D reference standards, developed to support accurate and
traceable Vitamin D metabolite value assignments, are fundamentally essential and a metrological necessity.
Acknowledgements
Partial funding for this work was provided by the National Institutes of Health Office of Dietary Supplements (NIH-
ODS). Some of the statistical analyses of results presented in this work were performed by James Yen of the NIST
Mean 98.43 (1.01) 0.4 (0.04) 98.03 (1.03) 1 Results reported as % amount of the principal component species relative to the total estimated amount of organics. 2Standard uncertainties expanded by a coverage factor (k) of 2 (Uk=2) 3 qNMR result expanded uncertainties (Uk=2) are assessed as the 1-ฯ interval of a Gaussian curve fit to the distribution of results from an n x 100,000-iteration Monte Carlo simulation of Equation 1, expanded by a factor of 2 (n=3; no. of sample replicates).
sample data sets randomized during Monte Carlo analysis), multiplied by the appropriate coverage factor, k. 4 Purity estimate calculated with qNMR result quantified with C18 and C21 methyl 1H signal integrals. 5Combined purity estimate uncertainty (Uk=2) determined by Gaussian random effects-modeled bootstrap simulation of all contributing results and corresponding standard uncertainties.
16
6Quantification based only the integral of C18 methyl 1H signal. 7Combined purity evaluated using Two-Piece Normal PDF; useful approach when the result of direct method is held in higher confidence and the PDFs of contributing data do not demonstrate
overlap of 95 % coverage intervals. 8Combined purity evaluated using Bayes MCMC with a triangular, qNMR-favored triangular prior distribution. 9Combined purity evaluated using Bayes MCMC that is constrained by qNMR and mass balance means, but is otherwise non-informative
17
Figure 1. Structures of 25-hydroxyvitamin D2, 25-hydroxyvitamin D3, and 3-epi-25-
hydroxyvitamin D3 with carbon nomenclature relevant to identifying quantified protons of
qNMR assessment.
18
Figure 2 Overlay of 25-hydroxyvitamin D2, 25-hydroxyvitamin D3, and 3-epi-25-hydroxyvitamin D3 1H{
13C} 600 MHz spectra using
90 degree excitation pulses.
S-19
Figure 3 a.) Overlay of 1H{
13C} spectra of 25(OH)D regions (0.7 ppm to 0.5 ppm) containing C18
methyl proton peaks; 25(OH)D3 spectrum scaled to โ1 % intensity of that of 3-epi-25(OH)D3 b.) C18
methyl proton peak, c.) C6 and C7 proton peaks and d.) C9, C4, and C1 proton peaks.
S-20
Figure 4 Probability Distribution Functions (PDFs) for 3-epi-25(OH)D3 consensus purity values
evaluated using a.) two-piece Normal distribution, b.) Markov Chain Monte Carlo Method
(MCMC) with a triangular, qNMR-favored prior distribution and c.) MCMC that is constrained
only by the mean values of the qNMR and mass balance methods.
S-21
Electronic Supplementary Information
Higher-order metrological approaches to organic chemical purity: primary reference materials
for vitamin D metabolites
Michael A. Nelson*1, Mary Bedner
1, Brian E. Lang
2, Blaza Toman
3, Katrice A. Lippa
1
National Institute of Standards and Technology
Material Measurement Laboratory, Chemical Sciences Division1 and Biosystems and
Biomaterials Division2
Information Technology Laboratory, Statistical Engineering Division3