Real-Time PCR: A Review of Approaches to Data Analysis.
D. V. Rebrikov and D. Yu. Trofimov
DNA-Technology JSC, Moscow, 115478 Russia
Applied Biochemistry and Microbiology, 2006, Vol. 42, No. 5, pp. 455–463.

The registration of the accumulation of polymerase chain reaction (PCR) products in the course of amplification (real-time PCR) requires specific equipment, i.e., detecting amplifiers capable of recording the level of fluorescence in the reaction tube during amplicon formation. When the time of the reaction is complete, researchers are able to obtain DNA accumulation graphs. This review discusses the most promising algorithms of the analysis of real-time PCR curves and possible errors, caused by the software used or by operators' mistakes. The data included will assist researchers in understanding the features of a method to obtain more reliable results.

Calculator to convert the slope produced by a QPCR standard curve to % efficiency. It also gives the exponent and amplification. This calculator uses the slope produced by a QPCR standard curve to calculate the efficiency of the PCR reaction. Slopes between -3.1 and -3.6 giving reaction efficiencies between 90 and 110% are typically acceptable.
The formula for this calculation is    Efficiency  =  -1 + 10(-1/slope)

Estimation via "calibration dilution curve and slope calculation"

real-time PCR efficiency:    E  =  10^[–1/slope]

Efficiency of PCR Reactions
Mx4000 Application Note #10  by Stratagene

Quantification on the LightCycler
Rasmussen, R (2001)
In: Meuer, S, Wittwer, C, Nakagawara, K, eds.
In:   Rapid Cycle Real-time PCR, Methods and Applications Springer Press, Heidelberg; page 21-34.

Figure 1: Quantification of purified PCR product of the human HER2/neu gene in the LightCycler Instrument. The reaction was monitored with SYBR Green I. Acquisitions were taken once per cycle after extension.

Figure 2: A standard curve constructed from the data in figure 1. The slope of the line is -1/log (efficiency) giving an efficiency in this case of 1.73. The intercept is the log of the amount of DNA at threshold divided by the log of the efficiency.

A quantitative real-time PCR method for detection of B-Lymphocyte Monoclonality
by comparison of kappa and lambda Immunoglobulin Light Chain Expression.

Anders Ståhlberg, Pierre Åman, Börje Ridell, Petter Mostad, and Mikael Kubista (2003)
Clinical Chemistry 49(1): 51-59

A new mathematical model for relative quantification in real-time RT-PCR.
Michael W. Pfaffl  (2001) 
Nucleic Acids Res. 2001 May 1; 29(9): E45-E45.

Experimental validation of novel and conventional approaches
to quantitative real-time PCR data analysis.

Stuart N. Peirson, Jason N. Butler and Russell G. Foster (2003)

Real-time PCR is being used increasingly as the method of choice for mRNA quantification, allowing rapid analysis of gene expression from low quantities of starting template. Despite a wide range of approaches, the same principles underlie all data analysis, with standard approaches broadly classiffed as either absolute or relative. In this study we use a variety of absolute and relative approaches of data analysis to investigate nocturnal c-fos expression in wild-type and retinally degenerate mice. In addition, we apply a simple algorithm to calculate the amplifcation effciency of every sample from its amplifcation profle. We confrm that nocturnal c-fos expression in the rodent eye originates from the photoreceptor layer, with around a 5-fold reduction in nocturnal c-fos expression in mice lacking rods and cones. Furthermore, we illustrate that differences in the results obtained from absolute and relative approaches are underpinned by differences in the calculated PCR effciency. By calculating the amplifcation effciency from the samples under analysis, comparable results may be obtained without the need for standard curves. We have automated this method to provide a means of streamlining the real-time PCR process, enabling analysis of experimental samples based upon their own reaction kinetics rather than those of artificial standards.
DART-PCR provides a simple means of analysing real-time PCR data from raw flurescence data. This allows an automatic calculation of amplification kinetics, as well as performing the subsequent calculations for relative quantification and calculation of assay variability. Amplification efficiencies are also tested to dtect anomalus samples within groups (outlayers) and differences between experimatal groups (amplification equivalence).

Mathematics of quantitative kinetic PCR and the application of standard curves.
Rutledge RG, Cote C.
Nucleic Acids Res.  2003 Aug 15;31(16):e93
Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre, 1055 du P.E.P.S., PO Box 3800, Sainte-Foy, Quebec G1V 4C7, Canada

Fluorescent monitoring of DNA amplification is the basis of real-time PCR, from
which target DNA concentration can be determined from the fractional cycle at which a threshold amount of amplicon DNA is produced. Absolute quantification can be achieved using a standard curve constructed by amplifying known amounts of target DNA. In this study, the mathematics of quantitative PCR are examined in detail, from which several fundamental aspects of the threshold method and the application of standard curves are illustrated. The construction of five replicate standard curves for two pairs of nested primers was used to examine the reproducibility and degree of quantitative variation using SYBER Green I fluorescence. Based upon this analysis the application of a single, well-constructed standard curve could provide an estimated precision of +/-6-21%, depending on the number of cycles required to reach threshold. A simplified method for absolute quantification is also proposed, in which quantitative scale
s determined by DNA mass at threshold.

Accurate and statistically verified quantification of relative mRNA abundances using SYBR Green I and real-time RT-PCR.
Marino JH, Cook P, Miller KS.
J Immunol Methods. 2003 Dec;283(1-2):291-306.
Faculty of Biological Sciences, The University of Tulsa, 600 S. College Avenue, Tulsa, OK 74104-3189, USA.

Among the many methods currently available for quantifying mRNA transcript abundance, reverse transcription- polymerase chain reaction (RT-PCR) has proved to be the most sensitive. Recently, several protocols for real-time relative RT-PCR using the reporter dye SYBR Green I have appeared in the literature. In these methods, sample and control mRNA abundance is quantified relative to an internal reference RNA whose abundance is known not to change under the differing experimental conditions. We have developed new data analysis procedures for the two most promising of these methodologies and generated data appropriate to assess both the accuracy and precision of the two protocols. We demonstrate that while both methods produce results that are precise when 18S rRNA is used as an internal reference, only one of these methods produces consistently accurate results. We have used this latter system to show that mRNA abundances can be accurately measured and strongly correlate with cell surface protein and carbohydrate expression as assessed by flow cytometry under different conditions of B cell activation.

Impact of DNA polymerases and their buffer systems on quantitative real-time PCR.
Wolffs P, Grage H, Hagberg O, Radstrom P.
J Clin Microbiol. 2004 Jan;42(1):408-11.
Applied Microbiology, Lund Institute of Technology, Mathematical Statistics, Lund University, SE-221 00 Lund, Sweden.
An investigation of the influence of five DNA polymerase-buffer systems on real-time PCR showed that the choice of both DNA polymerase and the buffer system affected the amplification efficiency as well as the detection window. The analytical repeatability of the data for different systems changed clearly, leading us to conclude that basing quantitative measurements on single-data-set standard curves can lead to significant errors.

Addressing fluorogenic real-time qPCR inhibition using the novel custom Excel file system 'FocusField2-6GallupqPCRSet-upTool-001' to attain consistently high fidelity qPCR reactions.
Jack M. Gallup and Mark R. Ackermann
Department of Veterinary Pathology, College of Veterinary Medicine, Iowa State University. Ames, Iowa 50011-1250. USA.
Biol. Proced. Online 2006;8:87-152.

The purpose of this manuscript is to discuss fluorogenic real-time quantitative polymerase chain reaction (qPCR) inhibition and to introduce/define a novel Microsoft Excel-based file system which provides a way to detect and avoid inhibition, and enables investigators to consistently design dynamically-sound, truly LOG-linear qPCR reactions very quickly. The qPCR problems this invention solves are universal to all qPCR reactions, and it performs all necessary qPCR set-up calculations in about 52 seconds (using a pentium 4 processor) for up to seven qPCR targets and seventy-two samples at a time – calculations that commonly take capable investigators days to finish. We have named this custom Excel-based file system "FocusField2- 6GallupqPCRSet-upTool-001" (FF2-6-001 qPCR set-up tool), and are in the process of transforming it into professional qPCR set-up software to be made available in 2007. The current prototype is already fully functional.

Download Excel file

Effect of DNA damage on PCR amplification efficiency with the relative threshold cycle method.
Sikorsky JA, Primerano DA, Fenger TW, Denvir J.
Biochem Biophys Res Commun. 2004 Oct 22;323(3):823-30.
Department of Microbiology, Immunology and Molecular Genetics, Joan C. Edwards
School of Medicine, Marshall University, Huntington, WV 25704, USA.

Polymerase stop assays used to quantify DNA damage assume that single lesions are sufficient to block polymerase progression. To test the effect of specific lesions on PCR amplification efficiency, we amplified synthetic 90 base oligonucleotides containing normal or modified DNA bases using real-time PCR and determined the relative threshold cycle amplification efficiency of each template. We found that while the amplification efficiencies of templates containing a single 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodG) were not significantly perturbed, the presence of a single 8-oxo-7,8-dihydro-2'-deoxyadenosine, abasic site, or a cis-syn thymidine dimer dramatically reduced amplification efficiency. In addition, while templates containing two 8-oxodGs separated by 13 bases amplified as well as the unmodified template, the presence of two tandem 8-oxodGs substantially hindered amplification. From these findings, we conclude that the reduction in polymerase progression is dependent on the type of damage and the relative position of lesions within the template.

The E-Method: a highly accurate technique for gene-expression analysis
Gudrun Tellmann
Nature, Application Note, July 2006

Roche Applied Science has repeatedly set standards for high-speed real-time PCR systems. The newLightCycler® 480 System offers different methods of data analysis for relative quantification of geneexpressionbehavior. Whereas the ∆∆CT Method provides fast, easy analysis of gene expression, the E-Method from Roche Applied Science can produce more accurate relative quantification data bycompensating for differences in target and reference-gene amplification efficiency, either within anexperiment or between experiments.

LC 480 System - Innovative solutions for relative quantification

Estimation via increase in "absolute fluorescence" method 1  (regression)

Development and validation of an externally standardised quantitative Insulin like 
growth factor-1 (IGF-1) RT-PCR using LightCycler SYBR ® Green I technology.

Pfaffl, MW (2001)
In: Meuer, S, Wittwer, C, Nakagawara, K, eds. Rapid Cycle Real-time PCR, Methods and Applications
Springer Press, Heidelberg, ISBN 3-540-66736-9

Estimation via increase in "absolute fluorescence"  method 2

Pfaffl (2002) unpublished

E  =  ( Rn B / Rn A ) ^ [ 1 / CP B - CP A ]


A new quantitative method of real time RT-PCR
assay based on simulation of polymerase chain reaction kinetics.

Liu W & Saint DA.  (2002)
Anal Biochem. 2002  302(1): 52-59.

PS: The following formula [3] used in the Liu & Saint publication is not working !!!

Please note that a typographical error occurred in equation 3 in this paper. 
Here is the correct equation for calculating efficiency, and its derivation.

Estimation via increase in "absolute fluorescence"  method 3   (3 data points)

Statistical estimations of PCR amplification rates
Peccoud J  &  Jacob C.  (1998)
In: Gene Quantification (eds. Francois Ferre) 

Quantitative applications of the Polymerase Chain Reaction (PCR), also known as Quantitative-PCR (Q-PCR) are intended either to determine the number of copies of a given nucleic acid sequence, or more generally, to determine the relative abundance of two sequences. Current methods to determine exact numbers of molecules overcome the determination of the amplification rate by assuming identical amplification rates for a target DNA sequence and a standard of known quantity introduced into the experiment design, so that only the ratio of amplified products need be determined. Violations of the hypothesis of identical amplification rates for two sequences will result in a systematic bias in the experiment results that underestimates or overestimates the initial copy numbers. Acquisition of kinetic PCR data was pioneered by Higuchi et al. (Higuchi et al., 1993; Higuchi et al., 1992) and commercial instruments have been available since early 1996. Kinetic data provide a new way to determine the amplification rate, and we can foresee that their availability will rekindle interest in the algorithms used to compute the initial quantities of DNA sequences. Analysis of kinetic PCR patterns will soon make its way into the family of recipes that have been in use for some years in this field. This chapter provides evidence that a statistical analysis of the amplification rate is critical to ensuring a reliable estimate of the initial copy number.

Estimation via increase in "absolute fluorescence
method 4   (window-of-linearity)

Assumption-free analysis of quantitative real-time PCR data.
Ramakers C, Ruijter JM, Deprez RH, Moorman AF. (2003)
Neurosci Lett  2003 Mar 13;339(1): 62-66

Department of Anatomy and Embryology K2-283, Experimental and Molecular Cardiology Group, Academic Medical Centre, University of Amsterdam, Meibergdreef 15, 1105 AZ, Amsterdam, The Netherlands



Quantification of mRNAs using real-time polymerase chain reaction (PCR) by monitoring the product formation with the fluorescent dye SYBR Green I is being extensively used in neurosciences, developmental biology, and medical diagnostics. Most PCR data analysis procedures assume that the PCR efficiency for the amplicon of interest is constant or even, in the case of the comparative C(t) method, equal to 2. The latter method already leads to a 4-fold error when the PCR efficiencies vary over just a 0.04 range. PCR efficiencies of amplicons are usually calculated from standard curves based on either known RNA inputs or on dilution series of a reference cDNA sample. In this paper we show that the first approach can lead to PCR efficiencies that vary over a 0.2 range, whereas the second approach may be off by 0.26. Therefore, we propose linear regression on the Log(fluorescence) per cycle number data as an assumption-free method to calculate starting concentrations of mRNAs and PCR efficiencies for each sample.

A computer program to perform this calculation is available on request 
e-mail:                subject:       LinRegPCR

=>  direct download here
Table 1:
Illustration of the effect of unequal PCR efficiencies on the result of the comparative Ct method

Illustration of the linear regression calculations implemented in a Microsoft Excelw spreadsheet for determining starting concentrations and PCR efficiencies per sample.

A new reverse transcription-polymerase chain reaction method for accurate quantification.
Yih-Horng Shiao
BMC Biotechnology (2003)

Background: Reverse transcription-polymerase chain reaction (RT-PCR) is a very sensitive technique to measure and to compare mRNA levels among samples. However, it is extremely difficult to maintain linearity across the entire procedure, especially at the step of PCR amplification. Specific genes have been used as baseline controls to be co-amplified with target genes to normalize the amplification efficiency, but development or selection of reliable controls itself has created a new challenge.
Results: Here, we describe a new quantitative RT-PCR to compare two mRNA samples directly without the requirement of synthetic control DNAs for reference. First, chimeric RT primers carrying gene-specific and universal PCR priming sequences with or without a linker for size distinction were utilized to generate cDNAs. The size-different cDNAs were then combined in a single reaction for PCR amplification using the same primer set. The two amplified products were resolved and detected with gel electrophoresis and fluorescence imaging. Relative abundance of the two products was obtained after a baseline correction.
Conclusion: This methodology is simple and accurate as indicated by equal amplification efficiency throughout PCR cycling. It is also easily implemented for many existing protocols. In addition, parameters affecting RT linearity are characterized in this report.

Potential influence of the first PCR cycles in real-time comparative gene quantifications.
Nogva HK, Rudi K.
Biotechniques. 2004 Aug;37(2):246-8, 250-3.
Norwegian Food Research Institute, AS, Norway.
There is an underlying assumption in real-time PCR that the amplification efficiency is equal from the first cycles until a signal can be detected. In this study, we evaluated this assumption by analyzing genes with known gene copy number using real-time PCR comparative gene quantifications. Listeria monocytogenes has six 23S rRNA gene copies and one copy of the hlyA gene. We determined 23S rRNA gene copy numbers between 0.9 and 1.6 relative to hlyA when applying the comparative gene quantification approach. This paper focuses on the first cycles of PCR to explain the difference between known and determined gene copy numbers. Both theoretical and experimental evaluations were done. There are three different products (types 1-3) dominating in the first cycles. Type 1 is the original target, type 2 are undefined long products, while type 3 are products that accumulate during PCR. We evaluated the effects of type 1 and 2 products during the first cycles by cutting the target DNA with a restriction enzyme that cuts outside the boundaries of the PCR products. The digestion resulted in a presumed increased amplification efficiency for type 1 and 2 products. Differences in the amplification efficiencies between type 1, 2, and 3 products may explain part of the error in the gene copy number determinations using real-time PCR comparative gene quantifications. Future applications of real-time PCR quantifications should account for the effect of the first few PCR cycles on the conclusions drawn.

Bias in the Cq value observed with hydrolysis probe based quantitative PCR can be corrected with the estimated PCR efficiency value.
Tuomi JM, Voorbraak F, Jones DL, Ruijter JM.
Methods. 2010 Apr;50(4): 313-22
For real-time monitoring of PCR amplification of DNA, quantitative PCR (qPCR) assays use various fluorescent reporters. DNA binding molecules and hybridization reporters (primers and probes) only fluoresce when bound to DNA and result in the non-cumulative increase in observed fluorescence. Hydrolysis reporters (TaqMan probes and QZyme primers) become fluorescent during DNA elongation and the released fluorophore remains fluorescent during further cycles; this results in a cumulative increase in observed fluorescence. Although the quantification threshold is reached at a lower number of cycles when fluorescence accumulates, in qPCR analysis no distinction is made between the two types of data sets. Mathematical modeling shows that ignoring the cumulative nature of the data leaves the estimated PCR efficiency practically unaffected but will lead to at least one cycle underestimation of the quantification cycle (C(q) value), corresponding to a 2-fold overestimation of target quantity. The effect on the target reference ratio depends on the PCR efficiency of the target and reference amplicons. The leftward shift of the C(q) value is dependent on the PCR efficiency and with sufficiently large C(q) values, this shift is constant. This allows the C(q) to be corrected and unbiased target quantities to be obtained.

A new method for robust quantitative and qualitative analysis of real-time PCR.

Eric B. Shain & John M. Clemens
Abbott Molecular Inc., 1300 E. Touhy Avenue, Des Plaines, IL 60018, USA
Nucleic Acids Research, 2008, Vol. 36, No. 14 e91

An automated data analysis method for real-time PCR needs to exhibit robustness to the factors that routinely impact the measurement and analysis of real-time PCR data. Robust analysis is paramount to providing the same interpretation for results regardless of the skill of the operator performing or reviewing the work. We present a new method for analysis of real-time PCR data, the maxRatio method, which identifies a consistent point within or very near the exponential region of the PCR signal without requiring user intervention. Compared to other analytical techniques that generate only a cycle number, maxRatio generates several measurements of amplification including cycle numbers and relative measures of amplification efficiency and curve shape. By using these values, the maxRatio method can make highly reliable reactive/nonreactive determination along with quantitative evaluation. Application of the maxRatio method to the analysis of quantitative and qualitative real-time PCR assays is shown along with examples of method robustness to, and detection of, amplification response anomalies.

Q-Gene: processing quantitative real-time RT–PCR data
Perikles Simon
University Eye Hospital Tuebingen, 72076 Tuebingen, Germany
Paper:       Online Presentation. 

Q-Gene is an application for the processing of quantitative real-time RT–PCR data. It offers the user the possibility to freely choose between two principally different procedures to calculate normalized gene expressions as either means of Normalized Expressions or Mean Normalized Expressions. In this contribution it will be shown that the calculation of Mean Normalized Expressions has to be used for processing simplex PCR data, while multiplex PCR data should preferably be processed by calculating Normalized Expressions. The two procedures, which are currently in widespread use and regarded as more or less equivalent alternatives, should therefore specifically be applied according to the quantification procedure used.

A kinetic model of quantitative real-time polymerase chain reaction.
Mehra S, Hu WS.
Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN 55455-0132, USA.
Biotechnol Bioeng. 2005 Sep 30;91(7):848-60.

Real-time polymerase chain reaction (PCR) is one of the most sensitive and accurate methods for quantifying transcript levels especially for those expressed at low abundance. The selective amplification of target DNA over multiple cycles allows its initial concentration to be determined. The amplification rate is a complex interplay of the operating conditions, initial reactant concentrations, and reaction rate constants. Experimentally, the compounded effect of all factors is quantified in terms of an effective efficiency, which is estimated by curve fitting to the amplification data. We present a comprehensive model of PCR to study the effect of various reactant concentrations on the amplification efficiency. The model is used to calculate the kinetic progression of the target DNA concentration with cycle number under conditions when different species are stoichiometrically or kinetically limiting. The reaction efficiency remains constant for the initial cycles. As the primer concentration becomes limiting, the efficiency is marked by a gradual decrease. This is in contrast to a steep decline under nucleotide limiting conditions. Under some conditions, commonly used experimentally, increasing primer concentration has the adverse effect of reducing the final amplified template concentration. This phenomenon seen at times experimentally is explained by the simulation results under rate limiting enzyme concentrations. Primer dimer formation is shown to significantly affect the reaction rates, effective efficiency, and the estimated initial concentrations. This model, by describing the interplay of the many operating variables, will be a useful tool in designing PCR conditions and evaluating its results.

Kinetic Outlier Detection (KOD) in real-time PCR
Tzachi Bar, Anders Stahlberg, Anders Muszta and Mikael Kubista
NAR Vol 31 (17):  e105

1Department of Chemistry and Bioscience, Chalmers University of Technology, Medicinargatan 7B,
405 30 Gothenburg, Sweden, 2Department of Mathematical Statistics, Eklandagatan 86, 412 96, Gothenburg,
Sweden and 3TATAA Biocenter, Medicinargatan 7B, 405 30 Gothenburg, Sweden

Real-time PCR is becoming the method of choice for precise quantification of minute amounts of nucleic acids. For proper comparison of samples, almost all quantification methods assume similar PCR effciencies in the exponential phase of the reaction. However, inhibition of PCR is common when working with biological samples and may invalidate the assumed similarity of PCR effiencies. Here we present a statistical method, Kinetic Outlier Detection (KOD), to detect samples with dissimilar effiiencies. KOD is based on a comparison of PCR effciency, estimated from the amplifiation curve of a test sample, with the mean PCR effiency of samples in a training set. KOD is demonstrated and validated on samples with the same initial number of template molecules, where PCR is inhibited to various degrees by elevated concentrations of dNTP; and in detection of cDNA samples with an aberrant ratio of two genes. Translating the dissimilarity in efficiency to quantity, KOD identifies outliers that differ by 1.3±1.9-fold in their quantity from normal samples with a P-value of 0.05. This precision is higher than the minimal 2-fold difference in number of DNA molecules that real-time PCR usually aims to detect. Thus, KOD may be a useful tool for outlier detection in real-time PCR.

Kinetics quality assessment for relative quantification by real-time PCR.
  Bar T, Muszta A.
  Biotechniques. 2005 Sep;39(3): 333-338
  halmers University of Technology, Gothenburg, Sweden.

For proper relative quantification by real-time PCR, compared samples should have similar PCR efficiencies. To test this prerequisite, we developed two quality tests: (i) adjustment of a test for kinetic outlier detection (KOD) to relative quantification; and (ii) comparison of the efficiency variance of test samples with the efficiency variance of samples with highly reproducible quantification. The tests were applied on relative quantification of two genes in 30 sets of 5 replicate samples (same treatment, different animals). Ten low-quality sets and 28 outliers were identified. The low-quality sets showed higher coefficient of variation (cv)% of DNA quantities in replicate experiments than high-quality sets (63% versus 26%; P = 0.001) and contained a higher proportion of outlying quantities (35% versus 5.9%; P = 0.001) when individual samples were detected by adjusted KOD. Outlier detection with adjusted KOD reduced the false detection of outliers by 2/3 compared with the previous, nonadjusted version of KOD (20% versus 5.9%; P = 0.001). We conclude that the presented tests can be used to assign technical reasons to outlying observations.

Quality control for quantitative PCR based on amplification compatibility test.
Tichopad A, Bar T, Pecen L, Kitchen RR, Kubista M, Pfaffl MW.
Methods. 2010 50(4): 308-312

Quantitative qPCR is a routinely used method for the accurate quantification of nucleic acids. Yet it may generate erroneous results if the amplification process is obscured by inhibition or generation of aberrant side-products such as primer dimers. Several methods have been established to control for pre-processing performance that rely on the introduction of a co-amplified reference sequence, however there is currently no method to allow for reliable control of the amplification process without directly modifying the sample mix. Herein we present a statistical approach based on multivariate analysis of the amplification response data generated in real-time. The amplification trajectory in its most resolved and dynamic phase is fitted with a suitable model. Two parameters of this model, related to amplification efficiency, are then used for calculation of the Z-score statistics. Each studied sample is compared to a predefined reference set of reactions, typically calibration reactions. A probabilistic decision for each individual Z-score is then used to identify the majority of inhibited reactions in our experiments. We compare this approach to univariate methods using only the sample specific amplification efficiency as reporter of the compatibility. We demonstrate improved identification performance using the multivariate approach compared to the univariate approach. Finally we stress that the performance of the amplification compatibility test as a quality control procedure depends on the quality of the reference set.

Efficiency clustering for low-density microarrays and its application to qPCR
Eric F Lock, Ryan Ziemiecke, J. S. Marron and Dirk P Dittmer
BMC Bioinformatics 2010, 11

Background -Pathway-targeted or low-density arrays are used more and more frequently in biomedical research, particularly those arrays that are based on quantitative real-time PCR. Typical QPCR arrays contain 96-1024 primer pairs or probes, and they bring with it the promise of being able to reliably measure differences in target levels without the need to establish absolute standard curves for each and every target. To achieve reliable quantification all primer pairs or array probes must perform with the same efficiency.
Results -Our results indicate that QPCR primer-pairs differ significantly both in reliability and efficiency. They can only be used in an array format if the raw data (so called CT values for real-time QPCR) are transformed to take these differences into account. We developed a novel method to obtain efficiency-adjusted CT values. We introduce transformed confidence intervals as a novel measure to identify unreliable primers. We introduce a robust clustering algorithm to combine efficiencies of groups of probes, and our results indicate that using n < 10 cluster-based mean efficiencies is comparable to using individually determined efficiency adjustments for each primer pair (N = 96-1024).
Conclusions - Careful estimation of primer efficiency is necessary to avoid significant measurement inaccuracies. Transformed confidence intervals are a novel method to assess and interprete the reliability of an efficiency estimate in a high throughput format. Efficiency clustering as developed here serves as a compromise between the imprecision in assuming uniform efficiency, and the computational complexity and danger of over-fitting when using individually determined efficiencies.

Shape based kinetic outlier detection in real-time PCR.
Sisti D, Guescini M, Rocchi MB, Tibollo P, D'Atri M, Stocchi V.
BMC Bioinformatics. 2010 12;11: 186

BACKGROUND - Real-time PCR has recently become the technique of choice for absolute and relative nucleic acid quantification. The gold standard quantification method in real-time PCR assumes that the compared samples have similar PCR efficiency. However, many factors present in biological samples affect PCR kinetic, confounding quantification analysis. In this work we propose a new strategy to detect outlier samples, called SOD.
RESULTS - Richards function was fitted on fluorescence readings to parameterize the amplification curves. There was not a significant correlation between calculated amplification parameters (plateau, slope and y-coordinate of the inflection point) and the Log of input DNA demonstrating that this approach can be used to achieve a "fingerprint" for each amplification curve. To identify the outlier runs, the calculated parameters of each unknown sample were compared to those of the standard samples. When a significant underestimation of starting DNA molecules was found, due to the presence of biological inhibitors such as tannic acid, IgG or quercitin, SOD efficiently marked these amplification profiles as outliers. SOD was subsequently compared with KOD, the current approach based on PCR efficiency estimation. The data obtained showed that SOD was more sensitive than KOD, whereas SOD and KOD were equally specific.
CONCLUSION - Our results demonstrated, for the first time, that outlier detection can be based on amplification shape instead of PCR efficiency. SOD represents an improvement in real-time PCR analysis because it decreases the variance of data thus increasing the reliability of quantification.

WEB INTERFACE - Cy0 is a new method in Real-time PCR analysis that does not require the assumption of equal efficiency between unknowns and standard curve (Michele Guescini, Davide Sisti, & Renato Panebianco, 2010)