Clinical Chemistry
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Clinical Chemistry 51: 1132-1136, 2005; 10.1373/clinchem.2004.039909
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(Clinical Chemistry. 2005;51:1132-1136.)
© 2005 American Association for Clinical Chemistry, Inc.

Molecular Diagnostics and Genetics

Calibration Curves for Real-Time PCR

K. Kay-Yin Lai1, Linda Cook1, Elizabeth M. Krantz1, Lawrence Corey1,2,3 and Keith R. Jerome1,3,a

Departments of1 Laboratory Medicine and2 Medicine, University of Washington Medical Center, Seattle, WA.
3 Program in Infectious Diseases, Fred Hutchinson Cancer Research Center, Seattle, WA.

aAddress correspondence to this author at: Fred Hutchinson Cancer Research Center, 1100 Fairview Ave. N, D3-100, Seattle, WA 98109. Fax 206-667-4411; e-mail kjerome{at}fhcrc.org.


   Abstract
Top
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 References
 
Background: Despite the increasing use of real-time PCR in the diagnosis and management of viral infections, there are no published studies adequately addressing the optimum number of calibrators, the number of replicates of each calibrator, and the frequency with which calibration needs to be repeated. This study was designed to address these issues.

Methods: Cycle threshold data (ABI 7700) was collected from >50 consecutive real-time PCR runs for hepatitis B and Epstein–Barr viruses. Our routine calibration curve made from serial 10-fold dilutions run in duplicate was compared with alternative options, including duplicate 100-fold dilutions, inclusion of a low-copy calibrator, and omission of the duplicate determination. Control data were used to examine the use of an average calibration curve made from multiple runs.

Results: Use of duplicate serial 10-fold dilutions led to the least imprecision, duplicate 100-fold dilutions had slightly higher imprecision, and calibration curves obtained with singlet measurements showed the greatest imprecision. For patient data, the duplicate 100-fold dilution calibration curve produced results that best matched those from the routine calibration curve. Use of singlet dilutions or inclusion of a low-copy calibrator produced poorer agreement. Variability in controls was lower with a daily calibration curve than with an average calibration curve.

Conclusions: Duplicate 100-fold dilution calibration curves produced equivalent results and the same imprecision as curves with more calibrators, and thus are a valid alternative. Laboratories should carefully evaluate the variability resulting from the use of average calibration curves before adopting this approach.


   Introduction
Top
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 References
 
Whereas most previous diagnostic PCR assays for viral detection have been qualitative or at best semiquantitative, real-time PCR has allowed simple and accurate quantitative measurement of viral load (1) with low inter- and intraassay imprecision (1)(2)(3)(4). Despite the increasing use of real-time PCR testing, there are no published studies adequately addressing the optimum number of calibrators, the number of replicates of each calibrator, and the frequency with which calibrations need to be repeated. We therefore evaluated several strategies for calibration.


   Materials and Methods
Top
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 References
 
study population and design
Cycle threshold (Ct)1 data from calibrators were collected from consecutive real-time PCR assays performed in the clinical molecular virology laboratory at the University of Washington. We used 64 hepatitis B virus (HBV) runs from the period September 2001 to October 2002 and 59 Epstein–Barr virus (EBV) runs from July 2002 to December 2002 that had positive patient samples and met established quality-control criteria. For HBV, the criteria required that the slope of the calibration curve be between –3.8 and –3.2 and that the correlation coefficient be ≥0.99. For EBV, no restrictions were made regarding the slopes and correlation coefficients because the assay is slightly inefficient and some runs had slopes slightly less than –3.8. Calibrators were developed previously to encompass the range of concentrations typically observed in clinical samples.

Ct data for clinical specimens were also collected from the same consecutive assays described in the previous paragraph. For the HBV runs, Ct data were extracted for 1 high positive, 1 medium positive, and 1 low positive when present. The 64 HBV runs provided a total of 177 positive patient samples: 51 runs contained 3 patient samples each, 11 runs contained 2, and 2 runs contained 1 positive sample each. For the EBV runs, Ct data from 1 high positive and 1 low positive were extracted when present. For EBV, a total of 72 patients were available: 13 runs had 2 positive samples each, and the remaining 46 runs contained 1 positive sample each.

Additionally, Ct data for the positive control were collected from 98 EBV real-time runs. These data were used to compare run-to-run variability for individual run-specific calibration curves to variability for an average fixed calibration curve.

real-time assays
The HBV calibrator was purified linearized plasmid containing a sequence spanning a portion of the HBV X and DNA polymerase genes. The EBV calibrator was purified DNA isolated from Raji cells containing integrated EBV viral sequence. Calibrator stock solution was diluted to the concentration corresponding to the top point of each calibration curve and then frozen in 250-µL aliquots at –20 °C. On the day of calibration, the aliquot was thawed and the remaining calibrators were made by serial 10-fold dilution. The calibrators were stable for at least 1 and 3 weeks for EBV and HBV, respectively. Purified DNA was extracted from patient samples by the Qiagen Biorobot 3000. Recovery of control plasmid DNA was ~70%. The real-time PCR assays were then performed on an ABI 7700 as published previously for HBV (5) and EBV (6). Ct values, patient results, and control results were determined from amplification curves calculated from the {Delta}Rn of the 6-carboxyfluorescein (FAM)/6-carboxy-X-rhodamine (ROX) signals, using ABI SDS software. The automatic analysis function of the SDS software was used to set the background and threshold values for each run.

statistical analysis
Ct and quantification data were extracted into a Microsoft Excel file and transferred to Splus and SPSS for statistical analysis. Concentrations (viral loads) for calibrators, patient samples, and controls were log-transformed before statistical analysis. Linear regression models were used to construct calibration curves and provide patient results. The 95% limits of agreement for patient differences were calculated as the mean difference ± 2 SD (7), using the normal approximation, as these data did not show departures from the gaussian distribution. The data for the log of the positive control copies did show evidence of departure from the gaussian distribution; thus nonparametric descriptive measures such as medians and interquartile ranges were used to describe the variability in the positive control.

The alternative calibration options for HBV and EBV are shown in Table 1 . Confidence bands obtained with the various options were calculated for each run separately using the Working-Hotelling equation (8):

(1)


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  		Table 1. Calibration curve options.

where i indicates the run and yi represents a Ct value on the confidence band for run i. 0i and 1i represent the intercept and slope estimates, respectively, for the calibration curve for run i, and X is any value of log copies per milliliter. Wi uses the F-statistic and is defined as Wi =

. The mean squared error, MSEi, measures the dispersion of the observed Ct values from the fitted Ct values and is defined as MSEi = {sum}j(yij – yij)2/(ni – 2). The number of calibrators used in each run i is represented by ni, and the observations within run i are indicated by j. Thus, Xij indicates the jth log calibrator value from the ith run, whereas represents the mean log calibrator copies per milliliter for run i.

For each calibration curve option, the upper bound curves from all the runs were combined by use of a lowess (9) smoothing function to produce a single upper bound curve. The lower bound curves were combined in the same way to produce a single lower bound curve. The area between these 2 summary measures defined an overall 95% confidence band for each calibration curve option.


   Results
Top
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 References
 
calibration curve options
Theoretical aspects.
For Eq. 1, we would expect that the use of fewer calibrators in the calculation would correspond to broader confidence bounds for that regression line. As n decreases, the F-statistic becomes larger, increasing the magnitude of the confidence bound at a given X value. Greater dispersion of the points from the fitted regression line has the same effect, as evident in the MSE component of Eq. 1. In the confidence bands for our calibration options (Table 1Up ) we observed both relationships (Fig. 1 ). In the HBV calibration curves, the option with the fewest calibrators, HBV-B, had the widest confidence band. Although option HBV-C, which includes the lowest calibrator, had 2 more calibrators than the routine calibration curve (HBV-A), the confidence bands for the 2 options were nearly identical, likely because of greater variability at low copies. The 3-point duplicate calibration curve (HBV-D) had similar, but slightly wider, bounds than both the routine calibration curve and the option incorporating the lowest calibrator, as expected because of the fewer calibrators.



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  		Figure 1. Confidence bands for calibration curve options.

Shown are the 95% confidence bands for the HBV calibration curve data (n = 64 runs; top) and the EBV calibration curve data (n = 59 runs; bottom). The x axis represents the calibration curve quantity (log copies/mL) and the y axis the Ct value for each calibration point. Each line represents a 95% lower or upper bound for one of the calibration curve options in Table 1Up .

Similar to HBV, the confidence bands for the EBV calibration curve options showed the widest intervals for the 2 options with the fewest calibrators (EBV-B and EBV-E with only 5 and 4 calibrators, respectively). The option that included the lowest calibrator (EBV-C), the 3-point duplicate calibration curve (EBV-D), and the routine calibration curve (EBV-A) had nearly identical confidence bands.

Patient data.
We then used the various calibration curve options to calculate patient data from multiple runs. All alternative calibration curves showed good agreement with the routine curves for the HBV and EBV data (Fig. 2 ).



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  		Figure 2. Agreement plots for calibration curve alternatives.

The y axis represents the differences, calculated as the log copy using the routine calibration curve minus the log copy obtained with the alternative calibration curve, and the x axis represents the mean log copy number obtained with the 2 methods being compared. Reference lines indicate the mean difference and 95% limits of agreement, defined by the mean ± 2 SD of the differences.

For HBV, all calibration curve options produced patient results similar to those resulting from the routine calibration curve, with mean differences within 0.02 logs (Table 1 in the Data Supplement that accompanies the online version of this article at http://www.clinchem.org/content/vol51/issue7/). Of the alternatives, the 3-point duplicate curve (calibration curve HBV-D) had 95% limits of agreement closest to no difference (–0.06; 0.10) from the results obtained with the routine calibration curve (HBV-A). The other options had wider 95% limits of agreement [HBV-B vs HBV-A (–0.12; 0.12); HBV-C vs HBV-A (–0.19; 0.21)]. The worst agreement was obtained with the HBV-C curve, which incorporated the lowest calibrator, and was probably the result of poor reproducibility at extremely low quantities of template.

To examine whether the effects of the alternative calibration curves were similar throughout the entire range of the calibration curve, we separated the HBV data into 3 groups: <3.0, 3.0–7.0, and >7.0 log copies/mL. Of 177 patients, 46 (26%) were in the low-copy category, 89 (50%) in the middle category, and 42 (24%) in the high category. In all categories, the 3-point duplicate option (calibration curve HBV-D) showed the least difference from the routine method, with the 95% limits of agreement closest to no difference (Fig. 1 in the online Data Supplement). Depending on the comparison, there is a suggestion of greater agreement as the patient copy number increases.

For EBV, the mean differences of the calibration curve alternatives from the routine calibration curve ranged from 0.04 to 0.10 logs (Table 1 in the online Data Supplement). The results obtained from all alternatives gave lower average copy numbers than those calculated from the routine curve. The 3-point duplicate curve (calibration curve EBV-D; Fig. 2Up ) had 95% limits of agreement closest to no difference (–0.06; 0.14). The other options had wider 95% limits of agreement [EBV-B vs EBV-A (–0.28; 0.48), EBV-C vs EBV-A (–0.17; 0.35), EBV-E vs EBV-A (–0.12; 0.28)]. The worst agreement was obtained with the EBV-B curve, which incorporated the lowest calibrator, and again was likely attributable to poor reproducibility at extremely low quantities of template.

We next looked at these comparisons in patient samples with low (0–3 log copies) and high (≥3 log copies) quantities of EBV. Of 72 patients, 44 (61%) had <3 log copies and 28 (39%) had ≥3 log copies. In both high- and low-copy groups, the EBV-D curve showed the smallest differences from EBV-A (Fig. 2 in the online Data Supplement).

positive control data: average calibration curve vs individual run-specific curves
To determine the frequency with which calibration curves should be generated, we compared average calibration curves for each lot of positive control against individual run-specific calibration curves for 98 EBV real-time runs with positive control data. The 98 runs were fairly equally distributed among 4 lots (Fig. 3 ). The use of average calibration curves calculated for each lot produced greater variability in positive control results than did individual run-specific calibration curves (Fig. 3 ). The interquartile range was greater for the average calibration curve option in all lots. Thus, our real-time PCR assays show better reproducibility when calibration curves are calculated for each run than when an average fixed calibration curve is used for a series of runs.



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  		Figure 3. Comparison of average vs run-specific calibration curves.

Shown is the distribution of log copy of the positive control for EBV, comparing variability in results derived from individual calibration curves ({cjs2108}) used in each run with those results derived from an average calibration curve ({square}) per lot of positive control. n indicates the number of runs in each lot. Boxes represent the interquartile range. {circ} indicate outliers, defined as values between 1.5 and 3 times the interquartile range from the upper or lower edge of the box. * indicate extreme values, defined as values more than 3 times the interquartile range from the upper or lower edge of the box. Whiskers indicate the range of the data, excluding outliers and extreme values.

We also evaluated the utility of combining the slope of the average calibration curve with an intercept derived from replicates of a single calibrator for each individual run. Because this approach would be most appropriate when the major source of the variability in the calibration curves was the intercept rather than the slope, we compared these sources of variability in the 98 runs described above. Across all runs, the intercept of the calibration curves had a CV of 0.03, and the slope of the calibration curves had a CV of 0.07. Thus, we observed greater variation in the slope than in the intercept of the calibration curve, arguing against the combined approach.


   Discussion
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
References
 
Real-time PCR methods are increasingly used in the clinical laboratory. However, there have been no published studies adequately addressing the optimum number of calibrators required and the frequency with which calibration curves need to be generated. To address these concerns we conducted the present study.

In the first part of our study, we used the Ct data for calibrators from many clinical HBV and EBV PCR runs to construct 95% confidence bands for the linear regression of a variety of calibration curve options. The calibration curves that included the fewest points showed the widest confidence bounds, and the options with the most points showed the narrowest confidence bounds, consistent with what we would expect from theory. However, the confidence bounds for the 3-point duplicate alternative calibration curves were only slightly wider than those from the routine calibration curves.

In the second part of our study, we compared quantitative patient results generated by the alternative calibration curves with those generated by the routine curve. Results obtained with the alternative curve were nearly equivalent to those obtained with the routine curve. The 3-point duplicate calibration curve displayed the least differences relative to the current option, demonstrating that this method is a valid alternative to the use of more complete sets of calibrators.

Agreement of patient values derived from the 3-point duplicate calibrators with those derived from the respective current options was excellent over the entire range of patient values, even at lower copy numbers, which tended to exhibit greater variability than samples with higher copy numbers.

Finally, we investigated the feasibility of using an average fixed calibration curve derived from a series of runs in place of individual calibration curves calculated for each run. The use of individual calibration curves gave lower variability than use of a fixed average calibration curve. When a fixed calibration curve was used, control values varied by as much as 1 log, a degree at which clinical treatment decisions could be influenced. The combination of an average calibration curve with a single calibrator did not offer a better solution because the slope of the calibration curves varied more than the intercept. Thus, we include a calibration curve with each run. However, use of an average calibration curve may be more acceptable if different extraction and/or amplification platforms are used, or in the future as improvements in instrumentation and automation reduce variability to clinically insignificant values.

Appreciable cost savings may result from the elimination of even a few points of the calibration curve. The amount saved depends on reagent costs. For example, elimination of 1 point on the calibration curve should lead to a savings per well of approximately $8.00 for master mixture and $1.00 for calibrator times 2, or $18.00 per run. At 2 runs a week for HBV, for which 2 calibrator points were deleted, the total savings will be nearly $4000.00 per year. At 5 runs a week for EBV, for which 1 calibrator point was deleted, the total savings will be almost $5000.00. Total savings will vary among laboratories depending on the source of reagents and the number of tests performed.

In summary, we have modeled calibration curve data collected from more than 50 clinical runs and examined the effect of various options on the calibration curve confidence bounds as well as the effect on clinical specimen results. We conclude that the use of 3-point duplicate calibrators is a viable cost-saving alternative to the use of larger sets of calibrators in the generation of calibration curves. In addition, we conclude that under the conditions tested here, real-time PCR shows greater reliability when calibration curves are calculated for each run than when an average fixed calibration curve is used for a series of runs. Laboratories should carefully evaluate the variability resulting from the use of average calibration curves before adopting this approach.


   Acknowledgments
 
We thank Ederlyn E. Atienza, Abby Hamad, and Shannon E. Nesbitt for technical assistance. K.K-Y. Lai also thanks K. Kai-Lam Tse, James S. Fine, and Sum P. Lee for their encouragement.


   Footnotes
 
1 Nonstandard abbreviations: Ct, cycle threshold; HBV, hepatitis B virus; EBV, Epstein–Barr virus; and MSE, mean squared error.


   References
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 References
 

  1. Mackay IM, Arden KE, Nitsche A. Real-time PCR in virology. Nucleic Acids Res 2002;30:1292-305.[Abstract/Free Full Text]
  2. Locatelli G, Santoro F, Veglia F, Gobbi A, Lusso P, Malnati MS. Real-time quantitative PCR for human herpesvirus 6 DNA. J Clin Microbiol 2000;38:4042-8.[Abstract/Free Full Text]
  3. Abe A, Inoue K, Tanaka T, Kato J, Kajiyama N, Kawaguchi R, et al. Quantitation of hepatitis B virus genomic DNA by real-time detection PCR. J Clin Microbiol 1999;37:2899-903.[Abstract/Free Full Text]
  4. Schutten M, van den Hoogen B, van der Ende ME, Gruters RA, Osterhaus AD, Niesters HG. Development of a real-time quantitative RT-PCR for the detection of HIV-2 RNA in plasma. J Virol Methods 2000;8:81-7.
  5. Loeb KR, Jerome KR, Goddard J, Huang M, Cent A, Corey L. High-throughput quantitative analysis of hepatitis B virus DNA in serum using the TaqMan fluorogenic detection system. Hepatology 2000;32:626-9.[CrossRef][Web of Science][Medline] [Order article via Infotrieve]
  6. Limaye AP, Huang ML, Atienza EE, Ferrenberg JM, Corey L. Detection of Epstein-Barr virus DNA in sera from transplant recipients with lymphoproliferative disorders. J Clin Microbiol 1999;37:1113-6.[Abstract/Free Full Text]
  7. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;8476:307-10.
  8. Neter J, Kutner MH, Nachtsheim CJ, Wasserman W. Applied linear statistical models, 4th ed. 1996:67-8 McGraw-Hill Burr Ridge. .
  9. Cleveland WS. Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 1979;74:829-36.[CrossRef][Web of Science]



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