Impact of Smoothing on Parameter Estimation inQuantitative DNA Amplification Experiments

Stefan Rödiger1, Andrej-Nikolai Spiess2, Michał Burdukiewicz3
1BTU Cottbus – Senftenberg, Senftenberg, Germany; 
2University Medical Center Hamburg-Eppendorf, Hamburg, Germany;
3University of Wroclaw, Wroclaw, Poland

Quantitative real-time polymerase chain reaction (qPCR) is one of the most precise DNA quantification methods. The parameters quantification cycle (Cq) and amplification efficiency (AE) are commonly calculated from distinct location indices of the amplification curve (threshold fluorescence, first- or second-derivative maxima) to quantify qPCR reactions. Consequently, a precise analysis is the requirement to quantify the copy number in samples [1]. Several smoother and filter methods for minimizing inherent noise in qPCR data have been proposed in the peer-review literature. Despite the fact that smoothing steps are so frequently employed during amplification curve analysis and generally taken for granted, the question that arises is if should we really accept to use any of these methods without paying attention to their possible implications.
The smoothers and filters we compared in our investigation are widely used to compensate for noisy data. We found no fundamental controversy in the scientific community about the smoothers and filters used in our study. All of them are thoroughly tested, peer-reviewed, and well accepted. In our study we specifically addressed the question, which of the smoothers is appropriate for amplification curve data acquired by isothermal amplification or qPCR.
Due to the lack of comprehensive models we have chosen an empirical approach in combination with amplification curve simulation to evaluate the smoother and filter functions in a testable scenario. For this purpose, we analyzed the impact of the smoother methods on real-world data from different thermo cycler equipment (low through-put and high-throughput cyclers) as well as different amplification methods. We also used in our analysis “user-controlled” noise structures based on Monte Carlo simulations.
Our results indicate that selected smoothing algorithms affect the estimation of Cq and AE considerably. The commonly employed moving average filter performed worst in all qPCR scenarios. Least bias was observed for the Savitzky-Golay smoother, Cubic Splines and Whittaker smoother. In general, we found a low sensitivity to differences in AE, whereas other smoothers like Running Mean introduced a significant AE dependent bias. We developed open source software packages to facilitate the selection of smoothing algorithms that can be incorporated in an analysis pipeline of qPCR experiments. The findings of our study were implemented in the R packages chipPCR and qpcR [2,3], freely available from “The Comprehensive R Archive Network”. We anticipate that our findings serve as guidelines for the selection of an appropriate smoothing algorithm in diagnostic qPCR applications. However, a general feasibility of qPCR data smoothing remains to be demonstrated.
[1] Pabinger and Rödiger et al., Biomolecular Detection and Quantification (2014), 1/1, 23-33. [2] Spiess AN et al., Clinical Chemistry (2015), preprint. [3] Rödiger et al. (under revision), Bioinformatics (Oxf.)

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