JlBaneiie Arlington Otnce 2101 Wilson Boulevard. Suite 800 \rlmgton V-\ :220l-Uir)H Iflecopiur irtl'il ~,5-~,Mn February 17, 1989 Ms. Mary Frankenberry U.S. Environmental Protection Agency Office of Toxic Substances 401 M Street, SW Washington, DC 20460 Dear Mary: Contract No. 68-02-4294 Enclosed is a copy of the Draft Final Report, for Task 2-22, "Quality Control Guidance," prepared under the above contract number. If you have any questions, please call me at (703) 875-2963 or Bertram Price at (202) 457-9007. Sincerely, Barbara Leczynski Project Manager Applied Statistics and Computer Applications Section BL:bs Enclosures cc: S. Dillman J. Glatz C. Stroup P. Cross, EED Contract Monitor E. Sterrett L. Farmer (Itr only) ------- February 16, 1989 DRAFT FINAL REPORT for Task 2-22 QUALITY CONTROL GUIDANCE by Bertram Price Anne Morris Price Price Associates 1825 K Street, N.W. Washington, D.C. 20006 Barbara Leczynski Task Leader BATTELLE Columbus Division - Washington Operations 2101 Wilson Boulvard Suite 800 Arlington, Virginia 22201 Contract No. 68-02-4294 Susan Dillman, Co-Task Manager Jay Glatz, Co-Task Manager Mary Frankenberry, Project Officer Design and Development Branch Exposure Evaluation Division Office of Toxic Substances Office of Pesticides and Toxic Substances U.S. Environmental Protection Agency Washington, D.C. 20460 ------- OTS DISCLAIMER This report was prepared under contract to an agency of the United States Government. Neither the United States Government nor any of its employees, contractors, subcontractors or their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third part's use of or the results of such use of any information, apparatus, product, or process disclosed in this report, or represents that its use by such third party would not infringe on privately owned rights. y Publication of the data in this document does not signify that the contents necessarily reflect the joint or separate views and policies of each sponsoring agency. Mention of trade names or commercials products does not constitute endorsement or recommendation for use. BATTELLE DISCLAIMER This is a report of research performed for the United States Government by Battelle. Because of the uncertainties inherent in experimental or research work, Battelle assumes no responsibility or liability for any consequences of use, misuse. inability to use, or reliance upon the information contained herein, beyond any express obligations embodied in the governinq written agreement between Battelle and the United States Government. 11 ------- TABLE OF CONTENTS TABLE OF CONTENTS iii EXECUTIVE SUMMARY v 1. 0 INTRODUCTION 1 2 . 0 CONCLUSIONS 5 3.0 INSTRUMENT RESPONSE MODEL AND ESTIMATION METHOD 10 3.1 The Calibration Step 13 3.2 Estimating Concentrations of Target Compounds.. 15 3 .3 Quality Control Samples 18 4 . 0 THE QC PROGRAM 22 4 .1 Description 22 4.1.1 Routine Calibration Check 25 4.1.2 Recovery 26 4.1.3 Post Analysis Review of QC Data 27 4.2 Discussion of QC Program Elements 30 4.2.1 Real Time QC 31 4.2.1.1 Routine Calibration Check Sample (RCC) 31 4.2.1.2 Recovery 33 4.2.2 Post Analysis Summary of Data Quality... 34 5. 0 SIMULATION ANALYSIS 36 5.1 Introduction 36 5.2 Description of Analysis and Parameter Values 38 5. 3 Results 45 REFERENCES 52 111 ------- TABLE OF CONTENTS (continued) LIST OF TABLES Table E-l Table E-2 Table 4-1 Table 5-1 Table 5-2 Table 5-3 Table 5-4 Probabilities of Detecting Calibration and Recovery Shifts viii TCDD Simulation Model Parameter Values: "In Control" Case QC Procedures and Criteria for Analysis of Human Adipose Tissue Samples for PCDDs and PCDFs TCDD Simulation Model Parameter Values: "In Control" Case TCDD Simulation Model Parameter Values: RRF Shift TCDD Simulation Model Parameter Values: Recovery Shift Probabilities of Detecting Calibration and Recovery Shifts ix 23 41 43 44 46 LIST OF FIGURES Figure 5-1 QC Tests, Decisions, and Corrective Actions 40 IV ------- DRAFT EXECUTIVE SUMMARY The U.S. Environmental Protection Agency (EPA) analyzes adipose tissue samples collected in the National Human Adipose Tissue Survey (NHATS) to estimate and monitor exposure to environmentally persistent toxic compounds. In 1982 the program was expanded to include analysis methods for determining concentrations of polychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs). The quality assurance project plan (QAPP) for the analysis of the 1987 samples specifies various types of quality control (QC) activities intended to assure and document data quality. Since QC costs can be significant, a study was initiated to investigate the effectiveness and costs of the current QC program as well as other QC programs that may be considered for the analysis of NHATS samples in future years. To advance the investigation, a computer simulation model of the laboratory process for adipose tissue analysis has been developed. The model simulates events in their sequence of occurrence in the laboratory. It distinguishes batches, days required to complete a batch, and the following QC activities: initial calibration; routine calibration check at the beginning and at the end of each day; a test of absolute recovery of the internal quantitation standard (IQS) in every sample; and a v ------- DRAFT test of method recovery (MR) following the completion of each batch. The simulation model may be applied to analyze effectiveness and costs for a variety of QC programs and data quality objectives including the QC program used for the 1987 samples. To demonstrate the analysis approach, the model has been used to address three questions concerning the current QC program for NHATS samples. A more comprehensive analysis, based on the simulation model, will be necessary to thoroughly evaluate costs and efficiency for NHATS QC program alternatives. The three questions are: 1. What are the false positive error rates associated with the routine calibration check, the test of absolute recovery of the internal quantitation standard, and the method recovery test? 2. What are the probabilities that these three components of the QC program will detect a change in the calibration coefficient (usually referred to as the relative response factor - RRF)? VI ------- DRAFT 3. What are the probabilities that these three components of the QC program will detect a ' degradation in method recovery? Simulation results have been developed that provide answers to the three questions. Results for TCDD are summarized in Table E-l and discussed below. (TCDD is used as an example throughout the study wherever specificity enhances the presentation.) Briefly, the analysis indicates that: o the routine calibration test is effective; o the absolute IQS recovery test as currently formulated may cause positive bias in concentration estimates; and o the relationship between tests of IQS recovery and method recovery needs better coordination with data quality objectives. When the analytical process is "in control," (the first column of Table E-l, based on the parameter values in Table E- 2), the probability of detecting a calibration failure is less than 0.01 (i.e., the false positive error rate is small). The column labeled "RRF Shift" in Table E-l refers to an increase vii ------- DRAFT Table E-l. Probabilities of Detecting Calibration and Recovery Shifts Status of Analytical Process PC Test In Control RFF Shift Recovery Shift Probability of Detection Routine Calibration <0.01 >0.99 <0.01 Check (RCC)* Internal Quantitation 0.39 0.45 • 0.14 Standard (IQS)2 Method Recovery (MR)3 0.09 0.10 0.69 Notes: 1 - probability of detecting at least one RCC failure (i.e, two consecutive RCC sample failures) per batch 2 - probability of detecting at least one IQS failure per batch 3 - probability of detecting an MR failure per batch viii ------- DRAFT Table E-2. TCDD Simulation Model Parameter Values: "In Control" Case Analysis Operation GC Resp. Parameter Recovery Intercept Slope TCDD IS Standard Deviation Batch Sample Analysis Calibration Std/IS IS/RS 0.00 0.00 0.80 1.73 1.000 1.000 1.000 1.000 0.00 0.00 0.0000 0.0000 0.0500 0.0800 Field Samples U/IS IS/RS 0.00 0.00 0.80 1.73 0.595 1.000 0.521 0.521 0.15 0.15 0.1250 0.0525 0.1000 0.1575 QC Samples Std/IS IS/RS 0.00 0.00 0.80 1.73 0.595 1.000 0.521 0.521 0.15 0.15 0.0150 0.0525 0.0450 0.1575 Notes: The symbols */* in the left hand column refer to ratios of areas that represent instrument responses. The numbers in each row are the parameter values used in the equation to generate an instrument response for the ratio indicated in the first column. For example, U/IS refers to the equation used to produce the ratio of areas corresponding to the concentration of TCDD in a primary sample and the concentration of the internal quantitation standard. Std - a sample spiked with a known amount of TCDD RS - recovery standard sample ix ------- DRAFT in the RRF of 37.5 percent immediately following the initial calibration. The detection probability of the routine calibration test in this situation is greater than 0.99. The routine calibration test, therefore, is extremely effective for detecting a change of this magnitude. When the analytical process is "in control" the internal quantitation standard (IQS) test has a probability of 0.39 for detecting failures, a large value for a false positive error rate. IQS absolute recovery test failures have two consequences. First, the batch must be reextracted and analyzed resulting in additional cost. Second, the test favors larger recovery values. Estimated concentrations of TCDD in primary tissue samples, therefore, will be biased toward larger values. These findings suggest that the IQS recovery test, which currently requires IQS recovery to be in the fixed interval between 0.40 and 1.50, should be based on a statistical interval with boundaries determined from the mean and standard deviation of the recovery estimate. The column labeled "Recovery Shift" reflects a change from the "in control" case in both IQS absolute recovery and method recovery. IQS recovery has been increased from 0.521 for the "in control" case to 0.600 and method recovery from 1.142 to 1.500. The IQS detection probability drops from 0.39 to 0.14 ------- DRAFT because the true IQS recovery value is closer to the center of the allowable range than it was in the other two cases. The detection probability for the method recovery test has increased from 0.09 to 0.69 because the hypothetical true MR value of 1.500 is also the upper boundary of the MR test interval. (Note that the range of values defining the IQS test and the MR test are the same.) The apparent inconsistency between the detection probabilities of the two recovery tests is, in part, a consequence of the fixed interval approach to defining the recovery tests. These tests should reflect DQO's associated with applications of the data and, as indicated above, should be based on statistical characteristics of the recovery estimates. The results discussed above reflect two sets of assumptions. The first assumptions, which are implicit in the QC program, form the basis for detecting and correcting recovery problems. These assumptions are: 1. when absolute recovery of the target compound in a primary sample declines as a result of sample processing, absolute recovery of the internal quantitation standard in the same sample also declines; and XI ------- DRAFT 2. when absolute recovery of the target compound in a primary sample declines as a result of sample processing, absolute recovery of that target compound in a QC sample also declines. Under these assumptions: (i) absolute recovery of the internal quantitation standard acts as a recovery adjustment applied to estimates of target compound concentrations; and (ii) method recovery computed from QC samples is representative of method recovery in primary tissue samples. Neither assumption is easily verified and if either assumption were violated, portions of the QC program may be ineffective. It is notable that under these assumptions a change in the value of absolute recovery of the internal quantitation standard does not signal a change in method recovery. The second set of assumptions concerns parameter values selected for the simulation that characterize recovery, variability, and the calibration curve of the analytical method. Most of the values used for the cases represented in Table E-l were derived from data generated in a method validation study (USEPA, 1986). A few of the values, which could not be derived from the method validation data were based purely on judgement. Additional values for the parameters, determined either subjectively or from more recent data, are xii ------- DRAFT needed to conduct a sensitivity analysis of the results in Table E-l and any subsequent findings regarding alternative QC proposals. The results presented in this report serve as one example of the type of analysis that can be conducted with the simulation model. Additional analyses using the model are needed to evaluate alternative QC programs and alternative data quality objectives. First, however, QC alternatives must be refined to ensure they are practical with respect to laboratory operating constraints and additional PCDD (PCDF) measurement data, if available, need to be analyzed to improve, if possible, estimates of model parameters. Xlll ------- DRAFT 1.0 INTRODUCTION The U.S. Environmental Protection Agency (EPA) analyzes adipose tissue samples collected in the National Human Adipose Tissue Survey (NHATS) to estimate and monitor exposure to environmentally persistent toxic compounds. NHATS is a statistically designed program intended to represent the general U.S. adult population. In 1982 the program was expanded to include analysis methods for determining concentrations of polychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs). A detailed quality assurance project plan (QAPP) was developed for the analysis of the 1987 samples (MRI, 1988). The QAPP specifies various types of quality control (QC) activities. These activities, which include analysis of QC samples, are intended to assure data quality and provide information that documents data quality. Since QC activities can add significant cost to an analytical program, the effectiveness and cost of alternative QC programs for the NHATS analysis is being investigated. To further that investigation, a model has been developed to analyze the effectiveness and cost of alternative QC programs. This report describes the model and its application for analyzing the QC program specified "in the QAPP for PCDD's (PCDF's). The analysis of tissue samples collected in 1987 involved 5 batches, each batch containing 12-15 composite samples. The analytical method is high resolution gas chromatography/high ------- DRAFT resolution mass spectrometry (HRGC/HRMS). The QAPP specifies analysis of QC samples including calibration checks, controls, and spikes. The purpose of QC samples, in general, is to monitor and document the quality of data being produced. Since the unit cost of a QC sample analysis is equal to the unit cost for analyzing a primary sample, efficient allocation of QC resources in terms of types and numbers of samples is essential. Each QC sample must contribute in a measurable way to the quality of data used for estimating PCDD (PCDF) concentrations in primary samples. To evaluate alternative QC plans from a cost-effectiveness perspective, quantitative data quality objectives (DQO's) are needed. DQO's should be associated with particular applications of the primary data. The types and numbers of QC samples necessary to achieve a DQO, then, can be assessed. For example, the PCDD (PCDF) estimates obtained by analyzing human adipose samples may be used: (i) to determine if the 1987 levels of PCDD (PCDF) are above or below an established standard (e.g., a standard based on health considerations); or ------- DRAFT (ii) to determine if there is a trend in PCDD (PCDF) levels (e.g., compare 1987 results with past results). The DQO in both of these examples may be specified as a pair of values for the Type I and Type II statistical error rates (e.g., a Type I error rate of 0.15 and a Type II error rate of 0.20) associated with statistical tests of the implied hypotheses . This approach to data quality, which focuses on error rates associated with statistical decisions based on monitoring data, is consistent with recent guidance on the development of DQO's prepared by the EPA/ORD Quality Assurance Management Staff. The magnitudes of statistical test error rates are affected by recovery of the analytical measurement method, variability of the method, and replication. Information about recovery and variability is obtained through analyses of QC samples. An analytical response model, introduced in Section 3, is used to describe the concentration estimates produced by the HRGC/HRMS method. The model includes explicit parameters that characterize calibration, recovery, and variability. The analysis of QC program effectiveness is based on the model and these parameters. Measurement characteristics of TCDD, one of ------- DRAFT the PCDD congeners, are used throughout this report as a specific example to'enhance exposition. The remainder of this report is presented in four sections. Conclusions are summarized in Section 2. Section 3 contains a description of the analytical response model and a discussion of the method employed for estimating concentrations of target compounds in adipose tissue. The current QC program is described in Section 4 and results of computer simulation analysis are presented in Section 5. ------- DRAFT 2.0 CONCLUSIONS A computer simulation model of the laboratory process for adipose tissue analysis of NHATS samples has been developed. The model simulates events in their sequence of occurrence in the laboratory. It distinguishes batches, days required to complete a batch, and the following QC activities: initial calibration; routine calibration check at the beginning and at the end of each day; a test of absolute recovery of the internal quantitation standard (IQS) in every sample; and a test of method recovery (MR) following the completion of each batch. With parameter values selected to represent a particular set of laboratory characteristics, the model may be used to evaluate the effectiveness of alternative QC programs for detecting laboratory circumstances that are considered "out of control." The model also provides information for comparing costs of QC programs. Costs depend on the total number of samples, including both primary and QC samples, that must be analyzed to complete a particular analytical program. The number of samples that must be analyzed may be greater than the minimum number specified in an analytical program plan for two reasons. First, false positive QC test results may require calibration to be repeated or primary samples to be reanalyzed. Second, an "out of control" situation that is not immediately detected by 5 ------- DRAFT QC tests could necessitate the reanalysis of many primary samples. Costs of alternative QC programs, therefore, can be compared by comparing the total number of sample analyses that must be conducted to complete the analytical program and achieve specified data quality objectives. At present, the simulation model has been used to address three questions concerning the current QC program. 1. What are the false positive error rates associated with the routine calibration check, the test of absolute recovery of the internal quantitation standard, and the method recovery test? 2. What are the probabilities that these three components of the QC program will detect a change in the calibration coefficient (usually referred to as the relative response factor - RRF)? 3. What are the probabilities that these three components of the QC program will detect a degradation in method recovery? One set of results has been developed that provides answers to the three questions. Briefly, the analysis indicates that: 6 ------- DRAFT o the routine calibration test is effective; o the absolute IQS recovery test as currently formulated may cause positive bias in concentration estimates; and o the relationship between tests of IQS recovery and method recovery needs better coordination with data quality objectives. A discussion of each result follows. The RCC test is extremely effective. The false positive error rate is less than 0.01. The probability of detecting changes of 40 percent or larger in the RRF is greater than 0.99. The false positive error rate for the IQS absolute recovery QC test is approximately 0.40 when IQS recovery is slightly greater than 0.5 and method recovery is approximately 1.1. IQS recovery test failures have two consequences. First, when a failure is detected, the batch must be reextracted and analyzed resulting in additional cost. Second, since method recovery and absolute recovery are correlated, method recovery in the batches that pass the test will reflect the characteristics of 7 ------- DRAFT the IQS samples that pass. This test favors larger recovery values. Estimated concentrations of target analyte in primary tissue samples, therefore, will be biased toward larger values. These findings suggest that the IQS recovery test, which currently requires IQS recovery to be in the fixed interval between 0.40 and 1.50, should be based on a statistical interval with boundaries determined from the mean and standard deviation of the recovery estimate. When IQS recovery is larger (e.g., 0.6) and method recovery is 1.5, the IQS detection probability drops to 0.14 because the IQS recovery value is closer to the center of the allowable range defining the test. The detection probability for the method recovery test in this case is 0.69 because the hypothetical MR value of 1.5 is also the upper boundary of the test interval. The apparent inconsistency between the detection probabilities of the two recovery tests is, in part, a consequence of the fixed interval approach to defining the recovery tests. These tests should reflect DQO's associated with applications of the data and, as indicated above, should be based on statistical characteristics of the recovery estimates. The results presented in this report serve as one example of the type of analysis that can be conducted with the simulation 8 ------- DRAFT model. Additional analyses using the model are needed to evaluate alternative QC programs and alternative data quality objectives. First, however, QC alternatives must be refined to ensure they are practical with respect to laboratory operating constraints and additional PCDD (PCDF) measurement data, if available, need to be analyzed to improve, if possible, estimates of model parameters. ------- DRAFT 3.0 INSTRUMENT RESPONSE MODEL AND ESTIMATION METHOD The procedure for estimating PCDD (PCDF). concentrations in human adipose tissue involves the analysis of calibration samples, quality control samples, and primary human adipose tissue samples. Each sample is fortified (spiked) with two internal standards prior to analysis: an internal quantitation standard; and a recovery standard. The internal quantitation standards are chemically almost identical to the target compounds. (For TCDD, the internal quantitation standard is a 13C12 labeled version of the same analyte - 13C12-2,3,7,8-TCDD. The recovery standard is 13C12-l,2/3,4-TCDD.) The analytical instrument responses associated with these samples are areas that are proportional to the analyte concentrations. The areas are summarized as two ratios: (i) the target compound area divided by the internal quantitation standard area; and (ii) the internal quantitation standard area divided by the recovery standard area. These ratios may be described mathematically as: A/A* = K0 + K1*(C/CI) + Za[K0 + K1*(C/c')] (Equation 1) where 10 ------- DRAFT A is the instrument response (an area) to concentration C ; - A is the instrument response to concentration C1; Kg and KI are the intercept and slope respectively of the straight line relationship; a is the coefficient of variation of the response ratio; and Z is a random deviate with distribution N(0,l). The term, Za[K0 + K1*(C/c')], represents a random error contribution to the instrument response which, in general, consists of three components. These are: (i) a batch component; (ii) a sample component; and (iii) an analytical replication component. The error term takes the general form: random error = (ZBaB + zsas + Zrar)*[K0 + K1*(C/C1)] (Equation 2) where aB represents batch variability; as represents sample variability; 11 ------- DRAFT ar represents analytical replication variability; and ZB' zs» zr are standard normal variates. There also is an instrument response relationship similar to Equations 1 and 2 for the ratio of the internal quantitation standard to the recovery standard. These response equations are discussed in more detail later. Estimates of PCDD (PCDF) concentrations are obtained as follows: 1. Establish an instrument calibration curve (i.e., obtain estimates of K0 and K±) . 2. Spike an adipose tissue sample with a known concentration of the internal quantitation standard; 3. Prepare (extract) the sample; 4. Add a known concentration of the recovery standard to the extract; 5. Analyze the sample and compute estimates. 12 ------- DRAFT Specification of these steps and subsequent details regarding the analytical method are based on the presentation in MRI, 1988. 3.1 THE CALIBRATION STEP Calibration solutions are prepared with known concentrations of the target compound, the internal quant itat ion standard, and the recovery standard. Eight samples, each with different concentrations of the target compound, are used. Concentrations of the two internal standards are constant across the calibration samples. The calibration relationship for the target compound is: = K0 + K1*(CSTD(i)/CIS) + (Zsi^s + Zri°r)*[K0 + K1*(CSTD(i)/CIS)] (Equation 3) where ASTD(i) is tne instrument response (area) corresponding to concentration CSTD(i) of the target compound; AIS i-s the instrument response corresponding to concentration CIS of the internal quantitation standard; 13 ------- DRAFT K0, K! calibration parameters to be estimated; and a's, Z's previously defined in Equation 2. aB does not enter Equation 3 since the calibration step does not involve batches. The calibration relationship for the internal quantitation standard relative to the recovery standard is: (AIS(i)/ARS) = L0 + L1*(CIS(i)/CRS) + (Zsias + Zriar)*[L0 + L1*(CIS(i)/CRS)] (Equation 4) CRS and ARS are tne concentration and instrument response respectively for the recovery standard. Further discussion of this relationship is found with the discussion of recovery in Section 3.2. Estimated values of K0 and Kx in Equation 3 are used to calculate target compound concentrations from analyses of primary samples. Typically, K0 is assumed to be zero (i.e., the calibration curve goes through the origin) and K± is referred to as the relative response factor (RRF). K^ may be estimated by the method of least squares. The approach used in 14 ------- DRAFT MRI, 1988 is a slight variation of the standard least squares approach. • An RRF is calculated for each calibration sample. That is: RRF(i) = (ASTD(i)/AIS)-r(CSTD(i)/CIS) (Equation 5) If the relative standard deviation (RSD) of the RRF's is less than 0.20 (or 0.30 depending on the target compound), i.e., if ({2[RRF(i)-ave{RRF(i) }]V(n-l)}* -=- ave{RRF(i)» < .20, then RRF is set equal to ave{RRF(i)}. This value of RRF is, in fact, the weighted least squares estimate of Kx when K0 is zero and the weights are [CsTDfiJ/Cjs]-1. Throughout the ensuing discussion, the operating calibration relationship will be (A/A1) = RRF*(C/C') (Equation 6) based on RRF as defined above. 3.2 ESTIMATING CONCENTRATIONS OF TARGET COMPOUNDS The procedure for estimating concentrations of the target compounds in tissue samples involves steps 2, 3, 4, and 5 listed in Section 3.0. Denote the unknown concentration of the target compound and the concentration of the internal 15 ------- DRAFT quantitation standard by Cy and CIS respectively. The internal quantitation standard is added to the sample before extraction. Denote by P^Cy and 02cis tne concentration of these two compounds in the final extract. /?]_ and /32 represent recovery proportions. Both values are expected to be between zero and one. The estimate of the unknown concentration is: est(Cu) = (Au/AIS)*(CIS/RRF) (Equation 7) where AU is the instrument response for the target compound of unknown concentration and RRF is the relative response factor determined in the calibration step. This estimate is potentially biased for a number of reasons, but most specifically because AU and AIS are instrument responses to concentrations of ^Cu and 02CIS respectively rather than GU and CIS. Using Equation 6 to substitute for AU/AIS in Equation 7 demonstrates that est(Cu) = (j9i//?2)-Cu. (Equation 8) The factor, (/3i//32) i is method recovery (MR). /3X represents recovery of the target compound. f32 represents recovery of the internal quantitation standard. If f32 = PI, then MR = 1 and the estimate of GU would be unbiased. The estimation method of Equation 7, therefore, implicitly utilizes the analytical 16 ------- DRAFT response for the internal quantitation standard as a recovery adjustment for estimating Cjj. 02 may be estimated from data generated for the internal quantitation standard and the recovery standard. Equation 4 represents the calibration relationship between instrument response and concentration for these compounds. When L0 is zero, the weighted least squares estimate of Llf which is the relative response factor for the internal quantitation standard (RRFIS), is RRFIS = ave{AIS/ARS)-5-(CIS/CRS) } (Equation 9) with the average taken over all calibration samples. The operating calibration relationship for the internal quantitation standard relative to the recovery standard, therefore, is (AIS/ARS)=RRFIS*(C/CRS). (Equation 10) An estimate of /?2 is est(02) = (Ais/ARS)-(CRS/CIS)-HRRFIs. (Equation 11) Substituting the right hand side of Equation 10 with C replaced by &2CIS' which is the concentration of the internal 17 ------- DRAFT quantitation standard in the extract, into Equation 11 confirms the estimating formula for 02 est(/32) = RRFIS()32CIS/CRS)'(CRS/CIS)H-RRFIS = 02 (Equation 12) Note that the value of 02 alone does not constitute sufficient information to assess the degree of bias in estimates of GU, the unknown concentration of the target compound. Assuming, however, that p: = 02 implies that estimates of GU are unbiased. Information about p-^ and method recovery (i.e., MR = /?i//32) may be obtained from QC samples as discussed below • 3.3 QUALITY CONTROL SAMPLES For purposes of this discussion, the term QC samples refers to samples of adipose tissue that originally contain, at most, the background concentration, C0, of the target compounds. (Other types of samples are used for QC purposes also. These samples - calibration samples and routine calibration check samples - are discussed in Section 4.1.) These QC samples, then, are spiked with known concentrations of the target compounds. Unspiked samples (i.e., a spiking concentration of zero) also are included in this definition. The unspiked samples of adipose tissue are referred to as "controls." 18 ------- DRAFT 3.3.1 Method Recovery Spiked QC samples may be used to estimate analytical method recovery. A QC sample is analyzed by following the same procedure used for primary adipose tissue samples. The internal quantitation standard is added to the spiked sample prior to extraction and the recovery standard is added to the final extract prior to analysis. The concentration of the target compound in a QC sample will be CSTD, the spiking concentration, plus C0/ the background concentration. Denoting the concentrations of the target compound and the internal quantitation standard in the final extract by 0' ^» (CSTD+C0) and ^ 2*CIS respectively, and applying the estimation method embodied in Equation 7, yields est(CSTD) = est(CSTD+C0) - est(C0) = (P* i/(3'2) *CSTD- (Equation 13) Since CSTD is a known quantity, an estimate of the method recovery factor is: est(MR) = est(CSTD)/CSTD. (Equation 14) Estimates of the concentration of the target compounds in primary tissue samples may be adjusted in an attempt to remove recovery bias. That is, 19 ------- DRAFT adj (Cjj) = est(Cu)/(est(MR) . (Equation 15) Using the results of Equations 8 and 13 in Equation 15 yields adj(Cu) = C(j8i//9I1) + (jS2//Sl2)]-Cu (Equation 16) The adjusted estimate is unbiased if the recovery proportions of the target compound in primary samples and QC samples are equal (i.e., p* ^ = p^ and the recovery proportions of the internal quantitation standard in primary samples and QC samples are equal (i.e., p ' 2 = /32) , or if method recovery is the same in both types of samples (i.e., P\/P* 2 = The potential differences among values of the /?'s result from differences in the effects of sample processing (i.e., extraction) on target compounds recently spiked into samples of adipose tissue and target compounds that were part of the sample at the time it was taken from its donor. In fact, the values of p\, p2, and 0*2 may be closer to each other than to the value of P1. Determining if p± and P2 have different values than p\ and /? ' 2 cannot be resolved without extensive, complex experimentation. Even if P2 = /?'2, which is likely and can be determined from QC data, the possibility that p\ and p-^ 20 ------- DRAFT may differ has implications for the allocation of QC resources and the use of QC analysis results. 21 ------- DRAFT 4.0 THE QC PROGRAM 4.1 DESCRIPTION The 1987 NHATS samples were analyzed in five batches consisting of 12 to 15 samples per batch. For purposes of the analysis undertaken in this report, there will be five batches each consisting of 12 primary samples plus QC samples. A batch requires two days to complete - six primary samples per day plus QC samples. The complete set of QC procedures and criteria for taking corrective action are summarized in Table 4-15 of the QAPP (MRI, 19-88) which is reproduced in this report for reference purposes as Table 4-1. The current analysis of QC effectiveness focuses on a subset of the QC procedures described in the table. These are: (i) the routine calibration check; (ii) absolute recovery of the internal quantitation standard in primary samples; (iii) absolute recovery of the internal quantitation standard in QC samples; (iv) method recovery determined from QC samples; and (v) post analysis review of all QC data to evaluate method precision, constancy of recovery across batches, and constancy of recovery with respect to concentration level of the target compound. Recall that the term "QC sample" in this report is used to describe: unspiked samples of human adipose tissue with naturally occurring background levels of PCDD (PCDF) which are 22 ------- Table 4-1 IdLle 4 IS (JL l-Mnedmes -1 LOU-, ,d lu, Analysis of ll,.jn Adipuse I ,ssue And I vs is event fo, PI IVIs dnd ICM »« Cdllbrdl ion • PUin/PC» dnd lysis U) (oluon perloradiiie lalibrdlion standards • lnili.il tdlibrdl ion • Nouline calibration Ir id« dne blank Sd«nleS/QL s a«|iles • Analysis Pel lurndiue evdliidl tun u dap Its Daily I n si event ol diiulysit Udy red I Pieiedes in it id I SJ*ple dndlysis It routine idl ibrdtian does not MCI outing i dl ibrdtian erf lend. Precedes staple dnjlysis on ddily bat is. Also oust dMonslrdle idlibrdlion ds IdSl injection or edch dndlyses ddy. A, VuLallKJ IH sample bdUh i u I I iii- »uil Jvauislrdle diiuidlc Bd^i cdlibidllun uilnj (PU). »inl dtlivily ol ltdy IKinij If K lunv to d ainiauB resolution ol 10 .000 (liH n.ilU-r) dml up! i«dl m|«me dnd |ivdk ihd|w •/< JUI Adjuil Bdyiiviic field lo pdii •/< JUU dl |