Bioinformatics Advance Access originally published online on May 14, 2008
Bioinformatics 2008 24(13):1549-1551; doi:10.1093/bioinformatics/btn227
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qpcR: an R package for sigmoidal model selection in quantitative real-time polymerase chain reaction analysis
1Statistics Group, Department of Natural Sciences, Faculty of Life Sciences, University of Copenhagen, Copenhagen, Denmark and 2Department of Andrology, University Hospital Hamburg-Eppendorf, Hamburg, Germany
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 SOFTWARE FEATURES3 CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Summary: The qpcR library is an add-on to the free R statistical environment performing sigmoidal model selection in real-time quantitative polymerase chain reaction (PCR) data analysis. Additionally, the package implements the most commonly used algorithms for real-time PCR data analysis and is capable of extensive statistical comparison for the selection and evaluation of the different models based on several measures of goodness of fit.
Availability: www.dr-spiess.de/qpcR.html.
Contact: a.spiess{at}uke.uni-hamburg.de
Supplementary Information: Statistical evaluations of the implemented methods can be found at www.dr-spiess.de under ‘Supplemental Data’.
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 SOFTWARE FEATURES3 CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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When investigating differential gene expression, quantitative real-time PCR (qPCR) data of two or more different conditions (such as control/treatment or healthy/pathological) are compared by using the fluorescence data acquired by the hardware. The basic approach for quantification between samples relies on the calculation of fold differences by means of the PCR efficiency and the threshold cycle (also often termed ‘crossing point’).
Many different methods have been developed that can mainly be divided into the following categories according to how they estimate the PCR efficiency and/or the threshold cycles:
Linear methods:
- calculation from the slope of a calibration curve (Pfaffl et al., 2001);
- based directly on the threshold values (Pfaffl, 2001);
- by mid-value-point regression (Peirson et al., 2003); and
- with the window-of-linearity method (Ramakers et al., 2003).
- fitting four-parameter sigmoidal models onto the fluorescence raw data (Liu et al., 2002; Rutledge, 2004);
- fitting an exponential model after identification of the exponential (log-linear) amplification phase (Tichopad et al., 2003; Zhao et al., 2005).
The major drawback of the four-parameter models is that they imply symmetry of the lower and upper part of the curve, inducing the same curvature on either side of the inflection point. Thus, we have also included a novel five-parameter sigmoidal model with an additional parameter for asymmetric data. Five-parameter models have only very recently found their way into the dose–response analysis of immunological data (Gottschalk et al., 2005).
Unfortunately it is a fact that different methods in qPCR analysis can yield very different values in respect to PCR efficiency, threshold cycle or estimation of the exponential phase (Karlen et al., 2007; Skern et al., 2005). The best model can severely depend on the used enzymatic system, detection technology or hardware platform. The qpcR package we present here will provide valuable assistance to the researcher in the selection of the best model.
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2 SOFTWARE FEATURES |
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TOPABSTRACT1 INTRODUCTION2 SOFTWARE FEATURES3 CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The qpcR package has been developed for the free statistical R environment (www.r-project.org) and will run under the major operating systems. The non-linear fitting engine is based on another add-on package (drc; Ritz et al., 2005).
The advantage is that all implemented methods are housed in one software package, and due to the open source nature of the software they can also easily be accessed for inspection, validation or modification purposes.
At present the following methods are available, but the package is in constant development to include novel and interesting approaches:
- Fitting of three-, four- and five-parameter logistic (Boltzmann) or log-logistic models onto qPCR data. The novel five-parameter models were included as these have shown to exhibit better performance for asymmetric data (Van der Graaf et al., 1999).
- Selection of the best model by performing nested F-tests essentially comparing residual sums of squares for competing models involving three, four or five parameters (Fig. 1A). This is common practise for non-linear fitting regimes (Bates et al., 1988).
- Evaluation of essential PCR parameters (efficiency, threshold cycles) from the sigmoidal fit of the best performing model and display as comprehensive graphics (Fig. 1B). The PCR efficiency can be calculated from any point of the sigmoidal fit, but is taken by default at the second derivative maximum of the curve as E = F(n)/F(n–1), with n being the cycle number at second derivative maximum.
- Further optimization of the sigmoidal fitting process by eliminating cycles in the plateau phase (Rutledge, 2004).
- Derivation of values using classical quantitation methods, such as the window-of-linearity method (Ramakers et al., 2003), exponential fitting (Tichopad et al., 2003) or calibration curves (Pfaffl et al., 2001).
- Model assessment and comparison through many measures of goodness of fit such as the residual variance, R2, the Akaike Information Criterion (AIC) and the root-mean-squared-error (RMSE).
- Batch analysis of many runs with all methods and summarization of these as tabular data.
- Prediction of either fluorescence or cycle values from data and calculation of confidence intervals. The confidence intervals are based on assuming asymptotical normality of the parameter estimates. For the sample sizes that we consider, we believe this approximation will yield a satisfactory coverage.
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3 CONCLUSIONS |
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TOPABSTRACT1 INTRODUCTION2 SOFTWARE FEATURES3 CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Currently, several methods for the analysis of qPCR data exist that unfortunately can lead to very different results in the estimation of the essential qPCR parameters, such as the PCR efficiency or the threshold cycle values. We have developed the qPCR package for the statistical R environment in order to deliver a software tool for the researcher such that the main algorithms are provided in one software. We have also implemented several new functions previously unavailable, such as finding the exponential region by minimizing residual variance or conducting a statistical model selection process for sigmoidal fitting of real-time PCR data. The latter includes the novel five-parameter sigmoidal models that are a viable alternative to the existing four-parameter models due to the inherent feature of taking asymmetrical data into account. Finally we have also added sensitive measures for assessing goodness of fit and for model selection (i.e. the AIC).
In summary, the qpcR package provides the researcher with a unifying software tool that is capable of state-of-the-art methods for sigmoidal model fitting in qPCR data analysis.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 SOFTWARE FEATURES3 CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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We thank C. Feig and H. Capallo-Obermann for fruitful discussions.
Funding: This work was supported by grant Sp721/1-1 of the German Research Foundation (DFG) to A.N.S.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: Trey Ideker
Received on October 22, 2008; revised on February 7, 2008; accepted on May 7, 2008
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REFERENCES |
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TOPABSTRACT1 INTRODUCTION2 SOFTWARE FEATURES3 CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Bates DM, et al. Nonlinear Regression Analysis and its Applications (1988) Hoboken, NJ, USA: John Wiley & Sons.
Gottschalk PG, et al. The five-parameter logistic: a characterization and comparison with the four-parameter logistic. Anal. Biochem. (2005) 343:54–65.[Web of Science][Medline]
Jagers P, et al. Random variation and concentration effects in PCR. J. Theor. Biol. (2003) 224:299–304.[CrossRef][Web of Science][Medline]
Karlen Y, et al. Statistical significance of quantitative PCR. BMC Bioinformatics (2007) 8:131.[CrossRef][Medline]
Liu W, et al. Validation of a quantitative method for real time PCR kinetics. Biochem. Biophys. Res. Commun. (2002) 294:347–353.[CrossRef][Web of Science][Medline]
Peirson SN, et al. Experimental validation of novel and conventional approaches to quantitative real-time PCR data analysis. Nucleic Acids Res. (2003) 31:e73.
Pfaffl MW. A new mathematical model for relative quantification in real-time RT-PCR. Nucleic Acids Res. (2001) 29:e45.
Pfaffl MW, et al. Tissue-specific expression pattern of estrogen receptors (ER): quantification of ER alpha and ER beta mRNA with real-time RT-PCR. Apmis (2001) 109:345–355.[CrossRef][Web of Science][Medline]
Ramakers C, et al. Assumption-free analysis of quantitative real-time polymerase chain reaction (PCR) data. Neurosci. Lett. (2003) 339:62–66.[CrossRef][Web of Science][Medline]
Ritz C, et al. Bioassay analysis using R. J. Stat. Soft. (2005) 12:1–22.
Rutledge RG. Sigmoidal curve-fitting redefines quantitative real-time PCR with the prospective of developing automated high-throughput applications. Nucleic Acids Res. (2004) 32:e178.
Skern R, et al. Relative transcript quantification by quantitative PCR: roughly right or precisely wrong? BMC Mol. Biol. (2005) 6:10.[CrossRef][Medline]
Tichopad A, et al. Standardized determination of real-time PCR efficiency from a single reaction set-up. Nucleic Acids Res. (2003) 31:e122.
Van der Graaf PH, et al. Analysis of asymmetry of agonist concentration-effect curves. J. Pharmacol. Toxicol. Methods (1999) 41:107–115.[CrossRef][Web of Science][Medline]
Zhao S, et al. Comprehensive algorithm for quantitative real-time polymerase chain reaction. J. Comput. Biol. (2005) 12:1047–1064.[CrossRef][Web of Science][Medline]
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