Unaccounted uncertainty from qPCR efficiency estimates entails uncontrolled false positive rates

Abstract

Background: Accurate adjustment for the amplification efficiency (AE) is an important part of real-time quantitative polymerase chain reaction (qPCR) experiments. The most commonly used correction strategy is to estimate the AE by dilution experiments and use this as a plug-in when efficiency correcting the Δ Δ C q . Currently, it is recommended to determine the AE with high precision as this plug-in approach does not account for the AE uncertainty, implicitly assuming an infinitely precise AE estimate. Determining the AE with such precision, however, requires tedious laboratory work and vast amounts of biological material. Violation of the assumption leads to overly optimistic standard errors of the Δ Δ C q , confidence intervals, and p-values which ultimately increase the type I error rate beyond the expected significance level. As qPCR is often used for validation it should be a high priority to account for the uncertainty of the AE estimate and thereby properly bounding the type I error rate and achieve the desired significance level.

Results: We suggest and benchmark different methods to obtain the standard error of the efficiency adjusted Δ Δ C q using the statistical delta method, Monte Carlo integration, or bootstrapping. Our suggested methods are founded in a linear mixed effects model (LMM) framework, but the problem and ideas apply in all qPCR experiments. The methods and impact of the AE uncertainty are illustrated in three qPCR applications and a simulation study. In addition, we validate findings suggesting that MGST1 is differentially expressed between high and low abundance culture initiating cells in multiple myeloma and that microRNA-127 is differentially expressed between testicular and nodal lymphomas.

Conclusions: We conclude, that the commonly used efficiency corrected quantities disregard the uncertainty of the AE, which can drastically impact the standard error and lead to increased false positive rates. Our suggestions show that it is possible to easily perform statistical inference of Δ Δ C q , whilst properly accounting for the AE uncertainty and better controlling the false positive rate.

Keywords: Amplification efficiency; Delta-delta Cq; Efficiency adjusted; Error propagation; qPCR; Δ Δ C q.

Fig. 1

Overview of CIC experiment data. a Raw C _q-values for different cell lines (samples) for each gene type and sample type. The point type and colour differentiates the different gene types. b Dilution data for reference genes (ACTB, GAPDH) and target genes (MGST1, MMSET)

Fig. 2

Overview of DLBCL testis data. a Raw C _q-values for different patient samples for each gene type and sample type. The point type and colour differentiates the different gene types. b Dilution data for reference genes (RNU-24, RNU-6B) and target genes (miR-127, miR-143)

Fig. 3

Overview of Arabidopsis thaliana data [7]. C _q-values against the dilution step for case and control samples. Dilution data are present for both the target (MT7) and reference genes (Tublin, UBQ)

Fig. 4

Method performance. Plot of the false positive rates (FPR, black) and true positive rates (TPR, grey) and their 95 % confidence intervals achieved simulation experiments for each method at various p-value cut-offs (0.05, 0.01, 0.1) shown by solid red horizontal lines. The FPR and TPR are computed completely analogous to Table 4. The rates are plotted for each combination of 4 or 8 samples with 4 or 8 fold dilution curves

Fig. 5

Standard error comparison. The mean standard error of the Δ Δ C _q for two methods (EC and EC&VA1) over 2000 repeated simulations under the null (panel a) and alternative hypothesis (panel b) as a function of the number of dilution steps for a different number of samples in each group