Critique of the pairwise method for estimating qPCR amplification efficiency: beware of correlated data!

Abstract

Background: A recently proposed method for estimating qPCR amplification efficiency E analyzes fluorescence intensity ratios from pairs of points deemed to lie in the exponential growth region on the amplification curves for all reactions in a dilution series. This method suffers from a serious problem: The resulting ratios are highly correlated, as they involve multiple use of the raw data, for example, yielding ~ 250 E estimates from ~ 25 intensity readings. The resulting statistics for such estimates are falsely optimistic in their assessment of the estimation precision.

Results: Monte Carlo simulations confirm that the correlated pairs method yields precision estimates that are better than actual by a factor of two or more. This result is further supported by estimating E by both pairwise and C_q calibration methods for the 16 replicate datasets from the critiqued work, and then comparing the ensemble statistics for these methods.

Conclusion: Contrary to assertions in the proposing work, the pairwise method does not yield E estimates a factor of 2 more precise than estimates from C_q calibration fitting (the standard curve method). On the other hand, the statistically correct direct fit of the data to the model behind the pairwise method can yield E estimates of comparable precision. Ways in which the approach might be improved are discussed briefly.

Keywords: Amplification efficiency; Calibration; Correlated data; Data analysis; Statistical errors; Weighted least squares; qPCR.

Fig. 1

qPCR fluorescence data displayed in Fig. 2a in ref. [11]. The dilution factor is 2 for these curves, which represent the lowest 3 concentrations in the first C series. The horizontal dashed lines demarcate the exponential growth zone; this was set lower — 20-180 — for the full analysis in [11]. The RFU (relative fluorescence units) plateau values are ~ 600

Fig. 2

Fit of the growth-zone points in Fig. 1 (solid) to the model of Eq. 2. Open points are calculated values. “Error” is the estimated SE. Chisq is the sum of squared residuals, from which the estimated variance is s_y² = 794.3/7 = 113.5, giving s_y = 10.7

Fig. 3

Histogrammed E values from 4 × 10⁴ simulations of the 9-point model described in text, fitted directly to Eq. 2 and converted to differences for fitting to Eq. 3. The boxes show the results from fitting to the normal distribution, in which the counts were weighted inversely as the count (Poisson approximation)

Fig. 4

E estimates obtained analyzing the 16 6-replicate data sets from PGDW using Eqs. 2–4, and their averages (lines). The x-axis numbers represent the data sets, as A1–6, A7–12, …, H7–12, with points for Eqs. 3 and 4 displaced slightly for display purposes. The KaleidaGraph fit results include a priori SEs (Error) [14]. The post-SEs are these values × (χ²/ν)^1/2 = 0.0045, 0.0051, and 0.0047

Fig. 5

LS fits of all 96 C_q values from [11] and those obtained for 4 different C_q markers using the methods of ref. [7]. The χ² values (Chisq) are a direct measure of the precision of the data and indicate that the Cy0 estimates are best [15]

Fig. 6

Calibration-based E estimates for the 16 6-point replicate datasets from [11], from C_q values reported by PGDW and from Cy0 values obtained using methods of [7]. The lines are results from weighted LS fits; the slope is − 0.0043(7) from the present results

Fig. 7

Statistical weights for pairwise E estimates from the A1–6 dataset, displayed as a function of E. A single value at E = 1.58 has w_i = 351; all others in the outlier zone (E < 1.60 and E > 2.15) have w_i < 60. The full range of w_i is 1.3–3000