Letter pubs.acs.org/journal/estlcu
New Performance Metrics for Quantitative Polymerase Chain Reaction-Based Microbial Source Tracking Methods Dan Wang,*,† Hyatt C. Green,‡ Orin C. Shanks,‡ and Alexandria B. Boehm† †
Environmental and Water Studies, Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, United States ‡ Office of Research and Development, National Risk Management Research Laboratory, U.S. Environmental Protection Agency, Cincinnati, Ohio 45268, United States S Supporting Information *
ABSTRACT: The ability to select the best quantitative microbial source tracking method for a particular application is paramount. Binary sensitivity and specificity metrics are not adequate to describe the performance of the quantitative methods because the estimates depend on the amount of material tested and the limit of detection. We introduce a new framework for comparing the performance of quantitative fecal source identification methods.
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INTRODUCTION Microbial pollution of surface waters is a primary public health concern in the United States and worldwide.1,2 Pollution can originate from a number of fecal and nonfecal sources,3 and different sources can pose different levels of human health risk.4 Microbial source tracking (MST) methods seek to differentiate fecal pollution sources to enhance water quality management efforts. MST method performance is most commonly based on estimates of sensitivity and specificity obtained through the analysis of a set of samples of known fecal origin,5−10 where sensitivity (true positive rate) measures the proportion of actual positives that are correctly identified and specificity (true negative rate) describes the proportion of negatives that are correctly identified as such. However, new methods, such as quantitative polymerase chain reaction (qPCR), provide information beyond binary presence versus absence designations, which should be embraced in the evaluation of method performance. Although sensitivity and specificity are widely used to evaluate the performance of qPCR MST methods, it is difficult to reconcile results across studies because of a lack of standardization in performance testing protocols, namely the quantity of reference fecal material added to each qPCR reaction (denoted as “unit of measure” by Ervin et al.11) and the definition of the limit of detection (LOD) that has been used to classify a sample as being either positive or negative. First, it is well-documented that a larger quantity of fecal reference material added to qPCR test reaction mixtures can increase sensitivity estimates7 and decrease specificity estimates.11 This problem is further complicated because the unit © 2013 American Chemical Society
of measure used to assess sensitivity and specificity often varies between and within studies. In addition, the unit of measure has been expressed using various measurement scales such as DNA mass,6−8,12−15 wet or dry fecal mass,16−20 Escherichia coli or enterococci,21 or total Bacteroidales.5 Second, different definitions of LOD lead to dramatic shifts in sensitivity and specificity estimates.22,23 The primary challenge to determine the LOD of a qPCR assay is the stochastic effect observed at low copy numbers of a target DNA marker.24,25 In this study, we evaluate the performance of three MST qPCR assays using a range (6 orders of magnitude) of fecal reference material to illustrate the shortcomings of the traditional sensitivity−specificity approach and to introduce alternative metrics that circumvent the limitations described above. The requirement to test the reference fecal samples across a range of testing concentrations could be prohibitively expensive. Hence, we illustrate how an in silico calculation11,22,23 using data from a single test concentration can achieve the same objective.
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MATERIALS AND METHODS MST Assays and Fecal Reference Sample Collection. Three human-associated assays (HumM2,13 HF183Taqman,6 and BsteriF16) with varying sensitivity and specificity22 were Received: Revised: Accepted: Published: 20
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the Cq value at each dilution level (Shapiro-Wilk normality test; p > 0.05) using the Cq_LOD value corresponding to the LOD [for example, 10 copies per reaction is equivalent to a Cq_LOD of 36.02 for the HF183Taqman assay (Figure 1, middle panel)].
tested following previously published protocols (lab 2 in ref 10) for five fecal reference sources (human, canine, cattle, chicken, and swine) that have been reported to react with humanassociated methods.22 DNA from individual animal fecal samples collected from different states was used to create a DNA composite for each source group: Oregon humans (n = 6), Florida (n = 9) and Wyoming (n = 10) canines, Nebraska cattle (n = 9), Kentucky chicken (n = 9), and Georgia swine (n = 9). DNA was extracted from each individual fecal sample using the DNA-EZ kit (GeneRite, North Brunswick, NJ), and DNA concentrations were quantified using the Quant-iT PicoGreen dsDNA kit (Invitrogen, Grand Island, NY). For each animal composite, an equal amount of DNA mass from each individual was combined, serially diluted, and used as qPCR template at concentrations ranging from 10 to 10−4 ng of DNA per reaction for human fecal extract and from 100 to 10−4 ng of DNA per reaction for other animals. The Oregon human composite did not have enough volume for all three assays, so a different human composite [California (n = 12), described by Boehm et al.10] was tested for BsteriF1 assay. No inhibition was observed for these composites according to the results from their serial dilutions.26 All process and no template controls were negative. qPCR Standard Curve. Decimal dilutions of an artificial plasmid standard27 ranging from 105 to 101 copies per reaction were used to generate calibration curves for the three assays. Six replicated qPCRs were tested at each dilution level. Standard curves were fit by weighted linear least-squares regression (WLS)28 to address the heteroscedascticity;24,25 i.e., reactions with smaller amount of plasmids have greater measurement variance in the quantification cycle, Cq.29 The weights used were the reciprocals of the variance, calculated at concentrations of 10 and 102 copies per reaction as well as the group variance for concentrations higher than 102 copies per reaction (calculated from the centralized Cq values, namely Cq values from which the mean Cq value of each concentration level was subtracted), because the F-test confirmed that the variance at concentrations higher than 102 copies per reaction was consistent but the variance at 10 and 102 copies per reaction was significantly larger (p < 0.05). All statistical analyses in this study were conducted using the base and stats packages in R (http://www.r-project.org/). In Silico Calculation. An in silico approach was developed using data from a single high-concentration sample that shows no signs of inhibition26,30 to predict results for other dilutions. The mean marker concentration in 10 (human) or 100 (other animals) ng of DNA per reaction was calculated from the standard curve using the mean Cq value of replicated qPCRs. The mean marker concentrations for other dilution levels were calculated in silico by dividing the mean concentration measured for 10 or 100 ng of DNA per reaction by appropriate dilution factors. The mean marker concentration was then translated to the mean Cq value by substitution into the standard curve. The standard deviation of this mean Cq value was extracted from the linear interpolation of the standard deviation estimated from the standard curve (standard deviation of HF183Taqman illustrated in Figure 1 of the Supporting Information). The 95% confidence interval (CI) of mean marker concentration at each dilution level was determined by the upper and lower boundaries of the Cq values (mean Cq ± 2 × standard deviation). The in silico probability that a dilution level will yield a measurement above the LOD was calculated according to the normal distribution of
Figure 1. Performance of the HF183Taqman assay. The middle panel illustrates the relationship between the target marker concentration and DNA mass per reaction established from qPCR (×) and in silico calculation (the solid line is the mean concentration, and dashed lines are the 95% confidence intervals of the DNA marker). The bottom and top panels show the probability that the observed concentration will be higher than the limit of detection (LOD) of 10 or 100 marker copies per reaction. The equivalent threshold (ET) for a source is the quantity of fecal material per reaction corresponding to the mean number of target marker copies per reaction (solid line in the middle panel) at the LOD, which also corresponds to the probability of 0.5 where half of the observed concentration is above the LOD. The false positive index (FPI) is the difference between the log10(ET) of the target and a nontarget source. It should be noted that the largest amount of fecal material tested is 100 ng of DNA per reaction following recommendations of the manufacturer of the qPCR instrument (Applied Biosystems).
This probability is the chance that the measured marker concentration equals ≥10 copies per reaction or Cq ≤ Cq_LOD. Thus, this probability can be calculated using the z-score in the standard normal distribution as p (Z ≤ z-score), where z-score is Cq_LOD − mean Cq standard deviation of Cq 21
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RESULTS AND DISCUSSION For both the target and nontarget sources, results from the in silico calculation at each dilution level matched the actual qPCR measurement on the corresponding dilution level. The 95% CI of the in silico calculation encompassed the actual qPCR measurements, even for the heteroscedascticity region (Figure 1, middle panel). The fraction of replicated qPCRs that will have a concentration higher than the LOD fell on the probability curve calculated from the in silico approach (Figure 1, top and bottom panels). Figure 1 illustrates that the probability that a measurement is above the LOD increases as the amount of DNA added to the qPCR reaction increases. The figure also illustrates that, given a fixed amount of DNA in a qPCR reaction, the probability that the measurement is above the LOD decreases as the LOD increases (Figure 1, top panel vs bottom panel). This illustrates why it is difficult to directly compare samples that are not tested with the same amount of DNA (or other unit of measure based on E. coli, enterococci, or Bacteroidales, for example) per reaction or the same LOD definition. In addition, Figure 1 shows that different sources actually have the same serial dilution pattern because qPCR detection is a function of the target marker copy numbers in the reaction. However, nontarget sources (chicken and cattle) shift to the right, relative to the target source (human), on the axis of DNA mass added to each reaction. This is because the prevalence of the qPCR marker in nontarget sources is typically lower than that in the target source; therefore, it takes more DNA from the nontarget sources to provide the same amount of target molecular marker to be detected by qPCR. In the study, each dilution level was assigned a probability that it would be detected above the LOD. This approach considers the “Poisson effect”-induced stochastic behavior observed at low copy numbers of a target DNA marker,24,25 namely, a large variance in Cq values around the LOD (Figure 1, middle panel). In fact, it is the measurement variance in the stochastic range that generates the S-shaped probability curve.24 The smaller the variance, the narrower the S-shaped curve will be (in Figure 1, the top panel with an LOD of 100 copies per reaction has a narrower S-shaped curve than the bottom panel with an LOD of 10 copies per reaction). The measurement variance has not been considered by other researchers from a review of the literature largely because the target source has typically been tested at a concentration above the stochastic range. However, many nontarget sources may yield results in the stochastic range where a sample has a probability between 0 and 100% to be above LOD. In the literature,7−9,21 such samples have been treated as having either 0 or 100% probability of being above the LOD, which biases the estimated specificity. Because of the influence that the quantity of fecal reference material tested in a qPCR reaction has on traditional specificity and sensitivity estimates, we propose two new performance metrics: the equivalent threshold (ET) and false positive index (FPI). ET is defined as the quantity of fecal reference material per reaction that corresponds to the LOD of an assay. Figure 1 indicates that the ET of a particular fecal source is the quantity of fecal material per reaction, for example, DNA mass per reaction that provides the amount of target marker (mean concentration, solid line in the middle panel) equal to the LOD, which also corresponds to the probability of 0.5 at which half of the observed concentration is above the LOD (top and bottom panels for two different LODs). Fecal sources with
varying prevalence of an assay’s target marker will have different ET values because it takes different amounts of fecal material to provide the amount of target marker per reaction at the LOD (Figure 1). Because the DNA mass per reaction (or other measurement scales) and the mean concentration of the target marker of a particular sample follow a linear relationship (Figure 1, solid lines in the middle panel), ET values can be calculated for different LOD values by scaling a previously calculated ET. For example, if an LOD of 100 marker copies per reaction is used (Figure 1, top panel), a new ET can be calculated by scaling the ET value based on an LOD of 10 marker copies per reaction by 10 (Table 1 and Figure 1, bottom panels). Given this relationship, the ET values of a fecal source from any two LOD definitions at the same measurement scale (e.g., DNA mass) can be readily converted from one to another. The ET value for a target source (e.g., human in this study) is closely related to what has been previously defined as sensitivity because ET value indicates the marker prevalence in the target source feces. The ET value, based on DNA mass, is similar for HF183Taqman and BsteriF1 for human fecal composites [although there are two different human composites, they had almost identical ET values for HF183Taqman (data not shown)], but ∼1 order of magnitude higher for HumM2 (Table 1 and Figure 2 of the Supporting Information). This is an indication that HF183 and BsteriF1 are ∼1 order of magnitude more sensitive for human feces than HumM2. When the ET value is defined on other measurement scales (fecal mass, FIB, Bacteroidales, etc.),11 the difference in ET values between two assays for the same source material will not vary from the difference when DNA mass is used as the scale,10 providing that DNA extraction does not preferentially yield more of the target marker for one assay versus another. Therefore, the relative ET of two assays is typically independent of measurement scale. The false positive index (FPI) of an assay is defined as the difference between the log10 transformed ET values of the target source and a nontarget source. It is closely related to what previously has been defined as specificity or cross reactivity. FPI is independent of the LOD definition (Table 1 and Figure 1). The FPI of chicken feces for the HF183Taqman assay (1.22 order of magnitude difference) and the FPI of canine feces for the BsteriF1 assay (0.35 and 1.30 order of magnitude differences for the two canine composites from different states) are 3.62
specificity has been reported to vary between groups of hosts5,13 or even between different subpopulations of the same animal host.7,31 Therefore, the conventional practice of combining representative samples from all nontarget sources to calculate one specificity value is problematic. We recommend only combining representative samples from closely related animal populations to calculate a corresponding range of ET and FPI.32 This will therefore allow comparisons of ET and FPI across animal groups from different geographic areas or from different times, as well as with different diets, ages, and health status.12 In summary, we introduce new performance metrics for quantitative MST methods designed to address current limitations in conventional sensitivity and specificity approaches. The conventional framework can be biased by the amount of reference fecal material tested in qPCR amplifications and LOD definition. We recommend providing the following information when evaluating assay performance: (1) Provide the measurement variance or standard deviation for Cq values generated from the standard curve experiments. (2) Test samples from a reference fecal pollution source by qPCR at a single high DNA concentration. Report the qPCR results in marker copies per reaction and DNA mass (other scales such as fecal mass, FIB, and Bacteroidales are useful as well) added to the reaction. Provision of this information could allow qPCR results from different studies to be converted and compared using the ET and FPI metrics outlined in this report assuming that potential differences in protocols across studies such as DNA extraction method, source of qPCR reagents, thermal cycling instrumentation, and the method for determining a Cq threshold do not bias the estimation of the mean marker concentration in a sample. This approach may also be used to compare different quantitative technology platforms such as digital PCR, microarray, and next-generation sequencing.
Note that the equivalent threshold is based on DNA mass per reaction. HF183Taqman amplified the human, chicken, and cattle composites. BsteriF1 amplified the human, canine, and swine composites. HumM2 amplified the human composite only when the total amount of DNA was ≤100 ng per reaction. bThe weighted-least-square (WLS) standard curve for each assay. cThe equivalent threshold is defined as the DNA mass per reaction that corresponds to the LOD. The ET value of human composites for the three assays indicates their relative sensitivity. BsteriF1 is slightly more sensitive than HF183, and both are ∼1 order of magnitude more sensitive than HumM2. dThe false positive index is defined as the difference in log10 transformed ET values of the target source (human) and a nontarget source. The FPI indicates the specificity of an assay. The larger the FPI is, the higher the specificity. The FPI is independent of the LOD. eNA indicates that there is no need to evaluate specificity for the target human source.
NAe >4.74 >4.74 1.30 0.35 NAe >4.42 NAe
1.22
>4.42
0.35 4.03 × 10−3 NAe 1.80 × 10−3 >5.42 >1.00 × 102 5.10 >1.00 × 102 1.22 6.38 × 10−2 NAe 3.83 × 10−3
4.03 × 10 1.80 × 10 >1.00 × 10 4.80 × 10 6.38 × 10 3.83 × 10
ET [DNA (ng/reaction)] for an RDL of 10 copies per reactionc FPI relative to humand ET [DNA (ng/reaction)] for an RDL of 100 copies per reactionc FPI relative to humand
Letter
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ASSOCIATED CONTENT
S Supporting Information *
Figures S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Department of Civil and Environmental Engineering, 473 Via Ortega, Room M08, Stanford University, Stanford, CA 94305. Telephone: (650) 725-3025. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge Yiping Cao for providing comments on the manuscript. Funding for this project has been provided in part through an agreement with the California State Water Resources Control Board. H.C.G. was supported by the National Research Council. The contents of this document do not necessarily reflect the views and policies of the California State Water Resources Control Board and USEPA, nor does mention of trade names or commercial products constitute endorsement or recommendation for use.
a
>4.62 >1.00 × 102 NAe 2.38 × 10−2 >5.74 >1.00 × 102 5.18 >1.00 × 102
2.38 × 10 >1.00 × 10 2.75 × 10 3.60 × 10
1.30 3.60 × 10−2
>1.00 × 102
others
−3
human swine canine 2
−3 −4
canine 1
−4
human others human
−4
chicken
−3
cattle
2
others
2
HumM2 (slope, −3.48; intercept, 42.06; R2, 0.9966)b BsteriF1 (slope, −3.58; intercept, 40.42; R2, 0.9759)b HF183 (slope, −3.47; intercept, 39.49; R2, 0.9916)b
Table 1. Comparison of the Equivalent Threshold (ET) and False Positive Index (FPI) for Limits of Detection (LODs) of 10 and 100 Marker Copies per Reaction for Different Source Compositesa
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