Statistical analysis of real-time PCR data

Background  

Even though real-time PCR has been broadly applied in biomedical sciences, data processing procedures for the analysis of quantitative real-time PCR are still lacking; specifically in the realm of appropriate statistical treatment. Confidence interval and statistical significance considerations are not explicit in many of the current data analysis approaches. Based on the standard curve method and other useful data analysis methods, we present and compare four statistical approaches and models for the analysis of real-time PCR data.     

Statistical aspects of quantitative real-time PCR experiment design

Experiments using quantitative real-time PCR to test hypotheses are limited by technical and biological variability; we seek to minimise sources of confounding variability through optimum use of biological and technical replicates. The quality of an experiment design is commonly assessed by calculating its prospective power. Such calculations rely on knowledge of the expected variances of the measurements of each group of samples and the magnitude of the treatment effect; the estimation of which is often uninformed and unreliable. Here we introduce a method that exploits a small pilot study to estimate the biological and technical variances in order to improve the design of a subsequent large experiment. We measure the variance contributions at several ‘levels’ of the experiment design and provide a means of using this information to predict both the total variance and the prospective power of the assay. A validation of the method is provided through a variance analysis of representative genes in several bovine tissue-types. We also discuss the effect of normalisation to a reference gene in terms of the measured variance components of the gene of interest. Finally, we describe a software implementation of these methods, powerNest, that gives the user the opportunity to input data from a pilot study and interactively modify the design of the assay. The software automatically calculates expected variances, statistical power, and optimal design of the larger experiment. powerNest enables the researcher to minimise the total confounding variance and maximise prospective power for a specified maximum cost for the large study.     

Statistical methods for efficiency adjusted real-time PCR quantification

The statistical treatment for hypothesis testing using real-time PCR data is a challenge for quantification of gene expression. One has to consider two key factors in precise statistical analysis of real-time PCR data: a well-defined statistical model and the integration of amplification efficiency (AE) into the model. Previous publications in real-time PCR data analysis often fall short in integrating the AE into the model. Novel, user-friendly, and universal AE-integrated statistical methods were developed for real-time PCR data analysis with four goals. First, we addressed the definition of AE, introduced the concept of efficiency-adjusted Delta Delta Ct, and developed a general mathematical method for its calculation. Second, we developed several linear combination approaches for the estimation of efficiency adjusted Delta Delta Ct and statistical significance for hypothesis testing based on different mathematical formulae and experimental designs. Statistical methods were also adopted to estimate the AE and its equivalence among the samples. A weighted Delta Delta Ct method was introduced to analyze the data with multiple internal controls. Third, we implemented the linear models with SAS programs and analyzed a set of data for each model. In order to allow other researchers to use and compare different approaches, SAS programs are included in the Supporting Information. Fourth, the results from analysis of different statistical models were compared and discussed. Our results underline the differences between the efficiency adjusted Delta Delta Ct methods and previously published methods, thereby better identifying and controlling the source of errors introduced by real-time PCR data analysis.     

Comparison of real-time quantitative PCR and culture for the diagnosis of emerging Rickettsioses

Background

Isolation of Rickettsia species from skin biopsies may be replaced by PCR. We evaluated culture sensitivity compared to PCR based on sampling delay and previous antibiotic treatment.

Methodology/Principal Findings

Skin biopsies and ticks from patients with suspected Rickettsia infection were screened for Rickettsia spp. using qPCR, and positive results were amplified and sequenced for the gltA and ompA genes. Immunofluorescence for spotted fever group rickettsial antigens was done for 79 patients. All skin biopsies and only ticks that tested positive using qPCR were cultured in human embryonic lung (HEL) fibroblasts using the centrifugation-shell vial technique. Patients and ticks were classified as definitely having rickettsioses if there was direct evidence of infection with a Rickettsia sp. using culture or molecular assays or in patients if serology was positive. Data on previous antibiotic treatments were obtained for patients with rickettsiosis. Rickettsia spp. infection was diagnosed in 47 out of 145 patients (32%), 41 by PCR and 12 by culture, whereas 3 isolates were obtained from PCR negative biopsies. For 3 of the patients serology was positive although PCR and culture were negative. Rickettsia africae was the most common detected species (n = 25, [17.2%]) and isolated bacterium (n = 5, [3.4%]). The probability of isolating Rickettsia spp. was 12 times higher in untreated patients and 5.4 times higher in patients from our hometown. Rickettsia spp. was amplified in 24 out of 95 ticks (25%) and we isolated 7 R. slovaca and 1 R. raoultii from Dermacentor marginatus.

Conclusions/Significance

We found a positive correlation between the bacteria copies and the isolation success in skin biopsies and ticks. Culture remains critical for strain analysis but is less sensitive than serology and PCR for the diagnosis of a Rickettsia infection.     

Kinetics quality assessment for relative quantification by real-time PCR

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.     

Genomic DNA functions as a universal external standard in quantitative real-time PCR

Real-time quantitative PCR (qPCR) is a powerful tool for quantifying specific DNA target sequences. Although determination of relative quantity is widely accepted as a reliable means of measuring differences between samples, there are advantages to being able to determine the absolute copy numbers of a given target. One approach to absolute quantification relies on construction of an accurate standard curve using appropriate external standards of known concentration. We have validated the use of tissue genomic DNA as a universal external standard to facilitate quantification of any target sequence contained in the genome of a given species, addressing several key technical issues regarding its use. This approach was applied to validate mRNA expression of gene candidates identified from microarray data and to determine gene copies in transgenic mice. A simple method that can assist achieving absolute quantification of gene expression would broadly enhance the uses of real-time qPCR and in particular, augment the evaluation of global gene expression studies.     

Statistical quality control of variety trial data

I propose detection criteria for identifying an abnormal or erroneous data vector provided by a single variety trial in a longer series of variety trials. The test criteria are based on the linear effects estimated separately for each studied trial using global variance components estimated from the whole series of variety trials. The criteria comprise three mutually independent test statistics. The first one is a quadratic form in the estimated fixed effects, the second one is a quadratic form in the estimated realized linear random effects not including the residual effects, and the third one is a quadratic form in the estimated realized residual effects. Under the null hypothesis defining a valid data vector, the three quadratics have independent chi2 distributions. Under natural alternative hypotheses, they have noncentral chi2 distributions. Decomposing the total variation of the data vector studied into quadratic forms due to different types of the realized linear effects intuitively justifies the resulting test criteria. The decomposition may also be used to show that the resulting tests are likelihood ratio tests. I further present computational procedures that allow us to dispense with the need for prior estimation of the linear effects.     

The power of real-time PCR

In recent years, real-time polymerase chain reaction (PCR) has emerged as a robust and widely used methodology for biological investigation because it can detect and quantify very small amounts of specific nucleic acid sequences. As a research tool, a major application of this technology is the rapid and accurate assessment of changes in gene expression as a result of physiology, pathophysiology, or development. This method can be applied to model systems to measure responses to experimental stimuli and to gain insight into potential changes in protein level and function. Thus physiology can be correlated with molecular events to gain a better understanding of biological processes. For clinical molecular diagnostics, real-time PCR can be used to measure viral or bacterial loads or evaluate cancer status. Here, we discuss the basic concepts, chemistries, and instrumentation of real-time PCR and include present applications and future perspectives for this technology in biomedical sciences and in life science education.     

Evaluation of real-time PCR data

If real-time PCR is to be of much worth to its user, some idea regarding the reliability of its data is essential. We discuss here some of the problems associated with interpreting numerical real-time PCR data that lend themselves to analytical evaluation. We translate into the language of molecular biology some of the criteria which are used to evaluate the performance of any new method (linearity, precision, specificity, limit of detection and quantification).     

Detection of anthrax spores from the air by real-time PCR

AIMS: To detect and isolate Bacillus anthracis from the air by a simple and rapid procedure. METHODS AND RESULTS: One hundred litres of air were filtered through an air monitor device. After the membrane was suspended in PBS, spores of B. anthracis were added. The suspension was plated on Bacillus cereus selective agar (BCA) plates to detect B. anthracis colonies. The suspension was also heated at 95 degrees C for 15 min and used for real-time PCR using a Light Cycler system and anthrax-specific primers. CONCLUSION: A single cell of B. anthracis was detected by real-time PCR within 1 h and was also isolated on a BCA plate within two d. SIGNIFICANCE AND IMPACT OF THE STUDY: Our results provide evidence that anthrax spores from the atmosphere can be detected rapidly, suggesting that real-time PCR and a Light Cycler provides a flexible and powerful tool to prevent epidemics.     

Statistical significance of quantitative PCR

Background  

PCR has the potential to detect and precisely quantify specific DNA sequences, but it is not yet often used as a fully quantitative method. A number of data collection and processing strategies have been described for the implementation of quantitative PCR. However, they can be experimentally cumbersome, their relative performances have not been evaluated systematically, and they often remain poorly validated statistically and/or experimentally. In this study, we evaluated the performance of known methods, and compared them with newly developed data processing strategies in terms of resolution, precision and robustness.     

Standardized determination of real-time PCR efficiency from a single reaction set-up

We propose a computing method for the estimation of real-time PCR amplification efficiency. It is based on a statistic delimitation of the beginning of exponentially behaving observations in real-time PCR kinetics. PCR ground fluorescence phase, non-exponential and plateau phase were excluded from the calculation process by separate mathematical algorithms. We validated the method on experimental data on multiple targets obtained on the LightCycler platform. The developed method yields results of higher accuracy than the currently used method of serial dilutions for amplification efficiency estimation. The single reaction set-up estimation is sensitive to differences in starting concentrations of the target sequence in samples. Furthermore, it resists the subjective influence of researchers, and the estimation can therefore be fully instrumentalized.     

Adapting a conventional PCR assay for Toxoplasma gondii detection to real-time quantitative PCR including a competitive internal control

We have developed a quantitative PCR assay (LightCycler* using the pair of primers JW58 and JW59 for the detection of the 35-fold repeated B gene of oxoplasma gondii. This real-time PCR, using fluorescence resonance energy transfert (FRET) hybridization probes, allows the quantification of . gondii with several technical requirements not previously described: i) an internal amplification control (co-amplified in a single tube with the same primers), ii) Uracil-N-Glycosylase and iii) a standard curve corresponding to a serial dilution from a calibrated suspension of T. gondii ranging from 40 to 4.106( )parasites in one ml of amniotic fluid (1 to 105( ) . gondii/PCR). In artificial samples, one parasite could be detected if at least three reactions were performed.     

Mathematical model of real-time PCR kinetics

Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification techniques, it is assumed that the efficiency of rtPCR is constant. Our analysis of rtPCR data shows, however, that even during the exponential phase of rtPCR, the efficiency of the reaction is not constant, but is instead a function of cycle number. In order to understand better the mechanisms belying this behavior, we have developed a mathematical model of the annealing and extension phases of the PCR process. Using the model, we can simulate the PCR process over a series of reaction cycles. The model thus allows us to predict the efficiency of rtPCR at any cycle number, given a set of initial conditions and parameter values, which can mostly be estimated from biophysical data. The model predicts a precipitous decrease in cycle efficiency when the product concentration reaches a sufficient level for template-template re-annealing to compete with primer-template annealing; this behavior is consistent with available experimental data. The quantitative understanding of rtPCR provided by this model can allow us to develop more accurate methods to quantify gene expression levels from rtPCR data.     

Direct quantification of fungal DNA from soil substrate using real-time PCR

Detection and quantification of genomic DNA from two ecologically different fungi, the plant pathogen Fusarium solani f. sp. phaseoli and the arbuscular mycorrhizal fungus Glomus intraradices, was achieved from soil substrate. Specific primers targeting a 362-bp fragment from the SSU rRNA gene region of G. intraradices and a 562-bp fragment from the F. solani f. sp. phaseoli translation elongation factor 1 alpha gene were used in real-time polymerase chain reaction (PCR) assays conjugated with the fluorescent SYBR(R) Green I dye. Standard curves showed a linear relation (r(2)=0.999) between log values of fungal genomic DNA of each species and real-time PCR threshold cycles and were quantitative over 4-5 orders of magnitude. Real-time PCR assays were applied to in vitro-produced fungal structures and sterile and non-sterile soil substrate seeded with known propagule numbers of either fungi. Detection and genomic DNA quantification was obtained from the different treatments, while no amplicon was detected from non-seeded non-sterile soil samples, confirming the absence of cross-reactivity with the soil microflora DNA. A significant correlation (P<0.0001) was obtained between the amount of genomic DNA of F. solani f. sp. phaseoli or G. intraradices detected and the number of fungal propagules present in seeded soil substrate. The DNA extraction protocol and real-time PCR quantification assay can be performed in less than 2 h and is adaptable to detect and quantify genomic DNA from other soilborne fungi.     

Detection of Mycoplasma pneumoniae in respiratory samples by real-time PCR using an inhibition control

Polymerase chain reaction (PCR) with real-time detection using two adjacent fluorescent probes in a Lightcycler instrument was applied for detection of the Mycoplasma pneumoniae P1 protein gene. To monitor inhibition in each sample an internal control was constructed that can be amplified by the same primers but detected by different probes and dual color detection. The real-time PCR was applied on 115 respiratory samples from 82 patients and compared to a conventional PCR. There was 100% agreement between the assays, but the real-time PCR proved to be highly superior in speed with a much lower risk of false positives by laboratory contamination.