TY - JOUR
AU - Goebel, Neal C
AB - Abstract Calculating measurement uncertainty is a helpful exercise for identifying components or steps in a forensic analytical procedure that contribute to measurement variance. In this study, we used a bottom up approach to identify components in our procedures that contribute to measurement variance in our Department of Defense (DoD) Drug Demand Reduction Program (DDRP) Gas Chromatography Mass Spectroscopy (GCMS) analytical procedures for benzoylecgonine (BZE) and the THC metabolite, 11-nor-Δ9-THC-9-carboxylic acid (THCA) at 125% the DDRP concentration threshold (cutoff). Each assay was run 10 times over 30 days, each assay containing five calibrators and five samples (125%). Measurement uncertainty was estimated to be ±7.6 and ±0.6 ng/mL, for the BZE and THCA methods, respectively (α = 0.05). In both assays, method precision and the preparation of calibrator and samples were major contributors to measurement uncertainty. While this exercise will help with evaluating assay performance from a Quality Assurance perspective, these estimates should not be applied in interpreting DDRP test results. DDRP cut offs are already inherently conservative being above the Limit of Quantitation and were developed taking into consideration variability in assay performance across instruments and laboratories within the DDRP drug testing system. Introduction All analytical measurements possess some degree of measurement uncertainty. In a forensic toxicology laboratory, measurement uncertainty is inevitable given the complex procedures involved in producing analytical measurements. Possible sources of measurement uncertainty include variability in the function of instruments used, specimen extraction, purity and variability in calibrator and control concentrations, and human performance variability. Although many of the sources are kept to a minimum through use of strict procedures, internal and external quality control programs, matched deuterated internal standards, etc., not all sources of variability can be perfectly controlled as illustrated by inherent variability in repeat measurements of the same specimen by the same technician using the same calibrators, methods and instruments. Measurements produced by analytical procedures can be affected by three types of measurement error: (a) gross/spurious, (b) random and (c) systematic (1). Ambrus provides an excellent summary of these types of errors (2). Gross errors are defined as errors from which there is no recovery such as when no measurement is produced or the measurement is invalid such as when instruments fail, a wrong reagent or method is used, etc. Conversely, measurement uncertainty in analytical procedures is mainly due to random effects. Random error is present in all measurements and causes the measurand to fall on either side of the mean or average value and arises from a combination of experimental steps each of which is not perfectly repeatable from one replicate to the next. Random errors result in measurements that are above and below the true value but which will eventually sum to zero when enough repeat measurements are performed. Systematic error is the third type of measurement error which affects a series of measures all in the same direction. Sample measurements with systematic error have measures that are too high or too low and will not sum to zero over repeat measurements resulting in a directional bias that cannot be detected by repeatedly measuring the same sample. Causes of this type of error are balances that provide incorrect measures of weight or use of a partly decomposed analytical standard and can only be identified if the method or technique in question is applied to a reference material containing a known amount of the measureand or target analyte (2). Systematic error associated with a method or procedure may be difficult to determine in cases where there is no general consensus as to a standard method or procedure for the analyte being measured. However, the potential for systematic error may be reduced by periodically checking the performance of instruments used in the method or technique against reference standards and tuning or replacing those that do not meet performance criteria. Laboratory participation in proficiency testing programs administered by outside agencies may also help identify potential systematic error albeit indirectly. Thus, measurement results are random representations from a distribution having a fixed mean and variance where the variance defines the random error while the mean relative to a reference defines their bias or systematic error (3). Measurement uncertainty is a characterization of analytical and procedural limitations that still produce “fit for purpose” results (3). In a forensic toxicology laboratory setting, high accuracy and precision is very desirable, particularly when quantitative measurements are used to show noncompliance with specified limits as in the case with the Department of Defense Drug Demand Reduction Program (DDRP). Accordingly, identifying and quantifying sources of measurement uncertainty in an analytical procedure is potentially beneficial if the exercise pinpoints sources of variability that can be mitigated. Identifying sources of and estimating measurement uncertainty in analytical procedures has been endorsed as a best practice by several organizations (4–7) and is standard operating procedure for many disciplines engaged in calibration and testing activities (8). In regards to forensic testing, the National Academy of Science has recommended that laboratory reports of scientific analysis contain both the sources and magnitudes of uncertainty (e.g., levels of confidence) (6). There have been a number of studies published that have identified and quantified sources of measurement uncertainty in forensic testing using different approaches (8–14) but measurement uncertainty estimates are not usually addressed in published forensic toxicology studies. It is generally agreed that there are two broad approaches for estimating measurement uncertainty in analytical procedures: the top-down and bottom-up approach (2, 8, 9, 12, 15, 16). In the top down approach, an estimate of combined variances for a procedure is made based on comparison of repeat measures to a known standard and that variance is deemed to be representative of the uncertainty for the procedure in any laboratory. This is commonly done by comparing analysis results across laboratories employing the same method, instruments, and quality control requirements, and laboratory operating procedures. The bottom up approach seeks to identify and quantify each potential source of variance in a measurement regardless of its significance and then add together all sources of measurement uncertainty to produce a combined measurement uncertainty estimate which allows the laboratory to improve the analytical procedure by reducing variability where it is most prominent (8). In this study, we estimated measurement uncertainty associated with our current methods for benzoylecgonine (BZE) and the THC metabolite, 11-nor-Δ9-THC-9-carboxylic acid (THCA) urinalysis via GCMS using a single-point calibration at concentration levels of 125% of the DDRP administrative cutoff. For both methods, we used a bottom-up approach to identify and evaluate each major sources of measurement uncertainty and then calculated a combined measurement uncertainty estimate for each method. Experimental Chemicals and reagents All solvents and reagents used were analytical grade or better and were purchased from Fisher Scientific (Fair Lawn, NJ) and Sigma-Aldrich (St. Louis, MO). Solid phase cartridges were purchased from SPEware (San Pedro, CA) and UCT (Bristol, PA). Benzoylecognine (BZE) and (±)-11-nor-9-carboxy-∆9-tetrahydrocannabinol (THCA) reference materials were obtained from Cerilliant (Round Rock, TX). THC-glucuronide (THCA-Gluc) urine solution (18.5 ng/mL) was obtained from ElSohly Laboratories, Inc. (Oxford, MS). Calibrators and controls were prepared from in-house reference materials. Negative human urine used in the manufacture of calibrators and control material was a mix of urines voluntarily donated by Navy Drug Screening Laboratory (NDSL) Jacksonville staff members. The negative urines were combined and screened by immunoassay (IA) and confirmed THCA and BZE negative by GCMS prior to use. Working materials were manufactured by spiking negative urine with 100 and 125 ng/mL BZE or 15 ng/mL THCA. Solution preparation The BZE calibrator was prepared by adding 2 mL of 100 μg/mL Cerilliant stock BZE solution by 2 mL glass volumetric pipette to a 2,000 mL volumetric flask partially filled with negative urine. The solution was brought to volume with negative urine and mixed thoroughly; 3–5 mL of 200 proof EtOH was added to eliminate foaming. The solution was then aliquoted using a Hamilton Microlab 600 to dispense 2 mL portions into test tubes. The samples were stored at –30°C until needed. The BZE samples analyzed in this study were laboratory BZE blind controls prepared by adding 125 μL of 1.0 mg/mL Cerrilliant stock BZE solution using a calibrated Gilson positive displacement pipette to a 1,000 mL volumetric flask partially filled with negative urine. BZE stock used to manufacture the BZE samples was prepared using a different lot of Cerilliant BZE standard solution. The solution was then brought to volume with negative urine (3–5 mL of 200 proof EtOH was added to eliminate foam) and mixed thoroughly and aliquoted in excess into test tubes using a Hamilton Microlab 600. The samples were then stored at –30°C until needed. The THCA calibrator was prepared using a 150 μL of 100 μg/mL Cerilliant stock THCA solution. The Cerilliant stock solution was sonicated and then added using a calibrated Gilson positive displacement pipette to a 1,000 mL volumetric flask partially filled with negative urine. The solution was brought to volume with negative urine and mixed thoroughly; 3–5 mL of 200 proof EtOH was also added to eliminate foaming. The solution was aliquoted in 3 mL portions into test tubes using the Hamilton Microlab 600. The samples were stored at –30°C until used. The THCA samples analyzed in this study were 3 mL THCA blind controls containing THCA-Gluc at a concentration of 18.5 ng/mL manufactured by ElSohly Laboratories, Inc. Experimental design Batches consisting of five replicates of calibrator and five replicates of the laboratory blind control (herein referred to as the samples throughout the rest of this paper) consisting of either 125 ng/mL BZE or THCA-Gluc equivalent to 18.5 ng/mL THCA were extracted and BZE and THCA concentrations were measured by GCMS. Batches were extracted and analyzed on different days. Two technicians extracted and analyzed five batches each per drug for a total of 10 batches per drug analyzed. Only one batch per drug was extracted per technician per day and all extractions and analyses took place over a 30-day period. Two identical GCMS instruments were used in this study. All BZE batches were analyzed using the same GCMS instrument while all THCA batches were analyzed on the other instrument. Solid phase extraction For extraction of BZE, a 2 mL urine aliquot, 0.100 mL internal standard solution (final concentration of 100 ng/mL) of BZE-d8 and 0.1 mL 1 M sodium phosphate buffer (pH 6) and 0.050 mL were combined. Tubes were capped, vortexed and the centrifuged for 5 min at 2,000 rpm. Samples were poured into 3 mL CEREX® CLIN II cartridges and positive pressure was applied to yield a sample flow rate of ~1 mL/min. The cartridge was then washed with 1 mL of deionized (DI) water and followed by 1 mL of 0.1 M HCl. The cartridge was then dried for 3 min with nitrogen at 50 psi on the PPM then rinsed with 1 mL methanol followed by 1 mL of ethylacetate before drying for a further 3 min. Analytes were eluted with 1 mL methylene chloride:methanol:ammonium hydroxide (85:10:5) into high recovery autosampler vials and then evaporated to dryness at 55°C using a turbovap. For extraction of THCA, a 3 mL urine aliquot, 0.100 mL internal standard solution (final concentration of 40 ng/mL) of THCA-d9 and 0.25 mL 45% (w/v) potassium hydroxide were combined. Tubes were capped, vortexed, incubated for 15 min at 55°C, cooled to ambient temperature and then centrifuged for 5 min at 2,000 rpm. Samples were poured into 3 mL CEREX-THC cartridges and positive pressure was applied to yield a sample flow rate of ~1 mL/min. The cartridge was then washed with 1 mL 85:15:1 water:acetonitrile:30% ammonium hydroxide, 1 mL of methanol, and 1 mL ethylacetate. The cartridge was then dried for 3 min with nitrogen at 50 psi on the PPM. The analytes were eluted with 1 mL hexane:ethylacetate:acetic acid (80:20:2) into high recovery autosampler vials and then evaporated to dryness at 55°C using a turbovap. Derivatization Both BZE and THCA analyses used the same derivatization method. Derivatization was accomplished by adding 0.025 mL of pentafluoropropanol (PFPOH) and 0.050 mL of pentafluororproprionic anhydride (PFPA) to the dried extracts. The vials were capped, vortexed and incubated for 10 min at 65°C. Samples were removed from the heat block and dried on a Turbovap at 55°C. The dried derivatization product was reconstituted with 60 μL of EtOAc and transferred to GCMS for analysis. GCMS analysis BZE and THCA concentrations were measured using an Agilent 7890 Gas Chromatograph with a 7693 Autosampler coupled to a 5975 MSD. Data analysis was done using Agilent Drug Analysis Chemstation, version E.02.02. The column used was the Agilent J&W HP-5ms (15 m × 0.25 mm × 0.25 μm) using helium as the carrier gas at a flow rate of 1.0 mL/min operating in split mode. All BZE batches were analyzed on one GCMS instrument, all THCA batches were analyzed on the other GCMS instrument. BZE analyses used GCMS parameters of 0.5 min hold at 220°C then 10°C/min to 245°C for a total run time of 3 min. Injection volumes were between 1.0 and 1.5 μL using a 5.0 μL syringe and a 1:20 split. MS analysis using was conducting using single ion monitoring (SIM) using the following masses with a dwell time of 20 ms: 429.0 (ISTD quant), 303.0 (ISTD Q1), 421.0 (BZE quant), 300.0 (BZE Q1), and 272.0 (BZE Q2). The BZE Limit of Detection (LOD) and Limit of Quantitation (LOQ) for the BZE instrument was 20.6 ng/mL. THCA analyses used GCMS parameters of a ramp from 200°C at 35°C/min to 290°C with a hold time of 0.5 min for a total run time of ~3.1 min. Injection volumes were between 1.0 and 1.5 μL using a 5.0 μL syringe and a 1:10 split. MS analysis using was conducting using selected ion monitoring (SIM) using the following masses with a dwell time of 25 ms: 468.0 (ISTD quant), 454.0 (ISTD Q1), 459.0 (THCA quant), 445.0 (THCA Q1), and 622.0 (THCA Q2). The THCA LOD and LOQ for the GCMS instrument used was 0.9 ng/mL. Sample concentrations (i.e., the measurand) were calculated utilizing the equation for one-point calibration as described previously (12): Cx=Yb whereby Cx is the concentration of BZE or THCA in a urine sample; Y is the ratio of the peak area of BZE or THCA in the sample (AS) to deuterated internal standard (AIS); and b is the slope of the one-point calibration curve: Y=ASAIS b=AStdAISCStd The slope (b) was established from a single calibration curve (CStd) with concentrations equal to the DDRP BZE administrative threshold value (100 ng/mL) or THCA administrative threshold value (15 ng/mL); AStd is the peak area of CStd. Methods and results Sources of uncertainty The bottom up approach was used to identify potential sources of variance in our analyses. All potential sources of variance were evaluated regardless of their potential significance in contributing to the overall uncertainty and are summarized in Figures 1 and 2. Sources of uncertainty affecting the true sample concentration were calibrator preparation u(Cal Prep), sample preparation u(Sample Prep), method precision and method recovery from a urine mix referenced in the Chemicals and reagents section. Figure 1. Open in new tabDownload slide Potential sources of measurement variance for BZE GCMS analytical method. Figure 2. Open in new tabDownload slide Potential sources of measurement variance for THCA GCMS analytical method. Preparation of calibrators, samples Tables I and II summarize uncertainty estimates for the preparation of BZE and THCA calibrators and samples. Uncertainty for the standard solutions used to prepare calibrators and samples was obtained from the manufacturer’s certificate of analysis. Standard uncertainties were then calculated by dividing the manufacture uncertainties by the coverage factor k = 2. The uncertainty for BZE 100 μg/mL calibrator stock solution per the manufacturer was ±0.6 μg/mL equating to a standard uncertainty of ±0.3 μg/mL. Per the manufacturer, the uncertainty for the 1 mg/mL BZE stock solution used to make BZE samples was ±0.005 mg/mL equating to a standard uncertainty of 0.0025 mg/mL. For THCA, the uncertainty associated with the 100.0 μg/mL calibrator stock solution per the manufacturer was ±0.5 μg/mL equating to a standard uncertainty of 0.25 μg/mL. No uncertainty information was available from the manufacturer for the 18.5 ng/mL THCA sample solution used in this study. Table I. Uncertainty estimates for BZE calibrator and sample preparation. Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.3 μg/mL 0.003  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.003   Precision 2.0 mL 0.00220 mL   Temp 2.0 mL 0.00545 mL  u Flask (2 L)   Bias 2000.0 mL 0.2041 mL 0.000258   Precision 2000.0 mL 0.1056 mL   Temp 2000.0 mL 0.4619 mL  u Dispenser (2 mL)   Bias 2.0 mL 0.0122 mL 0.00643   Precision 2.0 mL 0.0039 mL   Temp 2.0 mL 0.00121 mL u(Sample Prep)  u Purity 1 mg/mL 0.0025 mg/mL 0.0025  u pipette (125 μL)   Bias 0.125 mL 0.0082 mL 0.0079   Precision 0.125 mL 0.0004 mL   Temp 0.125 mL 0.00038 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000323   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.00239   Precision 2.0 mL 0.0041 mL   Temp 2.0 mL 0.00031 mL Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.3 μg/mL 0.003  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.003   Precision 2.0 mL 0.00220 mL   Temp 2.0 mL 0.00545 mL  u Flask (2 L)   Bias 2000.0 mL 0.2041 mL 0.000258   Precision 2000.0 mL 0.1056 mL   Temp 2000.0 mL 0.4619 mL  u Dispenser (2 mL)   Bias 2.0 mL 0.0122 mL 0.00643   Precision 2.0 mL 0.0039 mL   Temp 2.0 mL 0.00121 mL u(Sample Prep)  u Purity 1 mg/mL 0.0025 mg/mL 0.0025  u pipette (125 μL)   Bias 0.125 mL 0.0082 mL 0.0079   Precision 0.125 mL 0.0004 mL   Temp 0.125 mL 0.00038 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000323   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.00239   Precision 2.0 mL 0.0041 mL   Temp 2.0 mL 0.00031 mL u(Cal Prep) = √(0.003)2 + (0.003)2 + (0.000258)2 + (0.00643)2 = 0.0077. u(Sample Prep) = √(0.0025)2 + (0.0079)2 + (0.0003)2 + (0.00239)2 = 0.0086. Open in new tab Table I. Uncertainty estimates for BZE calibrator and sample preparation. Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.3 μg/mL 0.003  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.003   Precision 2.0 mL 0.00220 mL   Temp 2.0 mL 0.00545 mL  u Flask (2 L)   Bias 2000.0 mL 0.2041 mL 0.000258   Precision 2000.0 mL 0.1056 mL   Temp 2000.0 mL 0.4619 mL  u Dispenser (2 mL)   Bias 2.0 mL 0.0122 mL 0.00643   Precision 2.0 mL 0.0039 mL   Temp 2.0 mL 0.00121 mL u(Sample Prep)  u Purity 1 mg/mL 0.0025 mg/mL 0.0025  u pipette (125 μL)   Bias 0.125 mL 0.0082 mL 0.0079   Precision 0.125 mL 0.0004 mL   Temp 0.125 mL 0.00038 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000323   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.00239   Precision 2.0 mL 0.0041 mL   Temp 2.0 mL 0.00031 mL Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.3 μg/mL 0.003  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.003   Precision 2.0 mL 0.00220 mL   Temp 2.0 mL 0.00545 mL  u Flask (2 L)   Bias 2000.0 mL 0.2041 mL 0.000258   Precision 2000.0 mL 0.1056 mL   Temp 2000.0 mL 0.4619 mL  u Dispenser (2 mL)   Bias 2.0 mL 0.0122 mL 0.00643   Precision 2.0 mL 0.0039 mL   Temp 2.0 mL 0.00121 mL u(Sample Prep)  u Purity 1 mg/mL 0.0025 mg/mL 0.0025  u pipette (125 μL)   Bias 0.125 mL 0.0082 mL 0.0079   Precision 0.125 mL 0.0004 mL   Temp 0.125 mL 0.00038 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000323   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u pipette (2 mL)   Bias 2.0 mL 0.00245 mL 0.00239   Precision 2.0 mL 0.0041 mL   Temp 2.0 mL 0.00031 mL u(Cal Prep) = √(0.003)2 + (0.003)2 + (0.000258)2 + (0.00643)2 = 0.0077. u(Sample Prep) = √(0.0025)2 + (0.0079)2 + (0.0003)2 + (0.00239)2 = 0.0086. Open in new tab Table II. Uncertainty estimates for THCA calibrator and sample preparation. Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.25 μg/mL 0.0025  u pipette (150 μL)   Bias 0.150 mL 0.00082 mL 0.0061   Precision 0.150 mL 0.0001 mL   Temp 0.150 mL 0.00039 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000325   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u Dispenser (3 mL)   Bias 3.0 mL 0.0122 mL 0.005   Precision 3.0 mL 0.0087 mL   Temp 3.0 mL 0.00138 mL u(Sample Prep)  u Purity 18.5 ng/mL ? ?  u pipette (3 mL)   Bias 3.0 mL 0.0024 mL 0.00165   Precision 3.0 mL 0.0043 mL   Temp 3.0 mL 0.00047 mL Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.25 μg/mL 0.0025  u pipette (150 μL)   Bias 0.150 mL 0.00082 mL 0.0061   Precision 0.150 mL 0.0001 mL   Temp 0.150 mL 0.00039 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000325   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u Dispenser (3 mL)   Bias 3.0 mL 0.0122 mL 0.005   Precision 3.0 mL 0.0087 mL   Temp 3.0 mL 0.00138 mL u(Sample Prep)  u Purity 18.5 ng/mL ? ?  u pipette (3 mL)   Bias 3.0 mL 0.0024 mL 0.00165   Precision 3.0 mL 0.0043 mL   Temp 3.0 mL 0.00047 mL u(Cal Prep) = √(0.0025)2 + (0.0061)2 + (0.000325)2 + (0.005)2 = 0.0082. u(Sample Prep) = 0.0017. Open in new tab Table II. Uncertainty estimates for THCA calibrator and sample preparation. Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.25 μg/mL 0.0025  u pipette (150 μL)   Bias 0.150 mL 0.00082 mL 0.0061   Precision 0.150 mL 0.0001 mL   Temp 0.150 mL 0.00039 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000325   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u Dispenser (3 mL)   Bias 3.0 mL 0.0122 mL 0.005   Precision 3.0 mL 0.0087 mL   Temp 3.0 mL 0.00138 mL u(Sample Prep)  u Purity 18.5 ng/mL ? ?  u pipette (3 mL)   Bias 3.0 mL 0.0024 mL 0.00165   Precision 3.0 mL 0.0043 mL   Temp 3.0 mL 0.00047 mL Parameter . Value . Standard uncertainty . Relative standard uncertainty . u(Cal Prep)  u Purity 100 μg/mL 0.25 μg/mL 0.0025  u pipette (150 μL)   Bias 0.150 mL 0.00082 mL 0.0061   Precision 0.150 mL 0.0001 mL   Temp 0.150 mL 0.00039 mL  u Flask (1 L)   Bias 1000.0 mL 0.1225 mL 0.000325   Precision 1000.0 mL 0.0791 mL   Temp 1000.0 mL 0.2887 mL  u Dispenser (3 mL)   Bias 3.0 mL 0.0122 mL 0.005   Precision 3.0 mL 0.0087 mL   Temp 3.0 mL 0.00138 mL u(Sample Prep)  u Purity 18.5 ng/mL ? ?  u pipette (3 mL)   Bias 3.0 mL 0.0024 mL 0.00165   Precision 3.0 mL 0.0043 mL   Temp 3.0 mL 0.00047 mL u(Cal Prep) = √(0.0025)2 + (0.0061)2 + (0.000325)2 + (0.005)2 = 0.0082. u(Sample Prep) = 0.0017. Open in new tab For the volumetric pipettes, positive displacement pipettes, and volumetric flasks the tolerances were based on the manufacturer’s certificate. The standard uncertainty was calculated assuming a triangular distribution (divided by √6) for all three equipment. The precision was estimated by the standard deviation of at least six replicates for the pipettes and 10 replicates for the volumetric flasks based on gravimetric determination. Thermal expansion coefficients at 20°C for methanol and water were applied with the assumption of a rectangular distribution. The thermal expansion coefficients for methanol and water at 20°C were 1.18 × 10–3°C–1 and 2.10 × 10–4°C–1, respectively. Method precision (AS/AIS) Measurement uncertainty associated with BZE and THCA method precision (AS/AIS) was estimated by pooling the relative standard deviations for BZE and THCA sample signals for the 10 iterations of the analysis. The pooled relative standard deviation for BZE sample signals was 0.28. The pooled relative standard deviation for THCA sample signals was 0.012. The average (AS/AIS) for BZE was 1.3 with a pooled CV of 2.1% with BZE (AS/AIS) ranging from 1.3 to 1.4. The average concentration measured for BZE samples was 125.1 ng/mL and was associated with a corresponding CV of 1.6% (target concentration = 125.0 ng/mL). The average (AS/AIS) for THCA was 0.5 with a pooled CV of 3.0% with THCA (AS/AIS) ranging from 0.50 to 0.58. The average concentration measured for THCA samples was 19.3 ng/mL with a corresponding CV of 2.3% (target concentration = 18.5 ng/mL). Method recovery The results of the BZE and THCA method recovery studies are summarized in Table III. Percent mean recoveries for BZE and THCA were 100.1% and 104.2%, respectively for the 50 specimens evaluated corresponding to an average ratio of recovery of 1.00060 for BZE and 1.04169 for THCA. BZE and THCA sample recovery pooled standard deviations were 2.1% and 2.3%, respectively. The standard uncertainty for method recovery (u(⁠ Rec̅ ⁠)) for each analysis was then determined by dividing the pooled standard deviation of mean recovery by the square root of the number of samples analyzed: Table III. BZE and THCA method recovery studies. . Replicate 1 . Replicate 2 . Replicate 3 . Replicate 4 . Replicate 5 . BZE 1.00104 1.0228 1.02824 0.994 1.01776 1.01120 0.99976 1.02144 1.01496 1.01624 0.99056 0.9984 1.01808 1.00336 1.00512 1.00976 1.01456 0.99464 1.01552 1.00152 1.01008 1.02168 0.98976 1.0084 1.01744 0.99040 0.98568 1.00056 1.01072 0.9812 1.01912 0.97728 0.98928 1.0044 1.0136 0.97928 0.9748 0.9788 1.01856 0.99208 0.99472 0.99768 0.99752 1.0172 0.98872 1.00328 0.95728 0.95824 0.98856 0.98448 Mean 1.00094 0.99499 0.99766 1.00757 1.00182 Mean of mean recoveries 1.00060 u(⁠ Rec̅ ⁠)BZE 0.0023 THCA 1.03149 1.07617 1.05620 1.03456 1.05696 1.04356 1.09864 1.03046 1.00442 1.08336 1.01509 1.08932 1.09838 1.02602 1.08566 1.02831 1.04964 1.03606 1.01417 1.06289 1.02932 1.04753 1.11202 1.00631 1.08002 1.05367 0.97004 1.00190 1.04658 1.05548 1.02575 0.97181 1.01261 1.02909 1.07926 1.03712 0.99980 0.99637 1.01893 1.06271 1.07089 1.00051 1.04566 1.04467 1.07052 1.06583 1.00930 1.01100 1.04409 1.06447 Mean 1.04010 1.03128 1.04007 1.02688 1.07013 Mean of mean recoveries 1.04169 u(⁠ Rec̅ ⁠)THCA 0.0042 . Replicate 1 . Replicate 2 . Replicate 3 . Replicate 4 . Replicate 5 . BZE 1.00104 1.0228 1.02824 0.994 1.01776 1.01120 0.99976 1.02144 1.01496 1.01624 0.99056 0.9984 1.01808 1.00336 1.00512 1.00976 1.01456 0.99464 1.01552 1.00152 1.01008 1.02168 0.98976 1.0084 1.01744 0.99040 0.98568 1.00056 1.01072 0.9812 1.01912 0.97728 0.98928 1.0044 1.0136 0.97928 0.9748 0.9788 1.01856 0.99208 0.99472 0.99768 0.99752 1.0172 0.98872 1.00328 0.95728 0.95824 0.98856 0.98448 Mean 1.00094 0.99499 0.99766 1.00757 1.00182 Mean of mean recoveries 1.00060 u(⁠ Rec̅ ⁠)BZE 0.0023 THCA 1.03149 1.07617 1.05620 1.03456 1.05696 1.04356 1.09864 1.03046 1.00442 1.08336 1.01509 1.08932 1.09838 1.02602 1.08566 1.02831 1.04964 1.03606 1.01417 1.06289 1.02932 1.04753 1.11202 1.00631 1.08002 1.05367 0.97004 1.00190 1.04658 1.05548 1.02575 0.97181 1.01261 1.02909 1.07926 1.03712 0.99980 0.99637 1.01893 1.06271 1.07089 1.00051 1.04566 1.04467 1.07052 1.06583 1.00930 1.01100 1.04409 1.06447 Mean 1.04010 1.03128 1.04007 1.02688 1.07013 Mean of mean recoveries 1.04169 u(⁠ Rec̅ ⁠)THCA 0.0042 Open in new tab Table III. BZE and THCA method recovery studies. . Replicate 1 . Replicate 2 . Replicate 3 . Replicate 4 . Replicate 5 . BZE 1.00104 1.0228 1.02824 0.994 1.01776 1.01120 0.99976 1.02144 1.01496 1.01624 0.99056 0.9984 1.01808 1.00336 1.00512 1.00976 1.01456 0.99464 1.01552 1.00152 1.01008 1.02168 0.98976 1.0084 1.01744 0.99040 0.98568 1.00056 1.01072 0.9812 1.01912 0.97728 0.98928 1.0044 1.0136 0.97928 0.9748 0.9788 1.01856 0.99208 0.99472 0.99768 0.99752 1.0172 0.98872 1.00328 0.95728 0.95824 0.98856 0.98448 Mean 1.00094 0.99499 0.99766 1.00757 1.00182 Mean of mean recoveries 1.00060 u(⁠ Rec̅ ⁠)BZE 0.0023 THCA 1.03149 1.07617 1.05620 1.03456 1.05696 1.04356 1.09864 1.03046 1.00442 1.08336 1.01509 1.08932 1.09838 1.02602 1.08566 1.02831 1.04964 1.03606 1.01417 1.06289 1.02932 1.04753 1.11202 1.00631 1.08002 1.05367 0.97004 1.00190 1.04658 1.05548 1.02575 0.97181 1.01261 1.02909 1.07926 1.03712 0.99980 0.99637 1.01893 1.06271 1.07089 1.00051 1.04566 1.04467 1.07052 1.06583 1.00930 1.01100 1.04409 1.06447 Mean 1.04010 1.03128 1.04007 1.02688 1.07013 Mean of mean recoveries 1.04169 u(⁠ Rec̅ ⁠)THCA 0.0042 . Replicate 1 . Replicate 2 . Replicate 3 . Replicate 4 . Replicate 5 . BZE 1.00104 1.0228 1.02824 0.994 1.01776 1.01120 0.99976 1.02144 1.01496 1.01624 0.99056 0.9984 1.01808 1.00336 1.00512 1.00976 1.01456 0.99464 1.01552 1.00152 1.01008 1.02168 0.98976 1.0084 1.01744 0.99040 0.98568 1.00056 1.01072 0.9812 1.01912 0.97728 0.98928 1.0044 1.0136 0.97928 0.9748 0.9788 1.01856 0.99208 0.99472 0.99768 0.99752 1.0172 0.98872 1.00328 0.95728 0.95824 0.98856 0.98448 Mean 1.00094 0.99499 0.99766 1.00757 1.00182 Mean of mean recoveries 1.00060 u(⁠ Rec̅ ⁠)BZE 0.0023 THCA 1.03149 1.07617 1.05620 1.03456 1.05696 1.04356 1.09864 1.03046 1.00442 1.08336 1.01509 1.08932 1.09838 1.02602 1.08566 1.02831 1.04964 1.03606 1.01417 1.06289 1.02932 1.04753 1.11202 1.00631 1.08002 1.05367 0.97004 1.00190 1.04658 1.05548 1.02575 0.97181 1.01261 1.02909 1.07926 1.03712 0.99980 0.99637 1.01893 1.06271 1.07089 1.00051 1.04566 1.04467 1.07052 1.06583 1.00930 1.01100 1.04409 1.06447 Mean 1.04010 1.03128 1.04007 1.02688 1.07013 Mean of mean recoveries 1.04169 u(⁠ Rec̅ ⁠)THCA 0.0042 Open in new tab u(Rec̅)BZE=0.01650=0.0023u(Rec̅)THCA=0.03050=0.0042 Combined uncertainty and expanded uncertainty The relative combined uncertainty uc (y) for the BZE and THCA analysis was estimated using the uncertainty data derived from the previous calculations. The relative combined uncertainty uc(y) was calculated using the following equation: uc(y)=Cy×u(Cal Prep)2+u(Sample Prep)2+u(Method Precision)2+u(Rec̅)2 The combined uncertainty calculations for our BZE and THCA analytical methods are as follows: uc(CBZE)=125×(0.0077)2+(0.0086)2+(0.028)2+(0.0023)2=125×0.03037=3.8ng/mL uc(CTHCA)=18.5×(0.0082)2+(0.0017)2+(0.012)2+(0.0042)2=18.5×0.01522=0.3ng/mL A 95% confidence range (U) was calculated for each combined uncertainty estimate by multiplying the combined uncertainty estimate by a coverage factor k which is determined by calculating the effective degrees of freedom for k using the Welch–Satterthwaite formula: veff=uc4(y)∑i=1Nui4(y)vi The estimated effective degrees of freedom for BZE and THCA were calculated to be 68 and 125, respectively. Given the high degree of freedom, k = 2 was considered appropriate. The expanded uncertainties for BZE and THCA at 95% confidence were then calculated as: UBZE=3.8×2=±7.6ng/mLUTHCA=0.3×2=±0.6ng/mL Discussion Our findings suggest that the methods used in our laboratory for analyzing BZE and THCA concentrations in urine at 125% of the DDRP cutoff value is associated with acceptable levels of measurement uncertainty. Some measurement uncertainty was expected given that generating an analytical concentration via GCMS is a multi-step, complex process with each step having its own inherent variability with repeated measure of the same specimen. Our estimated method measurement uncertainty (expanded) was ±6.0% and ±1.6% around the theoretical concentration for BZE and THCA, respectively, which compares very favorably with the DDRP laboratory external Quality Assurance (QA) proficiency testing requirement of ±20% (17). Potential systematic error in our method was not evaluated directly but the instruments, pipettes, and balances that were used in this study are the same ones that are used in monthly DDRP Quality Assurance (QA) proficiency testing. The laboratory’s DDRP proficiency testing results are monitored for consistent directional changes month to month over a span of a year to ensure drift due to potential systematic error is identified and addressed. Additionally, systematic error is monitored through regular evaluation of the performance of the laboratory’s instruments, pipettes, and balances by reputable companies and are either replaced or adjusted back into required tolerances when they do not perform to standard. Proportionally, method precision uncertainty estimates were the largest of the four contributing sources evaluated. In the 10 analyses conducted over the course of this study, the average sample concentration for BZE was 125.1 ng/mL with concentrations ranging from 119.7 to 128.5 ng/mL with a corresponding %CV of 1.6 (n = 50 samples). Comparatively, average THCA sample concentration had a slightly higher %CV among the 50 samples analyzed. The average concentration for THCA samples was 19.3 ng/mL with concentrations ranging from 17.9 to 20.1 ng/mL with a corresponding %CV of 3.1. Additionally, the % CV of the pooled average sample response ratios for BZE and THCA were 2.1% and 2.3%, respectively. These findings are nearly identical to the performance of these materials in production testing batches using the same calibrator materials. In 37 batches analyzed for BZE in production testing at Navy Drug Screening Laboratory Jacksonville (FL), the average concentration of the sample material was 125.5 ng/mL with concentrations ranging from 119.6 to 134.6 ng/mL and a %CV of 2.2. In 104 service member batches analyzed for THCA in the same laboratory using the same calibrator material used in this study, the average blind control concentration was 19.2 ng/mL with concentrations ranging from 17.9 to 20.7 ng/mL with a corresponding %CV of 3.2. Calibrator preparation was also a significant contributor of uncertainty for both BZE and THCA methods. BZE calibrator response ratios varied between 1.0 and 1.1 with an average of 1.1 and a CV of 1.8% and concentrations ranged from 97.0 to 102.4 ng/mL with an average of 97.6 ng/mL and a CV of 1.6%. THCA calibrator response ratios varied from 0.3 to 0.5 with an average of 0.4 and a coefficient of variation (CV) of 4.7%. THCA calibrator concentrations ranged from 11.9 to 16.7 ng/mL with an average of 14.9 ng/mL and a CV of 5.3%. Ideally, one would prefer for calibrator response ratios and corresponding concentration measurements to have near perfect precision and accuracy, but some variability is expected given that the measurements are the end products of a multi-step analysis in which each step has potential for variance over time with repeat measures. Average concentration measurements for both calibrators were within our laboratory’s internal quality assurance requirement of ±7% for calibrator concentrations and the concentration variance for both BZE and THCA correlate very closely with our calibration uncertainty estimates of 2.5 and 1.6 ng/mL for BZE and THCA, respectively, when calculated as recommended by Ma et al. (13) using the largest Y (AS/AIS) obtained and the smallest slope b of the 50 analyses. Additionally, uncertainty attributable to method recovery proportionally accounted for 0.6% of the total uncertainty for the BZE method and 7% for the THCA method. The pooled standard deviations for method recovery were 0.016 and 0.030 for BZE and THCA methods, respectively. It is important to note, however, that the samples in this study were dissolved in a urine mix that originated from several different persons. Therefore, uncertainty attributable to matrix variation in individual urines was not evaluated. Sample preparation proportionally accounted for 8% of the BZE method versus 1.26% for the THCA method but these methods were not comparable in this respect in that the THCA-Gluc stock solution used to manufacture samples was prepared by an outside source in mixed human urine and only required dispensing prior to extraction (Figure 2). Like many other forensic urinalysis programs, the DDRP confirms specimens for drug by GCMS or LC–MS/MS by extracting a small amount of specimen once and analyzing the extract one time. Specimens are determined to be positive for the tested drug if the resulting concentration is above the DDRP administrative cutoff and all forensic requirements are met. DDRP cut offs are conservative by design in that they are two or more times the Limit of Detection for most drugs tested in the DDRP and have a limited detection window (1–5 days in most exposure scenarios). Additionally, test results are adjudged administratively negative when the drug metabolite is present and below the cutoff level even though all other DDRP forensic testing criteria for a positive result are satisfied. Moreover, service members can request a re-test of their positive specimen at the same or different DDRP laboratory whereby the specimen is re-extracted and analyzed for the unequivocal analytical presence of the drug above the Limit of Detection which is usually a significantly lower concentration than the DDRP cutoff. As a result, the testing process is inherently conservative which benefits the service member. Furthermore, DDRP lab performance is monitored by an external Quality Assurance (QA) Program administered by the Armed Forces Medical Examiner System via a monthly open proficiency testing program where testing results must be within ±20% of the target concentration in confirmation testing. Therefore, because of the inherently conservative nature of DDRP testing, we do not advocate for using measurement uncertainty estimates as a “guard band” around DDRP cutoff concentrations (10). Unlike forensic blood alcohol analysis where there is a legal per se limit that is deemed intoxicated legally, effects and/or impairment are not being assigned at the DDRP cutoff concentration. Detection of the drug above the DDRP cutoff via a DOD-certified GCMS or LC–MS/MS method is all that is required. Conclusions In the context of the DDRP, calculation of measurement uncertainty using a bottom up approach is beneficial for identifying components of a laboratory’s multi-step analysis that introduce the greatest variability potentially affecting measurement results. For the two DDRP analytical methods chosen, we found that variability in method precision was the greatest contributor to measurement variance in our laboratory at 125% of the DDRP cutoff. Calibrator preparation was also a significant contributor to both methods as well. Method recovery was a source of significant variability in the THCA method. These findings will help direct future studies to: (1) determine what factors of these components contribute significantly to measurement variance; and (2) assist with developing strategies to reduce variance to lowest levels possible. In the case of DDRP testing, we believe that the calculated measurement uncertainty estimates assist in validating acceptable method performance within the laboratory but they should not be used in the evaluation or technical review process in determining whether a specimen is positive for the drug tested. DDRP cutoff levels are inherently conservative and are two or more times the Limit of Detection for most drugs tested in the DDRP. As a result, we do not believe that the method uncertainty estimates calculated here should be incorporated into the decision process of determining whether a specimen is positive for a drug in DDRP testing. Acknowledgments We thank the staff of Navy Drug Screening Laboratory Jacksonville, Florida, and the DoD Department of Defense Drug Demand Reduction Program (DDRP) for their efforts in support of this work. 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TI - Estimation of Measurement Uncertainty in Quantitation of Benzoylecgonine (BZE) and 11-nor-Δ9-THC-9-carboxylic acid (THCA)
JF - Journal of Analytical Toxicology
DO - 10.1093/jat/bkx100
DA - 2018-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/estimation-of-measurement-uncertainty-in-quantitation-of-qGIReU3egI
SP - 141
EP - 148
VL - 42
IS - 3
DP - DeepDyve
ER -