Statistical Procedures for Determination and Verification of Minimum

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Environ. Sci. Technol. 2006, 40, 281-288

Statistical Procedures for Determination and Verification of Minimum Reporting Levels for Drinking Water Methods

objectives at a given minimum reporting level (MRL) is also presented. The verification procedure requires a single set of seven samples taken through the entire method procedure. If the calculated prediction interval is contained within data quality recovery limits (50-150%), the laboratory performance at the MRL is verified.

STEPHEN D. WINSLOW* AND BARRY V. PEPICH Shaw Environmental and Infrastructure, Inc., 26 West Martin Luther King Drive, Cincinnati, Ohio 45268

Introduction

JOHN J. MARTIN AND GEORGE R. HALLBERG The Cadmus Group, Inc., 57 Water Street, Watertown, Massachusetts 02472 DAVID J. MUNCH AND CHRISTOPHER P. FREBIS Technical Support Center, Office of Ground Water and Drinking Water, United States Environmental Protection Agency, 26 West Martin Luther King Drive, Cincinnati, Ohio 45268 ELIZABETH J. HEDRICK National Exposure Research Laboratory/Office of Research and Development, United States Environmental Protection Agency, 26 West Martin Luther King Drive, Cincinnati, Ohio 45268 RICHARD A. KROP The Cadmus Group, Inc., 1620 Broadway, Suite G, Santa Monica, California 90404

The United States Environmental Protection Agency’s Office of Ground Water and Drinking Water has developed a single-laboratory quantitation procedure: the lowest concentration minimum reporting level (LCMRL). The LCMRL is the lowest true concentration for which future recovery is predicted to fall, with high confidence (99%), between 50% and 150%. The procedure takes into account precision and accuracy. Multiple concentration replicates are processed through the entire analytical method and the data are plotted as measured sample concentration (yaxis) versus true concentration (x-axis). If the data support an assumption of constant variance over the concentration range, an ordinary least-squares regression line is drawn; otherwise, a variance-weighted least-squares regression is used. Prediction interval lines of 99% confidence are drawn about the regression. At the points where the prediction interval lines intersect with data quality objective lines of 50% and 150% recovery, lines are dropped to the x-axis. The higher of the two values is the LCMRL. The LCMRL procedure is flexible because the data quality objectives (50-150%) and the prediction interval confidence (99%) can be varied to suit program needs. The LCMRL determination is performed during method development only. A simpler procedure for verification of data quality * Corresponding author phone: (513) 569-7035; fax: (513) 5697837; e-mail: [email protected]. 10.1021/es051069f CCC: $33.50 Published on Web 11/25/2005

 2006 American Chemical Society

An important mission of the United States Environmental Protection Agency (EPA) is providing the nation with clean and safe water. Contaminated drinking water can pose a serious health risk to the public because of the elevated potential for exposure. The regulation of the new contaminants in the nation’s drinking water, however, can have serious cost implications to the public. Taken together, these concerns place unique demands on occurrence survey data that are used to support regulation. Quantitation level procedures are not defined consistently throughout the literature, but a quantitation level is typically used to describe a reporting level for data of known quality. To address the need for a quantitation level procedure and for a verification of such a level, a number of procedures described in the literature (1-14) were evaluated. These procedures are summarized in Table 1. Most approaches describe quantitation and detection as a multiple of standard deviation only (1-11). Several of the quantitation procedures apply an analysis of accuracy as well as precision, though the criteria were independently applied (12-14). Key concepts from these procedures were used to develop a new statistical procedure to determine a single-laboratory quantitation level, which is termed in this paper as the lowest concentration minimum reporting level (LCMRL). As presented here, the LCMRL is the single-laboratory-determined value that is the lowest true concentration for which the future recovery is predicted to fall, with high confidence (99%), between 50% and 150% (inclusive). In addition, the procedure for the verification of laboratory capability at or below the minimum reporting level was developed as a simpler procedure to verify laboratory proficiency at a predefined minimum reporting level (MRL). The MRL represents an established quantitation level that is set by client needs or regulation. It should be noted that the decision to report data below the MRL rests with the data user and is not within the scope of this paper. The LCMRL and verification procedures take into account the simultaneous effects that precision and accuracy will have on a quantitation level. Flexibility in the procedures is incorporated by allowing the data user to define the data quality objective bounds and the statistical confidence. The LCMRL and the verification procedures were developed to be easy to use and understand. The focus of the paper is to describe the LCMRL and the verification procedures. Examples of the LCMRL procedure are provided from work conducted during development of EPA Method 527.

Experimental Section LCMRL Determination. The analytical instrument must be calibrated with a range of instrument calibration standards that encompass the concentration levels being evaluated. Specifically, the concentration of the lowest instrument calibration standard must be at or below the fortification level of the sample that is currently being evaluated; otherwise, the LCMRL determination may not be reliable. VOL. 40, NO. 1, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Procedures Reviewed by OGWDW source

procedure

description

LC, critical level (low false positive error); LD, detection level (low false negative error); LQ, quantitation level, defined as a multiple (default 10 times) of the std dev; std dev determined from method blank replicates Glaser et al. (3) MDL MDL ) std dev times Student’s t (df degrees of freedom, one-sided interval, 99% confidence); fortified replicate samples used; calcd MDL should be 1/3 to 1/5 the concn of the spike level; mathematically equivalent to Currie’s LC EPA Method 1631 (4) ML ML ) 3.18(MDL) (3); for seven replicates, ML ) 10 times the std dev American Chemical LOQ recommended LOQ ) signal from blank + 10 times Society (5) the std dev Standard Methods (6) LOQ and practical LOQ ) 10 times the std dev of blank replicates; quantitation limit (PQL) PQL ) 5(MDL), which is defined similarly to the MDL of Glaser et al. (3) USGS (7) long-term MDL (LT-MDL), LT-MDL is calculated as the MDL of Glaser et al. laboratory reporting (3); additional variance is included from multiple level (LRL) instruments, different matrixes, and over time; LRL ) 2(LT-MDL). Gibbons, Coleman, alternate minimum a regression approach that provides for the case of nonand Maddalone (8) level (AML) constant variance throughout the instrument calibration working range; calcd Currie-type LC, LD, and LQ; LQ is based on the std dev only ASTM (9) interlaboratory quantitation regression approach that provides for nonconstant estimate (IQEZ%) variance throughout the working range; an interlaboratory quantitation level is determined on the basis of the use of the std dev only Hubaux and Vos (10) yC and xD yC is the decision limit corresponding to Currie’s LC; xD is a detection limit corresponding to Currie’s LD; calibration design for detection limits; based on the std dev only Sanders, Lippincott, quantitation levels (QLs) and interlaboratory quantitation level: the median interlab MDL and Eaton reliable detection level (RDL) (3) is multiplied by a variable determined from laboratory performance data (values ∼4-7); RDL ) 2(MDL) (3) Oxenford, McGeorge, practical quantitation criteria of quantitation level set for accuracy at and Jennis (12) levels (PQLs) (40% and for precision at less than 20% RSDa Hertz, Bordovsky, Marrollo, MRL DQOs are specified for accuracy (70-130% recovery) and Harper (13) and precision (10% RSDa), though independently applied Kimbrough and quality control level (QCL) DQOs are specified for accuracy (% recovery) and precision Wakakuwa (14) and verification procedure (% RSDa), though independently applied; verification procedure suggested International Union of Pure and Applied Chemistry (IUPAC) (Lloyd Currie) (1, 2)

a

LC, LD, LQ

% RSD ) percent relative standard deviation.

Ideally, seven replicate fortified samples in reagent water at each of four concentration levels are processed through the entire method procedure. At an absolute minimum, five samples at each of four concentrations, or seven samples at each of three concentrations, must be processed through the entire method procedure. All specified steps such as sample extraction or sample preservation must be included. The outlier identification is by the Dixon Q test (15), which is presented in the Discussion below. The exclusion of more than one outlier per data set may produce an unreliable LCMRL. A plot is made of the measured concentrations of the processed samples (y-axis) versus the true values of the fortified concentrations (x-axis) (see Figure 1). An ordinary least-squares (OLS) linear regression is made with the plotted data, unless the p value of the CookWeisberg test for constant variance (16) is less than 0.01, in which case a variance-weighted least-squares (VWLS) regression is used. Details for the Cook-Weisberg test for constant variance and the VWLS regression are presented in the Discussion of this paper. The regression line is not forced through the origin. Prediction interval lines of 99% confidence are included about the regression line. Data quality objective (DQO) bounds that correspond to 50% and 150% recovery, which by definition pass through the origin, are superimposed on the graph. At the points where the upper and lower prediction interval lines intersect with the DQO bounds, perpendicular lines are dropped to the x-axis. The higher of the two values represented by the perpendiculars intersecting at the x-axis 282

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FIGURE 1. Example of an LCMRL graph. denotes the LCMRL. In an effort to generate a reliable LCMRL, the LCMRL procedure specifies that at least one fortified sample set be at or below the LCMRL. An LCMRL calculator and the protocol document for the LCMRL and verification procedures are available on the EPA Web site (17). The LCMRL may also be calculated with statistical software if it is equivalent to the EPA software. Verification of Laboratory Performance at or below the MRL. The verification of laboratory performance at or below the MRL is a much simpler procedure than LCMRL determination, because it only checks that DQOs at or below a

predefined MRL are met. Initially, the data user defines the confidence level for the double-tailed Student’s t value and the DQO bounds. For the purposes of this paper, the confidence level is 99% and the DQO bounds are 50% and 150%. Note that the confidence level and DQO bounds are flexible and can be adjusted to the needs of a particular program. The verification procedure requires that at least seven samples, which are fortified at or below the MRL in reagent water, are processed through all steps of the method procedure. For example, sample extraction and preservatives must be included if they are part of the method. The lowest instrument calibration standard should be at or below the concentration level being evaluated. The instrument calibration range should be typical of day-to-day analysis. Outliers cannot be excluded for the verification procedure. A prediction interval of results (PIR) is calculated on the basis of eq 1 (18),

(

PIR ) (mean ( s)tdf,1-(1/2)R 1 +

1 N

1/2

)

(1)

where the mean is the average of at least seven replicates, t is Student’s t value with df degrees of freedom associated with an overall confidence level (1 - R), s is the standard deviation of n replicate samples fortified at the MRL, and n is the number of replicates. Note that the confidence for t is given in eq 1 as (1 - (1/2)R) because the formula is for a two-sided interval. For laboratory performance to be successfully verified at the MRL, the calculated PIR must be within the bounds of the DQO interval (50% and 150%). That is, the PIR lower limits cannot be lower than the lower bound of the DQO interval (50%), and the PIR upper limits cannot be greater than the upper limits of the DQO interval (150%). If laboratory performance at the MRL does not pass verification, the analyst should check if recalibration is needed, if instrument maintenance is necessary, and/or if the laboratory technique can be improved before a new set of verification samples are processed.

Discussion In developing a new statistical procedure for a singlelaboratory quantitation level, many quantitation procedures were evaluated in the literature (1-14). On the basis of this evaluation, it was decided that a regression/prediction interval approach based on multilevel sampling was best. A multilevel evaluation minimizes the influence of the variance at a single concentration on a determined quantitation level, which can be a concern when the region being investigated has uncertainty with respect to nonconstant variance. A graphical solution is an intuitive way to impose DQOs on analyte uncertainty at low-level concentration. It was one of the main goals in the evaluation process to set DQOs for accuracy and precision at the quantitation level. The intersection of DQO lines with prediction interval lines is a graphical form of equating their standard equations to find the lowest level that meets DQOs. The greater of the two values found from the intersections of the lower and upper prediction intervals with the DQO lines is recognized as the LCMRL because the lesser value does not satisfy DQOs. A tolerance interval has been suggested as an alternative, but the use of a prediction interval was found to be more easily applied as well as appropriate. A tolerance interval estimates a proportion, P, of the normal population that is covered by the interval (18). For example, a tolerance level could be described as having a 99% confidence for covering 90% of the population. For the procedures described here, the concern is that the tolerance level will only cover a certain percentage of the population. The prediction interval is

formed from a mean and standard deviation s of a random sample for the next future observation from the whole of a normally distributed population (18). The prediction interval appeared to be more applicable. The LCMRL determination does involve considerable data generation, but is required only of laboratories that are participating in analytical method development. Laboratories are encouraged to determine LCMRLs when they need to better understand their analytical capabilities. The process of determining LCMRLs may be valuable for a laboratory because the procedure for verification of multianalyte methods may require a number of dilutions to find the proper concentration level of each individual analyte. A multilevel analysis did not appear necessary for the verification procedure. It is not necessary to burden analytical laboratories with redetermining the lowest limit possible when an assessment of laboratory capability to achieve DQOs at or below a predefined MRL is all that is needed. Perhaps the simplest way to evaluate laboratory performance at a given level is to compare defined DQOs to a prediction interval of results that is based on the accuracy and precision of seven or more samples at one concentration level. In this case where the MRL is already defined, the process will yield a decision: either performance meets DQOs and it is acceptable or it fails the criteria and is not acceptable. Laboratories that are participating in routine sample analysis with a predefined MRL need only satisfy the requirements of the verification procedure. An assessment that passes at a level below the MRL is considered acceptable as well. Several potential issues for the LCMRL procedure and verification procedure are discussed below, including instrument calibration, fortification levels for samples, nonconstant variance and VWLS, and outliers. The decision to report data that fall below a quantitation level and do not satisfy DQOs will depend on the data user and is not a point of discussion here. The procedures in this paper were designed for continuous (e.g., Gaussian) data, rather than discrete data, such as those found in “counting” methods. LCMRL Procedure. Fortified samples processed as described in the Experimental Section and data are plotted as in Figure 1, which shows seven replicates each at four different concentrations. The graph in Figure 1 contains two points where the DQO bounds intersect with prediction interval lines. The higher of the intersection points corresponds to the minimum concentration at which sample results would be expected to meet the 50-150% DQO criteria with 99% confidence. In this way, the LCMRL procedure is a graphical technique that takes into account the simultaneous effect on the quantitation level of accuracy and precision. Quantitation levels are ultimately defined by decisions that the data user makes in terms of the level of confidence and DQOs. A lower quantitation limit can always be cited, but there is a cost of increased uncertainty in the derived value. The DQO interval that was chosen for use in this paper, 50-150%, was based upon experienced judgment from experienced analysts. The 99% confidence level used for the prediction interval is conservative, but appropriate for drinking water surveys upon which decisions concerning regulation or compliance must be based. The user flexibility to adjust the confidence level and the DQOs has the potential to permit these procedures to be used by other quality assurance programs with different accuracy and precision requirements. Currently, there is no time requirement to process or analyze LCMRL replicate samples. If data users find time variability is an issue for their program, then it is certainly within their prerogative to require it. To determine a reliable LCMRL, the instrument calibration that is used to process samples must have instrument calibration standards that encompass the fortification levels VOL. 40, NO. 1, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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that are being investigated. The instrument calibration range used during the LCMRL determination may not be the same for all sets of the data. When an additional fortified sample set is needed at a lower concentration to bracket the LCMRL, an additional instrument calibration standard may be needed at a lower concentration. In general, the instrument calibration range must be typical of expected day-to-day routine sample analysis. The use of an instrument calibration that has an unreasonably narrow range may yield a lower LCMRL, but the LCMRL will not reliably reflect routine analysis when the instrument calibration is expanded beyond that which is used to process LCMRL data. The continued use of instrument calibration levels that are found to be below the LCMRL is at the discretion of the analyst. In most cases, four fortification levels of seven replicates will be prepared for the LCMRL, but for multianalyte methods, where target analytes may have different responses, more than four levels may be required. Often the best starting point for a spiking concentration is a level at which an experienced analyst considers reliable for quantitation. Other suggested levels would be concentrations about 50% above and below the estimated level of reliable concentration in an attempt to bracket the unknown LCMRL. When interferences are present, it is suggested to use a low-level estimate at 3 times the equivalent concentration of the analyte peak as found in the method blank. One way to minimize the number of fortification levels is to calculate an estimated LCMRL after the analysis of three fortification levels to gain a better idea of where to fortify the fourth level. In an effort to better define the region of lowest quantitation, it is recommended that the range of spike concentrations be around a factor of 5-10. This may not always be possible, because multianalyte solutions are often made with many analytes at the same concentration, but the analytes may show drastically different responses to detection. In this case, a factor of 20 may be more realistic. The LCMRL procedure specifies that the concentration of at least one fortified sample set be below the LCMRL. If the higher intersection of the prediction and DQO bounds is found to be lower in concentration than the lowest fortified set of samples, then another fortified sample set should be run at a lower concentration in an effort to bracket the LCMRL. If data are not available below this point, then the LCMRL is set at the lowest concentration of fortified samples. When the apparent intersection of the DQO bounds and the prediction interval occurs above the level of the highest fortified sample set being evaluated, the LCMRL cannot be determined, because the LCMRL cannot be estimated above the highest concentration of fortified samples. In such cases, it is recommended that another set of fortified samples be run at a higher concentration to bracket the LCMRL within the range of fortified samples. Outliers. Extreme data observations, or outliers, can occur. Outliers may represent the actual laboratory conditions, may result from changed conditions and represent a different population of data being investigated, or may be caused by analyst or instrument error. The removal of an outlier should be done with extreme caution. Two acceptable reasons to remove an outlier are because of known analyst/instrument error or because an outlier has been identified through a statistical test. For the LCMRL procedure, the Dixon Q test (15) with 99% confidence is used and is shown below:

Q)

|xo - xc| xhi - xlo

(2)

Here xo is the potential outlier, xc is the closest value to the potential outlier, xhi is the highest value in the data set (including the outlier, if applicable), and xlo is the lowest value in the data set (including the outlier, if applicable). The 284

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calculated Q value is compared to the critical value list in a table for Dixon’s r10 (Q) parameter, two-tailed test at the 99% confidence level. For n ) 7 and two-tailed 99% confidence, the critical value is 0.680. For seven samples if the calculated Q is greater than 0.680, then the data point is identified as an outlier and it can be discarded. Only one outlier per LCMRL determination is allowed to be discarded. It is suggested that the removal of an outlier be noted when an LCMRL is reported. The verification procedure does not permit the removal of outliers. Dixon’s Q test was chosen to identify outliers because it does not require knowledge (or an assumption of knowledge) of the population standard deviation or population mean, as do tests that rely on Student’s t distribution. Dixon’s Q test also has the advantage of ease of use. Nonconstant Variance. Variance tends to increase with concentration, but the use of OLS assumes constant variance. Once data are collected, the assumption of constant variance across the fortification levels must be tested. The CookWeisberg test for constant variance (16) is used in the LCMRL procedure. The data pass the constant variance test if the p value of the test is 0.01 or greater. If the data fail the constant variance test, a VWLS model must be used. For VWLS, the measured and spiked concentration data are weighted by the inverse of the standard deviation (i.e., the square root of the variance) of the measured concentrations at their corresponding spiking concentrations. Note that VWLS assumes that the population variance (and standard deviation) at each spiking concentration is known and that the replicate data are normally distributed. LCMRL Examples. It was a goal in developing the LCMRL procedure that both accuracy and precision would be used to determine a quantitation level. The sole use of standard deviation to determine a quantitation level ignores the existence in analytical instrumentation of nonideal processes, such as analyte degradation, analyte absorption, matrix enhancement, and interferences. In such cases, a quantitation limit based only on standard deviation may not be reliable and there may be a higher rate of false positive and false negative errors than theory would suggest. Table 2 is a list of target analytes from EPA Method 527 (19) with values for the LCMRL, the signal-to-noise measurements at the LCMRL, and values for a quantitation limit that is based on a factor of 10 times the standard deviation, which will be called here QL10(SD). Ten times the standard deviation has been commonly used as a value for the quantitation level. Currie described a default value for a quantitation limit as equivalent to 10 standard deviations of a series of replicate measurements (1). The standard methods LOQ (5) and the minimum level (ML) proposed by the EPA (4) also use this definition. The QL10(SD) was calculated by multiplying the MDL, found in the manner specified by Glaser et al. (3), by a factor of 3.18, which yields a level of 10 times the standard deviation. In Table 2, some QL10(SD) values are near the LCMRL and some are quite different. When analyte behavior is wellbehaved with respect to instrument calibration and sample processing, the QL10(SD) tends to be close to the LCMRL. Two examples of analyte behavior and the effect on the LCMRL are shown below for thiobencarb (Figures 2-4) and fenvalerate (Figures 5-7). An illustration of near ideal analyte behavior is shown by thiobencarb in Figures 2-4. The QL10(SD) and LCMRL were similar, 0.12 and 0.13 µg/L, respectively. Figure 2 shows the thiobencarb calibration curve as well-behaved, almost linear, with a near intersection of the origin. Figure 3 shows the mass/charge (m/z) 100 ion trace and spectrum of thiobencarb at 0.10 µg/L in a fortified reagent water sample. The level of 0.10 µg/L was a little less than the values for QL10(SD) and LCMRL. The analyte response was

TABLE 2. EPA Method 527 (18) Analytes Listed with Values for QL10(SD), the LCMRL, and the Signal-to-Noise Measurements at the LCMRL analyte

QL10(SD)a (µg/ L)

LCMRL (µg/L)

S/N at LCMRLb

dimethoate atrazine propazine vinclozolin prometryn bromacil malathion chlorpyrifos thiobencarb parathion terbufos sulfone oxychlordane esbiol nitrophen kepone norflurazon hexazinone bifenthrin BDE-47 mirex BDE-100 BDE-99 hexabromobiphenyl fenvalerate esfenvalerate BDE-153

0.080 0.11 0.12 0.27 0.089 0.30 0.18 0.083 0.12 0.20 0.13 0.35 0.13 0.23 0.24 0.24 0.15 0.13 0.089 0.070 0.16 0.31 0.35 0.25 0.20 0.45

0.36 0.16 0.18 0.29 0.20 0.45 0.51 0.12 0.13 0.29 0.27 0.27 0.31 0.51 0.35 0.53 0.41 0.21 0.18 0.21 0.29 0.39 0.44 0.67 0.48 0.40

7 12 15 15 17 9 12 11 10 5 18 9 15 13 5 14 22 21 6 13 6 6 10 16 12 11

FIGURE 3. Thiobencarb m/z 100 ion trace and spectrum at 0.10 µg/L in a fortified reagent water sample.

a QL 10(SD) is defined here as 10 times the standard deviation found in the MDL procedure as given by Glaser et al. (3). b The signal-to-noise (S/N) value for the LCMRL was estimated by dividing the signal of the closest spiking level to the LCMRL by the peak-to-peak noise in the blank and adjusting for the LCMRL concentration difference. Seven replicate samples were processed through the entire method procedure.

FIGURE 4. LCMRL graph for thiobencarb. and both appear to be a level that an analyst would feel comfortable using as a quantitation level.

FIGURE 2. Thiobencarb instrument calibration curve with a quadratic fit. seen to be well above the background noise in the m/z 100 trace and in the mass spectrum taken at midpeak. Figure 4 shows the LCMRL graph of thiobencarb. Note that the LCMRL regression line is fairly symmetrical with respect to the data quality objective lines at 50% and 150% and crosses the y-axis near the origin. The LCMRL and QL10(SD) are about the same,

An example of the effect of nonideal analyte behavior on the LCMRL is demonstrated by fenvalerate. As seen in Table 2, the QL10(SD) and LCMRL values for fenvalerate were quite different, 0.25 and 0.67 µg/L, respectively. The instrument calibration curve for fenvalerate shown in Figure 5 was used to quantitate the original data and shows quadratic character with the calibration line intersecting with the x-axis far short of the origin. Figure 6 shows the ion trace for quantitation ion m/z 167 at 0.20 µg/L for a fortified reagent water sample, which was the spiking level nearest the QL10(SD) of 0.25 µg/L. At a concentration of 0.20 µg/L, the signal-to-noise ratio was quite low, less than 3, and a manual integration of the analyte peak would have required a decision with a high level of subjectivity. The QL10(SD) here would pose problems with false positives and false negatives, and such a quantitation level would be used with low confidence. The spectrum in Figure 6 shows that the quantitation ion of 167 and a characteristic ion of fenvalerate, m/z 181, are much smaller than the ion m/z 149, which is a background interferent. VOL. 40, NO. 1, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 7. LCMRL graph for fenvalerate.

FIGURE 5. Fenvalerate instrument calibration curve with a quadratic fit.

FIGURE 8. Fenvalerate m/z 167 ion trace and spectrum at 0.50 µg/L.

FIGURE 6. Fenvalerate m/z 167 ion trace and spectrum at 0.20 µg/L. Figure 7 shows the LCMRL graph for fenvalerate, which yielded a value of 0.67 µg/L. Figure 8 shows the quantitation ion trace for m/z 167 at 0.5 µg/L for a fortified reagent water sample. Even though the 0.5 µg/L level was less than the LCMRL of 0.67 µg/L, it is clear upon inspection that the 0.5 µg/L ion peak could be manually integrated without controversy, and that the peak was significantly above the background noise. In light of the nonideal analyte behavior of fenvalerate, the LCMRL of 0.67 µg/L, as opposed to a QL10(SD) of 0.25 µg/L, appears to be a more reasonable quantitation level. Verification of Laboratory Performance at or below the MRL. Laboratories that are participating in routine sample analysis with a predefined MRL need only satisfy the 286

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requirements of the verification procedure. When DQOs for a predefined MRL have to be met, it is not necessary to redetermine a quantitation level, or to see “how low you can go”. Laboratory performance at an MRL is simply evaluated by comparing predefined DQO bounds to a PIR that is based on the accuracy and precision of seven or more samples at one concentration level. The verification procedure yields a “pass” or “fail” decision. An example of the verification procedure is shown in Figure 9. In this case, the laboratory passes the verification requirement for aldicarb sulfone at an MRL of 0.20 mg/L. It is recommended that a laboratory fortified blank (LFB), at or below the MRL, be run with each analytical batch to provide an ongoing verification that DQOs for low-level recovery are being met. The simpler and easier verification of the laboratory performance procedure permits laboratories that conduct routine sample analysis to demonstrate performance at or below an MRL without having to rederive a quantitation level. The more labor-intensive LCMRL is required only when laboratories participate in method development or wish to test “how low they can go”. Both procedures take into account

Literature Cited

FIGURE 9. Example of verification at the MRL of aldicarb sulfone from EPA Method 531.2. the combined effects of accuracy and precision on the quantitation limit. Future Development. The LCMRL and verification procedures have been in development for the past three years and have benefited from review from within and outside the EPA’s Office of Ground Water and Drinking Water (OGWDW). The last seven analytical methods from the OGWDW and from the EPA’s National Environmental Research Laboratory (NERL) in Cincinnati have included LCMRL determinations (19-25). Other analytical programs may find usefulness in this approach to defining the quantitation level and in the flexibility that these procedures can provide by adjusting the confidence level and data quality bounds. Future applications may include the application of a Hubaux-Vos plot using the data generated for the LCMRL to estimate detection limits (10). Public comment will be solicited on the LCMRL and verification procedures in conjunction with a rule proposal due out in the summer of 2005. In particular, OGWDW will continue to look at alternate mechanisms for cases of nonconstant variance. An evaluation of the procedures presented here will be expected in the context of a comprehensive assessment of various detection and quantitation approaches under the Clean Water Act program.

Acknowledgments This work has been funded in part by the United States Environmental Protection Agency under Contract No. 68C-01-098 with Shaw Environmental, Inc. and under Contract No. 68-C-02-026 with The Cadmus Group, Inc. This paper has been subject to the Agency’s review, and it has been approved for publication as an EPA document. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. We appreciate the input of the following individuals who contributed to peer review of the initial documents used to design the interlaboratory study and in the determination of LCMRLs/ MRLs: Richard Albert, United States Food and Drug Administration (retired); William Horwitz, AOAC International; William Foreman, United States Geological Survey; Andrew Eaton, MWH Laboratories; William Telliard and personnel from EPA’s Engineering and Analysis Division; Brad Venner of the U.S. EPA’s National Enforcement Investigations Center.

(1) Currie, L. A. Detection and quantification limits: origins and historical overview. Anal. Chim. Acta 1999, 391, 105-126. (2) Currie, L. A. Limits for qualitative detection and quantitative determination. Anal. Chem. 1968, 40, 586-593. (3) Glaser, J. A.; Forest, D. L.; McKee, G. D.; Quave, S. A.; Budde W. L. Trace analyses for wastewaters. Environ. Sci. Technol. 1981 15, 1426-1435. (4) EPA Method 1631, Revision E: Mercury in Water by Oxidation, Purge and Trap, and Cold Vapor Atomic Fluorescence Spectrometry; EPA-821-R-02-019; EPA Office of Science and Technology: Washington, DC, 2002; http://www.epa.gov/waterscience/methods/1631e.pdf. (5) Keith, L. H.; Crummet, W.; Deegan, J., Jr.; Libby, R. A.; Taylor, J. K.; Wentler, G. Principles of Environmental Analysis. Anal. Chem. 1983, 55, 2210-2218. (6) Clesceri, L. S., Greenberg, A. E., Trussell, R. R., Eds.; Method detection level. Standard Methods for the Examination of Water and Wastewater, 19th ed.; American Public Health Association: Washington, DC, 1995; Part 1030 E, pp 1-10-1-11. (7) Childress, C. J. O.; Foreman, W. T.; Conner, B. F.; Maloney, T. J. New reporting procedures based on long-term method detection levels and some considerations for interpretations of water-quality data provided by the U.S. Geological Survey National Water Quality Laboratory; U.S. Geological Survey Open-File Report 99-193; U.S. Geological Survey: Reston, VA, 1999; http:// water.usgs.gov/owq/OFR_99-193/ofr99_193.pdf. (8) Gibbons, R. D.; Coleman, D. E.; Maddalone, R. F. An alternative minimum level definition for analytical quantification. Environ. Sci. Technol. 1997, 31, 2071-2077. (9) American Society for Testing and Materials. 2002 Annual Book of ASTM Standards, Standard Practice for Interlaboratory Quantitation Estimate; ASTM D 6512-00; ASTM International: West Conshohocken, PA, 2002; Vol. 11.01, Section 11 Water, pp 888-902. (10) Hubaux, A.; Vos, G. Decision and detection limits for linear calibration curves. Anal. Chem. 1970, 42, 8 849-855. (11) Sanders, P. F.; Lippincott, R. L.; Eaton, A. A Pragmatic Approach for Determining Quantitation Levels for Regulatory Purposes. Proceedings of the Water Quality Technology Conference; American Water Works Association: Denver, CO, 1996; Vol. 2. (12) Oxenford, J. L.; McGeorge, L. J.; Jennis, S. W. Determination of Practical Quantitation Levels for Organic Compounds in Drinking Water. J.sAm. Water Works Assoc. 1989, 149-153. (13) Hertz, C. D.; Bordovsky, J.; Marrollo, L.; Harper, R. E. Minimum Reporting Levels Based on Precision and Accuracy for inorganic parameters in water. Proceedings of the Water Quality Technology Conference; American Water Works Association: Denver, CO, 1992. (14) Kimbrough, D. E.; Wakakuwa, J. Quality control level: an alternative to detection levels. Environ. Sci. Technol. 1994, 28, 338-345. (15) Rorabacher, D. B. Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon’s “Q” Parameter and Related Subrange Ratios at the 95% Confidence Level. Anal. Chem. 1991, 63, 139-146. (16) Weisberg, S. Applied Linear Regression, 2nd ed.; John Wiley & Sons: New York, 1985. (17) Statistical Protocol for the Determination of the Single-Laboratory Lowest Concentration Minimum Reporting Level (LCMRL) and Validation of Laboratory Performance at or Below the Minimum Reporting Level (MRL); EPA 815-R-05-006; EPA: Washington, DC, November 2004; see also the Internet-accessible LCMRL calculator at www.epa.gov/safewater/methods/sourcalt.html. (18) Dixon, W. J.; Massey, F. J., Jr. Introduction to Statistical Analysis 4th ed.; McGraw-Hill Book Co.: New York, 1983; p 92. (19) EPA Method 527 Rev. 1.0sDetermination of Selected Pesticides and Flame Retardants in Drinking Water by Solid-Phase Extraction and Capillary Column Gas Chromatography/Mass Spectrometry (GS/MS); EPA 815-R-05-005; U.S. EPA Office of Ground Water and Drinking Water: Washington, DC, 2005; http://www.epa.gov/OGWDW/methods/sourcalt.html. (20) EPA Method 314.1 Rev. 1.0sDetermination of Perchlorate in Drinking Water Using Online Column Concentration/Matrix Elimination Ion Chromatography with Suppressed Conductivity Detection; U.S. EPA Office of Ground Water and Drinking Water: Washington, DC, 2005; http://www.epa.gov/OGWDW/ methods/sourcalt.html. (21) EPA Method 331.0 Rev. 1.0sDetermination of Perchlorate in Drinking Water by Liquid Chromatography Electrospray Ionization Mass Spectrometry; EPA 815-R-05-007; U.S. EPA Office of Ground Water and Drinking Water: Washington, DC, 2005; VOL. 40, NO. 1, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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http://www.epa.gov/OGWDW/methods/sourcalt.html. (22) EPA Method 332.0sDetermination of Perchlorate in Drinking Water by Ion Chromatography with Suppressed Conductivity and Electrospray Ionization Mass Spectrometry; EPA/600/R-05/ 049; U.S. EPA Office of Research and Development, National Exposure Research Laboratory: Research Triangle Park, NC, 2005; http://www.epa.gov/nerlcwww/ordmeth.htm. (23) EPA Method 521sDetermination of Nitrosamines in Drinking Water by Solid-Phase Extraction and Capillary Column Gas Chromatography with Large Volume Injection and Chemical Ionization Tandem Mass Spectrometry (MS/MS); EPA/600/R05/054; U.S. EPA Office of Research and Development, National Exposure Research Laboratory: Research Triangle Park, NC, 2004; http://www.epa.gov/nerlcwww/ordmeth.htm. (24) EPA Method 529sDetermination of Explosives and Related Compounds in Drinking Water by Solid-Phase Extraction and

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Capillary Column Gas Chromatography/Mass Spectrometry (GC/ MS); EPA/600/R-05/052; U.S. EPA Office of Research and Development, National Exposure Research Laboratory: Research Triangle Park, NC, 2002; http://www.epa.gov/nerlcwww/ ordmeth.htm. (25) EPA Method 535 Rev. 1.1sMeasurement of Chloroacetanilide and Other Acetamide Herbicide Degradates in Drinking Water by Solid Phase Extraction and Liquid Chromatography/Tandem Mass Spectrometry (LC/MS/MS); EPA/600/R-05/053; U.S. EPA Office of Research and Development, National Exposure Research Laboratory: Research Triangle Park, NC, 2005; http:// www.epa.gov/nerlcwww/ordmeth.htm.

Received for review June 7, 2005. Revised manuscript received October 13, 2005. Accepted October 17, 2005. ES051069F