Limit of Detection (LOD) - CiteSeerX

CLIN. CHEM. 40/7, 1233-1238 (1994)

#{149} Laboratory

Management

and Utilization

Limit of Detection (LOD)/Limit of Quantitation (LOQ): Comparison of the Empirical and the Statistical Methods Exemplified with GC-MS Assays of Abused Drugs David A. Arinbruster,’

Margaret

D. Tillman,

and Linda M. Hubbs

The limit of detection (LOD) for any analytical procedure, the point at which analysis is just feasible, may be determined by a statisticalapproach based on measuring replicate blank (negative)samples or by an empiricalapproach, consistingof measuring progressivelymore dilute concentrations of analyte. The limitof quantitation(LOQ), or concentrationat which quantitativeresultscan be reported with a high degree of confidence, may likewise be determined by either approach. We used both methods to determine LOD and LOQ for forensic gas chromatographic-mass spectrometric (Gc-MS) analyses of abused drugs. The statistically determined LCD and LOQ values for these assays underestimated the LOD because of the large imprecisionassociated with blank measurements and the inabilityof blank samples to meet typical GC-MS acceptance criteria. The empirical method provided much more realistic LCD values, supported by reasonable experimental data, and are 0.5-0.03 the magnitude of the corresponding statistical LODs. The empirical LODs and LOQs are identical for these GC-MS assays. The observations made here about the LOD/LOQ for specificforensic GC-MS procedures are generally applicable to any type of analysis. IndexIngTerms: sensitivity/data

handling/statistics/gas chromatography-mass spectrometry/forensic chemistry

Analytical procedures are characterized by a variety of technical operating parameters, such as accuracy, bias, precision, percent recovery, and dynamic linear range. Another key parameter is the lowest concentration of analyte detectable or quantifiable with a stated degree of reliability, commonly (but incorrectly) called “sensitivity,” or the “limit of detection” (LOD).2 The proper or preferred nomenclature has been the cause of some comment and debate in this journal, as has the question of how to best determine its value (1, 2). The National Committee for Clinical Laboratory Standards (NCCLS) defines the detection limit as “the smallest concentration or amount of an analyte that can be reliably shown to be present or measured under defined Armstrong Laboratory Drug Testing Division, Human Systems Center (AFMC), 2601 West Road, Suite 1, Brooks AFB, TX 782355240. ‘Corresponding author. Fax 210-536-3219. 2Nonstandard abbreviations: LOD, limit of detection; NCCLS, National Committee for Clinical Laboratory Standards; IFCC, International Federation of Clinical Chemistry; GC-MS, gas chromatography-mass spectrometry; LOQ, limit of quantitation; HHS, US Department of Health and Human Services; NLCP, National Laboratory Certification Program; THC, 11-nor-9-tetrahydrocannabinol-9-carboxylic acid; BE, benzoylecgonine; AMP, amphetamine; MAMP, methaxnphetamine; and LOL, limit of linearity. Received December 27, 1993; accepted March 14, 1994.

conditions; the smallest amount that is clearly distinguishable from background or ‘blank” (1, 3). The International Federation of Clinical Chemistry (IFCC) uses a similar definition, adding that the LOD”... defines the point at which the analysis becomes just feasible” (1, 4). A more practical consideration is how to best determine the LOD. Two methods are commonly used, a statistical approach and an empirical one. Anderson has succinctly described the statistical method (2), and Long and Winefordner have reviewed in detail the variations of this approach (5). A series of blank (negative) samples (a sample containing no analyte but with a matrix identical to that of the average sample analyzed) are tested and the mean blank value and the SD are calculated. The LOD is the mean blank value plus 2 or 3 SDs. The rationale is that the SD for the blank sample is roughly equivalent to the SD for whatever finite, small concentration of analyte actually corresponds to the LOD. The LOD should be statistically distinguishable from a blank -95-99% of the time. The empirical (experimental) method consists of analyzing a series of samples containing increasingly lower concentrations of analyte. The LOD is the lowest concentration at which the results still satisfy some predetermined acceptance criteria. Below the LOD, the results fail to meet these criteria (analysis is not feasible). Needleman and Romberg (6) used this method to determine the LODs for gas chromatography-mass spectrometry (GC-MS) assays for abused drugs. They criticized the statistical method because, in effect, it measures the average noise level of the procedure and defines only the ability to measure nothing” [emphasis in original] instead of a very low concentration of analyte. The limit of quantit.ation (LOQ) is set at a higher concentration than the LOD; in the statistical method, it is 10 SD above the mean blank value (5), thus presenting a greater probability that a value at the LOQ is “real” and not just a random fluctuation of the blank “...

reading.

LOD and LOQ have a special significance in forensic drug testing. The US Department of Health and Human Services (HHS) National Laboratory Certification Program (NLCP) requires that the LOD and LOQ be determined for GC-MS confirmatory assays to prove that analytes can be measured well below the administrative cutoff concentrations. When a laboratory retests a sample previously confirmed positive by another laboratory that used the mandated cutoff, the LOD of the assay is used as the retesting cutoff to adjust for potential analyte deterioration during storage. We determined the LOD/LOQ by both the statistical CLINICAL CHEMISTRY,Vol. 40, No. 7, 1994

1233

and the empirical methods for GC-MS confirmatory assays for drugs of abuse to decide which approach is preferable

for forensic

testing

purposes.

Materials and Methods GC-MS assays. We used

our standard, validated GC-MS assays for 11-nor-9-tetrahydrocannabinol-9carboxylic acid (THC), benzoylecgonine (BE), amphetamine (AMP), methamphetamine (MAMP), codeine, and morphine. Some details of the assays are summarized in Table 1. THC is extracted on Clean Screen solid-phase columns (Worldwide Monitoring, Horsham, PA), and opiates are extracted with Bond Elut Certi1r columns (Analytichem International, Harbor City, CA). The BE and AMP/MAMP procedures use liquid/liquid extraction. The internal standards are all deuterated versions of the drugs. All procedures were performed on HewlettPackard (Atlanta, GA) 5890/5970 GC-MS systems with selected ion monitoring. Two different GC-MS systems were used to analyze each drug to check for comparability between ostensibly identical instruments. Our laboratory uses US Department of Defense-mandated cutoff values to determine positive samples: 15 /hgfL for THC, 100 ug/L for BE, 500 gfL for amphetamines, and 300 gIL for opiates. The BE cutoff is lower than the HHSmandated value of 150 p.g/L used by many laboratories. Statistical LOD/LOQ determination. Negative blind controls, prepared from certified negative commercial urine (Utak, Canyon Country, CA), are included in every GC-MS batch. Monthly, values for the negative blind controls are added to the existing database for these controls, and the updated average values and SDs are calculated. The LOD is defined as the mean value of the negative blind controls plus 3 SD of the mean. The LOQ is defined as the mean value of the negative blind controls plus 10 SD. CV values were calculated from the cumulative mean and SD figures. Empirical LOD/LOQ determination. In preliminary, range-finding experiments, we added to a series of negative urine samples certified stock solutions of drugs to produce samples with drug concentrations corresponding to serial dilutions of the cutoff calibrators. Based on these results, concentrations were selected for each drug

Table 1. Key informatIon about the GC-MS assays of abused drugs.a Derivatizing Cutoff, Drug Ions monitorede reagent” t*g/L THC 313, 357, 373*: 360, 375 TMAH 15 BE 224*, 272, 345: 227, 275, 348 TMAH 100’ AMP 91, 118, 240*: 123, 244 HFBA 500 MAMP 118, 210, 254*: 213, 261 HFBA 500 Codeine 229, 282, 341*: 232, 344 AA 300 Morphine 310, 369, 327*: 330, 372 M 300 #{149}M GC columnswere DB-1, 12 m (see text). #{176}Drug ions: internalstandard Ions. The ion used for quantifyingthe drugis designatedwithan asterisk. TMAH;tetramethylammonium hydroxide; HFBA.heptafluorobutyric anhydride;AA, acetic anhydnde. d The Department of Defensecutoffmandated forbenzoylecgonine is lower than the NLCP cutoff (150 g/L).

1234

CLINICAL CHEMISTRY, Vol. 40, No. 7, 1994

that

appeared

at these under routine conditions, with injection in duplicate. The mean, SD, and CV were calculated from 20 replicate values. By this method, the LOD is defined as the concentration at which all routine GC-MS acceptance criteria (retention time within 2% of calibrator, ion ratios within 20% of calibrator) are met at least 90% of the time. Routine acceptable chromatography criteria require sharp, symmetrical ion peaks; reasons for rejecting results include the appearance of peaks that are excessively broad, show tailing or shoulders, or do not resolve to within 10% of baseline. However, because less-thanoptimal peaks are expected at the analytical lower limit of a procedure, we accepted relatively small and broad peaks. The quantitative value had to be >0 because some finite amount of analyte was present. The LOQ is defined as the concentration at which all acceptance criteria are met and the quantitative value is within ±20% of the target concentration. GC-MS control values are commonly considered acceptable by investigators in this field if within 20% of the established mean value. For optimal accuracy, we prepared samples by adding stock solutions to drug-free urines. However, we used concentrations equivalent to those obtained by serial dilutions because the dilution approach is easy and practical and can be used when pure analyte preparations are not available to prepare samples with known, weighed-in amounts of analyte. concentrations

to bracket were

the LOD. Samples

prepared and analyzed

Results Preliminary

studies.

The results

ments to bracket the concentration

experirange of the LODs

of the initial

are given in Table 2. For THC, the LOD appeared to be around 1.8 gfL; for BE, between 3.125 and 6.25 p.gfL; for AMP and MAMP, between 62.5 and 125 9ugfL; for codeine, between 18.75 and 37.5 j.tgfL; and for morphine, between 4.7 and 18.75 p.gfL. Therefore, we prepared samples at about these concentrations and analyzed them on all the GC-MS systems that were validated for

the respective drugs. LOD studies. The LOD data were collected over -5 weeks. Final average values were based on at least 16 values (typically, 20), reflecting the day-to-day variability of the systems. The results are summarized in Table 3. Comparison of empirical and statistical LODs. Table 3 also compares the empirical and statistical LODs. The empirical values for all drugs are much greater than the statistical LODs. Because the empirical values are based on experimental data, their reliability, as reflected by the CV, is known. The statistical LODs are calculated values; their reliability is indicated by the CV of the raw data used in the calculation. Table 4 summarizes the database we used to calculate the sta-

tistical LODs. Clearly, a great deal of imprecision

is

associated with the statistical data, as reflected by the CVs, which range from 55% to 753%. Comparison of empirical and statistical LOQs. Table 5 compares the empirical and statistical LOQs. Any drug

Table 3. Empirical and statistIcal LOD values.

Table 2. Results of experiments to bracket LOD concentrations (igIL) of the assays.

Empirical

Observed values”

Dilution

Target value#{176}

Rang.0

No.3

mc 7.5 3.75 1.875 0.9375

1:2

1:4 1:8 1:16

GC-MS Instrument no.

No.4

6-9

767

755

3-4.5

390

362

1:87 0 0a No.7

1.80

1.5-2.25 0.75-1.12

3 4 5 7 2

50

1:4

25 12.5

1:8

6.25 3.125 1.5625

1:16

1:32 1:64

40-60

20-30 10-15 5-7.5 2.5-3.75 1.25-1.8

51.07 26.39

6

13.01

10

7.48 263d

No.?

AMP 1:2 1:4 1:8 1:16

250 125

62.5 31.25

15.625 7.81 25

1:32 1:64

200-300

100-150 50-75 25-37.5 12.5-18.75 6.25-9.375

244

115

118

250

200-300

125 62.5

100-150

31.25 15.625 7.81 25

1:32 1:64

50-75 25-37.5 12.5-18.75 6.25-9.375

235

No.6

150 75 37.5

18.75 9.375 4.6875

1:64

Morphine 1:2 1:4 1:8 1:16

120-180

238

GC-MS

119 54.9

56.1

d

Instrument

274d

7.0#{176} 7.4#{176}

60-90

155 75.1

30-45

39.5

15-22.5

209d

7.5-11.25 3.75-5.625

150 75 37.5 18.75 9.375 4.6875

120-180

sufficient

concentration

60-90 30-45

LOD, t&aJL

95.5 95.5 95.0

0.36 0.58 3.60

90.0

3.33

100

7.54

6.36

C

100

4.34

5.23

94.0 100

1.12

95.0

6.37

100

2.50

95.0

2.57

Table 4. NegatIve control values used to calculate the statistical LODs described in the text.

No.11

Codeine 1:4 1:8 1:16 1:32

CV, %

StatIstical

Injections, %

b The LOD for MAMP onGC-MS no.2is between 125 and200 zgIL A 200 ug/L open controlassayedwith each amphetamine batch routinely meets acceptance criteria for MAMP. The current mean value for this control is 52.50 607d 193.75 ioJL (CV 2.6%). 0.0#{176}29.10 C At 125 aJL 83% of Injections were acceptable; at 200 ,.ig/L 100% of 15.3#{176} 15.2#{176} injectionswere acceptable. 0.0#{176} 0.0#{176}

No. 10 1:2

Drug

Acc.ptabl.

#{176}Measured on different GC-MS instruments over -5 weeks. At least 90% of the injections had to meet theGC-MS acceptance criteria described inthetext.

No.6

233

No. 2

MAMP 1:2 1:4 1:8 1:16

11

421d

Mean (SD), 1igIL

THC 1.80 (0.09) 5.1 THC 1.81 (0.11) 5.9 BE 6.93 (0.25) 3.6 BE 7.01 (1.84) 16.2 AMP 123.1 (7.51) 6.1 MAMP >125, 125,