Real-time relative quantitative PCR in clinical settings is hampered by a lack of accurate and precise approaches to estimate the ratio between nucleic acid sequences without reference to a control sample. Also, conventional approaches for estimating internal PCR parameters are problematic in low capacity PCR machines. This paper concerns the establishment and examination of two new approaches for real-time quantitative PCR; namely RIMS and drqPCR. RIMS concerns estimation of run-internal specific PCR parameters, such as efficiency, from a minimum of samples. The drqPCR is a universal strategy for estimation of ratios directly in the sample, alleviating the need for control samples and therefore ideal for analysis of unpaired samples. We compared RIMS and drqPCR with conventional methods on a common data set. This data set was generated from samples with known target ratios. Therefore, both the precision and accuracy of the approaches could be evaluated.
Separately, RIMS gives target-specific and run-specific estimates of the standard curve's slope and intercept (measures of NCq and E, respectively). Estimates determined for the specific run are obviously preferable to those determined in separate runs. Run-specific differences of NCq for the targets can be corrected by inclusion of calibrator samples. However, run-to-run differences in E are not corrected by use of calibrator samples and are critical to the use of external standard curves. It is evident from our data that run-to-run differences of E are to be anticipated (). Testing the βs of the same target for significant differences over days discloses dissimilarity in 3 of the possible 6 comparisons (p<0.001 for ERV1 on day 1 vs. 3, TUPLE1 on day 1 vs. 3, and 2 vs. 3).
From Real-Time PCR data, we produced 8,694 individual RIMS. Not surprisingly, the number of RIMS-sample replicates and the value of C
were of immense importance for precision (). Compared with standard curves, RIMS provided the potential for attaining estimates of the highest precision. Obviously, a potential explanation could be large run-run external standard curve-variation in our study. Rutledge and Cote 
used a model comparable to ours, in which a PCR product was serially diluted and subjected to real-time PCR with two different primer sets five times. They reported E
CVs of 2.2% and 2.1% for five repeated standard curves for each of two targets. In comparison, E
CVs of our study were 2.9% (ERV1) and 2.5% (TUPLE1). The CVs of NCq
in the study of Rutledge and Cote were 19.0% and 14.7%. NCq
-detection was based on constant fluorescence threshold. We based our threshold setting on an error-minimizing strategy for the individual standard curve. Correction of our NCq
-data by fluorescence intensity at Cq
enables comparison. Threshold-corrected NCq
CVs of our study were 12.4% and 26.3% (data from ). However, the CVs of Rutledge et al do not include the variation associated with the construction of the dilution series, insofar as all standard curves were generated from sequential analysis of only one dilution series. In this light, our raw data are at least comparable in quality.
In our examination of the precision of RIMS-based estimates, the estimates were compared to the corresponding estimate of the internal standard curves. We found a close approximation (that is, a high precision) of the large-C-based RIMS estimates to the 28-sample internal standard curves' (). We perceive this as indicative of RIMS potential for high accuracy. Furthermore, the result illustrates the redundancy of the intervening data points. RIMS may therefore also be considered as a cost-saving alternative in high-capacity machinery.
The following points should be considered when constructing the RIMS in practice. First, RIMS samples should be selected from the dilution series based on a preliminary standard curve to maximize C
) while preserving linearity. Second, very dilute samples should be avoided completely (Appendix S1
, section 1). Third, the chosen samples should be aliquoted and stored. Fourth, two or more replicate Cq
-estimations of each RIMS sample are preferable. Fifth, the type of template (e.g. PCR-product, cDNA, or genomic DNA) chosen for RIMS-samples should permit appropriately sized C
s. Direct estimation of nucleic acid sequences ratio is attractive in many settings, yet difficult to obtain. The problem, associated with the (NCq
-term (cf. Eq. I.2
), can be dealt with in several ways. The simplest is to ignore it altogether. This is the case if ordinary relative standard curves are used. Such an approach confers systematic errors of magnitudes defined by the inverse of the (NCq
-term. In our example, we would have attained between 1.1-fold and 2.6-fold errors for same-day quantifications and as much as 20-fold errors for quantifications across days (cf. NCq
-values in ). Another approach is to rely on experimental conditions assumed to ensure equality of (NCq
. If equality is indeed ensured, the (NCq
-term can be safely ignored. A frequent perception in Real-Time PCR literature is that a similar detection threshold for different targets automatically ensures similar copy numbers at detection 
. As described earlier, this is unreliable because the proportionality factor between copy numbers and fluorescence intensity (k
) can differ between targets. The magnitude of the systematic error associated with the approach can be assessed as the inverse of the targets k
-ratio. With this approach, our results would have been off by factor of 1.2 to 1.6 or 2.0 to 2.7 with or without target length corrections, respectively (cf. k
-values of ). Although we observed a great deal of variability of the NCq
s across both days and targets, this does not prove the existence of a universal phenomenon. However, our findings do illustrate the importance of expecting variation. This definitely also applies if a common threshold setting is defined. Quantitative-methods with insufficient corrections of (NCq
-term variability can provide results of reasonable precision. But the systematic error is never spotted unless samples of known ratio are quantified. A third and more qualified approach is to use classical absolute quantifications 
. A drawback of absolute quantification is the considerable effort required to generate samples of known absolute target concentration. Typically, the targets are cloned into plasmids, which are subsequently biologically expanded and purified. The ensuing measurements of DNA concentrations and the derivation of absolute target concentrations are both prone to errors.
Instead, we advocate approaches based on internal, relative standard curves (derived from samples containing the targets of interest in equal amounts) and use of regression estimates. This ensures both target-specific and run-specific corrections of the underlying variable (NCq
. Ligated PCR products of the targets are the ideal theoretical choice. This generally applicable method has the potential for attaining the largest C
s and absolutely defining the targets' stoichiometry. For data handling, we suggest two different approaches: single-ratio or double-ratio-based drqPCR (Eq. R.1
and Eq. R.3
, respectively). In the double-ratio-based approach, a virtual control sample is constructed from the RIMS samples already used for β
-estimations. Such “recycling” of RIMS-samples is not problematic, inasmuch as the samples are used to estimate two independent quantities. The known relative concentration between the RIMS-samples (e.g. CA
) is used for β
-estimations, whereas the relative concentration of the targets of the virtual control sample (e.g. (N0
)) is used in corrections of the (NCq
-term. Steps to reduce the error of Ris
-estimation are of general importance. This is obvious in clinical settings but also applies to experimental comparison of groups. The larger the variance of a group mean, the more individuals, cell cultures or such, must be included to demonstrate a given significant difference between groups. With this in mind we allocated some efforts to choose the ideal raw data sampling approaches. Cq
-sampling by the FP-approach offered significantly better precision than the second derivatives maximum-approach, whereas estimations of relative target concentrations in standard curves based on weight as opposed to volumes was negligible (and insignificantly) better (see Appendix S1
section 3 and Figure S2
, Figure S3
, and Figure S4
We evaluated drqPCR based on RIMS in quantifications of samples containing the quantified targets in known stoichiometry. This model permitted us to evaluate both quantitative precision and accuracy. Not surprisingly, we found that increasing C
and the number of RIMS replicates increased the precision significantly (–
). However, C
was the most important parameter for improving precision. More than two replicates of each RIMS-sample conferred only minimal improvements of precision. Accuracy was within ±8%. Finally, we compared precision and accuracy of drqPCR based on the 2ΔΔCq
-approach, external standard curves, and RIMS. RIMS-based drqPCR demonstrated the largest potential for precision (). The accuracies of the conventional approaches were comparable. The conventional approaches were conducted in a double-ratio manner where Ris
s were normalised by the ratio derived from analysis of a sample containing the targets in equal concentrations, to maximize accuracy. When using our two approaches in practice, we suggest inclusion of an intermediate RIMS sample. The purpose is dual: to permit evaluation of linearity within the specific RIMS, and to provide more samples available for “virtual controls”. Also, the Cq
of samples to be quantified should be estimated in duplicates or more. For practical data handling, we have included an Excel-based spreadsheet in the supplementary material (Algorithm S1
Use of drqPCR has other beneficial side-effects. The principle renders calibrator samples (or reference-control samples) superfluous. Calibrators are a necessity when interest and control samples are not in the same PCR-run 
. Their purpose is to correct for run-to-run differences of targets Nq
-value. Briefly, the calibrator sample contains the targets-to-be-quantified and is PCR-expanded both in runs of controls and interest samples. Subsequently, interest and control data are made comparable by dividing each with the calibrator data of their respective runs. In drqPCR, data of control and interest samples are always immediately comparable, provided that the same RIMS samples are used in runs. Avoidance of calibrators is attractive to minimize the sources of errors of Ris
. The importance of drqPCR can be stretched further. Another important effect is that results obtained by drqPCR are immediately comparable between different labs. Thus, the problem of lab-to-lab comparability is avoided completely.
In summary, we suggest that RIMS and drqPCR be used separately or combined for relative quantifications of high precision and accuracyThe drqPCR allows determination of Ris directly in the sample, and RIMS can replace external standard curves.