Many official documents have discussed theories and procedures for the correct definition of the LOD for different methods. A general consensus was reached around the definition of the LOD as the lowest amount of analyte, which can be detected with more than a stated percentage of confidence, but, not necessarily quantified as an exact value Anonymous, , , In this regard, the confidence level obtained or requested for the definition of LOD can reflect the number of replicates both technical and experimental needed by the assay in order to reach the requested level of confidence e.
It is clear that the more replicates are tested, the narrower will be the interval of confidence. Another definition describes the LOD as the lowest concentration level that can be determined as statistically different from a blank at a specified level of confidence. This value should be determined from the analysis of sample blanks and samples at levels near the expected LOD Anonymous, a. However, it should be noted that LOD definitions described above were reported for chemical methods, and are not perfectly suited for PCR methods Burns and Valdivia, This is because, for limited concentrations of analyte nucleic acids , the output of the reaction can be a success amplification , or a failure no amplification at all , without any blank, or critical level at which it is possible to set a cut-off value over which the sample can be considered as positive one.
Moreover, it should be remembered here that, by definition, a blank sample should never be positive in PCR. Since the definitions reported above are not practicable for PCRs, other approaches have been proposed.
In practice, multiple aliquots of a specific matrix are spiked with serial dilutions of the target organism and undergo the whole process of nucleic acid isolation and qPCR. For example, 10 replicates of milk samples were spiked with serial dilutions of Campylobacter jejuni in amounts of 10 5 —10 0 cells per 1 ml of milk. The experimentally determined LOD of the method for the detection of C.
In order to better define the most precise value, more dilutions can be tested before reaching a final LOD value as close as possible to the real one. The number of replicates tested should be at least six Slana et al. Figure 2. According to the Poisson distribution, it was concluded that the LOD for PCR cannot be lower than at least three copies of the nucleic acid targets Bustin et al. Therefore, as stated above, the LOD must be related to the whole method that includes nucleic acid preparation and qPCR.
Only under these conditions can it represent a valid parameter that describes the features of the respective qPCR method Anonymous, a. However, sometimes it is not possible to obtain large numbers of replicates, for both financial and technical reasons.
Briefly, both mathematical functions are regressions used to analyse binomial response variables positive or negative and are able to transform the sigmoid dose-response curve, typical of a binomial variable, to a straight line that can then be analyzed by regression either through least squares or maximum likelihood methods. The final end-point of the analysis is a concentration coupled with relative intervals of confidence , associated to a probability e.
Moreover, Probit regression is exploitable only for normally distributed data, while Logit function can also be used for data not normally distributed; however, in this context, both functions have the same meaning. Finally, it must be noted that LOD is not a limiting value and therefore, that C q values below the LOD cannot automatically be considered as negative.
This feature is connected with the Poisson distribution when working with small numbers. The LOQ was defined as the smallest amount of analyte, which can be measured and quantified with defined precision and accuracy under the experimental conditions by the method under validation Armbruster and Pry, ; Anonymous, , An alternative definition is that the LOQ is the lowest amount or concentration of analyte that can be quantitatively determined with an acceptable level of uncertainty Anonymous, a.
In practice, the LOQ is determined as is the LOD, on replicates of spiked samples, but the assessment of results is quantitative. Numerically, the LOQ is defined as the lowest concentration of analyte, which gives a predefined variability, generally reported as the coefficient of variation CV. Hoverer, this value was proposed based on the experience accrued in GMO detection laboratories Broeders et al. A series of spiked samples with different concentrations of target DNA were analyzed and the J -values were calculated for each PCR cycle.
Finally, an issue that should be addressed for the determination of the LOQ as well as LOD is the efficiency of recovery of target molecules during the nucleic acid extraction phases. Generally, nucleic acids are extracted from different complex matrices, like food, feces, or other samples using different procedures. Due to the fact that these data are provided during the determination of the LOD and LOQ, it is not necessary to perform additional experiments.
It is recommended that the median of mean DNA isolation values from different dilutions is used as the practical overall DNA isolation efficiency Kralik et al. Similarly to the LOD, quantity can also be assessed in samples with numbers of organisms or concentrations of DNA lower than the LOQ, but the confidence of such quantification will be lower than that declared by the definition of LOQ.
Moreover, there are possibilities of how to refer to such quantities in terms of semi-quantitative interpretation, e. This parameter was mentioned above in the section dedicated to the mathematical description of qPCR Equation 4. This is difficult to reach repeatedly over time. This parameter can be estimated from the slope of the calibration curve. In connection to this issue, the lowest and highest concentrations of the standard included in the calibration curve, which can be truly quantified, should be determined according to the linear dynamic range of over at least 6 Log The dynamic range is defined by the MIQE guidelines as the range over which a reaction is linear Bustin et al.
The determination of PCR efficiency by the standard curve actually provides two pieces of information. If an inhibitor would be present in the most concentrated sample, there would be a visible increase in C q values in these and therefore a diminishment of the 3. However, this is not a frequent phenomenon, as standards are usually well-characterized and therefore, any inhibition is rather unlikely.
If there would be a similar situation in lower concentration samples, this suggests a possible pipetting error rather than the presence of inhibitors. An important function to assess this is the coefficient of determination R 2 value , that should be higher than 0. In reality, it is much more important to determine the PCR inhibition and subsequent diminishment of the PCR efficiency in analyzed samples.
There are approaches based on the analysis of the fluorescent curve of each sample by specific software LinRegPCR , which can calculate the PCR efficiency of each sample without the series of dilutions.
However, this approach is not flawless as it does not take into account all possible variables that can affect the analysis Ruijter et al. The following parameters of qPCR deal with ways of how to compare novel qPCR methods with reference methods or materials. Accuracy is defined as a measure of the degree of conformity of a value generated by a specific procedure to the assumed or accepted true value Anonymous, a.
In other words, accuracy describes the level of agreement between reference and measured values. There are several aspects that need to be considered in terms of defining accuracy. In binary classification tests qualitative detection , the samples analyzed by a novel alternative test that needs to be verified typically a novel qPCR assay are categorized according to their concordance with the reference method in four basic categories Table 1.
This division originates from the statistical classification known as error matrix and allows determination of several parameters that describe the diagnostic potential of the qPCR method. Table 1. The lower the diagnostic sensitivity, the poorer will be the inclusivity of the tested qPCR.
Another explanation could be that the analytical sensitivity LOD of the reference method is higher than the tested qPCR. The lower the diagnostic specificity, the poorer will be the exclusivity of the tested qPCR. Another explanation could be that the sensitivity of the reference method is quite bad, and the new qPCR method is capable of identifying more positive samples than the reference method. In quantitative determination, the accuracy numerically describes the distance of the value from the novel tested qPCR and some reference true value.
For this reason, accuracy is referred to as trueness in quantitative classification Anonymous, Trueness is defined as the degree of agreement of the expected value with the true value or accepted reference value. This is related to systematic error Anonymous, a , b. There are no fixed values of trueness that the novel tested qPCR method must meet in microbiological diagnostics. This might be caused by the fact that the trueness in qPCR can be determined by the comparison with some certified reference material, with the reference method or by proficiency testing.
Certified reference material with a quantified number of target organisms is available only for a limited number of organisms especially viruses like HIV, HBV, HCV, HAV, HPV, CMV, EBV , while for the remainder of clinically significant organisms, these materials are often available only for the qualitative analysis, and are therefore not suitable for trueness determination.
Reference methods usually have varying diagnostic sensitivities and specificities and often they do not fit for the purposes of the quantitative assessment of novel qPCR methods. Moreover, the organization of proficiency testing via ring trials is expensive and requires a supplier of the reference material like QCMD. These are the main reasons why determination of trueness in qPCR methods for the microbial detection in clinical, and especially in veterinary food safety areas, is rather limited.
Precision is defined as the degree of agreement of measurements under specified conditions. The precision is described by statistical methods such as SD or confidence limit Anonymous, a. From the definition of precision, it is evident that this qPCR parameter is quantitative. For practical determination of precision, two conditions termed repeatability, and reproducibility were introduced Anonymous, These two parameters are used to describe the variability of measurements introduced by the operator, equipment, and its calibration, environmental factors that can influence the measurement like temperature, humidity etc.
Repeatability is described as the closeness of agreement between successive and independent results obtained by the same method on identical test material under the same conditions apparatus, operator, laboratory, and short intervals of time and expresses within-laboratory variations Anonymous, , , a. Repeatability consists of two different variables: intra- and inter-assay variation. The intra-assay variation describes the variability of the replicates conducted in the same experiment; the inter-assay variation describes the variability between different experiments conducted on different days.
Numerically, the repeatability is characterized as the SD of replicates at each concentration of each matrix for each method Anonymous, If the measured value lies outside the SD, it should be considered as suspect Anonymous, It is necessary to perform the estimation of repeatability on 15 repeats at least Anonymous, , b.
Testing of repeatability requires analysis of the spiked relevant matrix at least at four levels—high, medium, low near to the LOD and negative in at least duplicates Anonymous, For more rigorous testing the use of five replicates and the addition of one more sample spiked with a competitor strain that gives similar results in the given detection system is recommended.
Natural background microflora can fulfill this requirement as long as they are present in the matrix at a level 1 Log 10 greater than the target analyte Anonymous, a. In clinical, veterinary and food microbial detection, there are no specific recommendations for the repeatability SD value in terms of its proportion with respect to the mean. On the other hand, reproducibility is the closeness of agreement between single test results on identical test material using the same method, obtained in different laboratories using different equipment and expresses the variation between laboratories Anonymous, , , a.
Numerically, the reproducibility is characterized as the SD replicates at each concentration for each matrix across all laboratories Anonymous, If the difference between two results from different laboratories exceeds R, the results must be considered suspect Anonymous, The reproducibility is usually defined by collaborative studies, which determine the variability of the results obtained by the given method in different laboratories using identical samples Anonymous, , ; Molenaar-de Backer et al.
The number of laboratories with valid results which should be included in the collaborative study is at least eight. Therefore, it is advisable to select 10—12 labs Anonymous, , a. In probe-based qPCR, many targets can be detected simultaneously in each sample but this requires optimization and design of a target specific probe s , used in addition to primers. There are several types of probe designs available, but the most common type is a hydrolysis probe, which incorporates the use of a fluorophore and quencher.
Fluorescence resonance energy transfer FRET prevents the emission of the fluorophore via the quencher while the probe is intact. However, during the PCR reaction, the probe is hydrolyzed during primer extension and amplification of the specific sequence it is bound to. The cleavage of the probe separates the fluorophore from the quencher and results in an amplification-dependent increase in fluorescence. Thus, the fluorescence signal from a probe-based qPCR reaction is proportional to the amount of the probe target sequence present in the sample.
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The amount of fluorescence is proportional to the amount of PCR product. The time point at which the fluorescence reaches a defined threshold is relative to the level of gene expression.
The design of real-time PCR experiments requires prior knowledge of the gene sequence and careful consideration of the types of controls to include. Functional genomics II Common technologies and data analysis methods.
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