Target concentration and replicate qPCR reactions

Jan M. Ruijter 1, *, Maurice W.J. de Ronde2, Antoni Bayes Genis3, Yigal Pinto4, Sara-Joan Pinto 2
1 Anatomy, Embryology and Physiology, Academic Medical Center, Amsterdam, the Netherlands
2 Vascular Medicine & Clinical Epidemiology, Biostatistics and Bioinformatics, Academic Medical Center, Amsterdam, the Netherlands
3 Heart Failure Unit, Germans Trias i Pujol Hospital, Universitat Autònoma, Barcelona, Spain
4 Experimental Cardiology, Academic Medical Center, Amsterdam, the Netherlands 

In the analysis of qPCR data, the criterion for reproducibility between replicate reactions is set to 0.5 cycles; when the Cq values of replicates differ more than 0.5, the results are often discarded. The idea is that this rule-of-thumb should be enforced to protect against the inclusion of technical variation in the analysis of the qPCR results. However, a technical pipetting error of 15% is required to reach a 0.5 cycles difference. Smaller technical errors are already unacceptably large but would go unnoticed and be tolerated. On the other hand, at high Cq values the sampling error that occurs when pipetting a low number of target molecules into the PCR plate is governed by the Poisson distribution. To calculate the magnitude of this sampling error for different Cq values, we started with the assumption that for a PCR efficiency of about 1.8, an input of 10 copies of target leads to a Cq value of about 35 when the primer and amplicon concentration become similar. The observed Cq value will depend on the actual PCR efficiency, the monitoring chemistry, the (pre-) processing of the fluorescence data and the way the Cq value is determined. When the PCR reaction reaches the quantification threshold the general kinetic equation can be written as
Nq = NEqC (1) which with the above assumption is equal to
Nq = 10E35 (2)
This equality provides us with an equation to estimate the target input from the observed Cq value and PCR efficiency:
Nq = 10E35-C (3) q
Using the relationship between Poisson and Chi2 distributions the 95% confidence interval of N is then given by:
0.5 20.025;2N ≤ N ≤ 0.5 20.975;2N+2 (4)
For each Cq and PCR efficiency value we can thus calculate a number of copies with Eq. (3), the sampling error range with Eq. (4) and then, with the inverse of Eq. (1), the expected range of Cq values due to unavoidable sampling variation. This range increases with higher Cq values (less target) and easily leads to a replicate variation above 0.5 cycles. Discarding such discordant replicates will lead to bias and loss of power in the analysis. For a dataset that resulted from the qPCR measurement of 12 miRNA targets in 834 patients with a total of 20,016 reactions, the strict application of the rule that the Cq values of replicates should be within 0.5 cycles led to rejection of 7752 (39%) measurements. When the unavoidable Cq range, calculated as described above, is used to determine which Cq difference between replicates should lead to the decision that the replicate discordance is still acceptable, the number of reac- tions that should be discarded decreases to 1414 (7%). Not only less reactions are discarded, also the distribution of Cq values changes showing that strict application of the Cq < 0.5 cycle rule has led to bias in the results of the qPCR experiment. A decision to exclude replicate reactions based on the expected sampling error avoids this bias, prevents unwanted loss of data and therefore increases the statistical power.

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