joss/paper.md

In devSJR/PCRedux: Quantitative Polymerase Chain Reaction (qPCR) Data Mining and Machine Learning Toolkit

title: 'PCRedux: A Quantitative PCR Machine Learning Toolkit' tags: - R - qPCR - bioinformatics - machine learning - reproducible research date: "12 May 2022" affiliations: - name: Autonomous University of Barcelona, Bellaterra, Spain index: 1 - name: Medical University of Białystok, Białystok, Poland index: 2 - name: Soilytix GmbH, Hamburg, Germany index: 3 - name: Warsaw University of Technology, Warsaw, Poland index: 4 - name: Pirogov Russian National Research Medical University, Moscow, Russia index: 5 - name: BTU Cottbus–Senftenberg, Faculty of Health Brandenburg, Senftenberg, Germany index: 6 - name: BTU Cottbus–Senftenberg, Faculty Environment and Natural Sciences, Senftenberg, Germany index: 7 authors: - name: Michał Burdukiewicz^[Co-first author] orcid: 0000-0001-8926-582X affiliation: 1, 2 - name: Andrej-Nikolai Spiess^[Co-first author] orcid: 0000-0002-9630-4724 affiliation: 3 - name: Dominik Rafacz orcid: 0000-0003-0925-1909 affiliation: 4 - name: Konstantin Blagodatskikh orcid: 0000-0002-8732-0300 affiliation: 5 - name: Stefan Rödiger^[Corresponding author] orcid: 0000-0002-1441-6512 affiliation: 6, 7 bibliography: paper.bib

Summary

qPCR (quantitative polymerase chain reaction) is indispensable in research, diagnostics and forensics, because it provides quantitative information about the amount of DNA in a sample [@pabinger_survey_2014]. The interpretation of amplification curves (ACs) is often difficult if the curve does not follow a typical sigmoidal trajectory.

PCRedux is an R package [@stats] for feature extraction and classification in the realm of explainable machine learning, which uses statistical functions to compute 90 boolean and numerical descriptors from ACs. It can also be used to determine Cq values and amplification efficiencies (E) for high-throughput analysis.

Given the lack of class-labeled qPCR data sets, PCRedux includes functions for aggregation, management and dissemination of qPCR datasets that can, but must not necessarily be, trichotomously classified into negative, positive and ambiguous curves.

Statement of need

qPCR is a widely used laboratory method for the precise detection and quantification of pathogens and gene expression. The latter has contributed significantly to the understanding of physiological and pathological processes in pharmacology, medicine and forensics. [@pabinger_survey_2014; @kok_small_2018] Although available software packages provide workflows and criteria for processing qPCR data (pre-processing of raw data, fitting of non-linear models, calculation of a threshold- or second derivative-based Cq or E, relative gene expression analysis, normalization procedures and data management), they lack functionality for machine learning. [@pabinger_survey_2014; @ruijter_evaluation_2013; @ruijter_efficiency_2021; @ramakers_assumption-free_2003].

qPCR curves must meet quality criteria for analysis and are often categorized by the user according to rather subjective criteria (e.g., sigmoidal shape, slope, noise, presence of a "hook effect") [@burdukiewicz_algorithms_2018; @spiess_system-specific_2016; @spiess_impact_2015; @hanschmann_looptag_2021_2]. While positive qPCR reactions usually exhibit a sigmoidal shape, negative ACs display a rather flat and linear trajectory (\autoref{fig:fig_1}).

So how can ACs be objectively and reproducibly assessed and automatically interpreted (e.g., as positive/negative/ambiguous or low/high quality)? For high-throughput experiments, manual evaluation is not feasible because of mental exhaustion errors or non-reproducibility from arbitrary thresholds or subjective assessments. While internal laboratory guidelines seem to partially remedy this, they are usually not standardized with other labs. [@bustin_why_2010; @taylor_ultimate_2019; @kim_experimenting_2018].

Automatically extracted features from ACs (e.g., Cq and E, slopes, change points, features of local curve segments) could provide a solid feature basis for classification by machine learning. Yet to date, no open-source software applies classical biostatistical methods for explainable machine learning on ACs. Furthermore, there are no class-labelled datasets that can be used in this context.

PCRedux is the first open-source software that can extract 90 mathematical descriptors (features) from raw ACs. The features are numerically or analytically derived, quantifiable, informative properties of scaled ACs in scalar units.

Software engineering

PCRedux (v.1.1-2, MIT license) is an R package (S3 class system). R was chosen because it provides comprehensive tools for reproducible statistical and bioinformatics analyses [@gentleman_bioconductor:_2004; @gentleman_statistical_2007; @rodiger_r_2015; @liu_r_2014; @leeper_archiving_2014]. Unit tests using the testthat package [@testthat] were used for software quality control of PCRedux.

Functions

Conceptually, we divide ACs into regions of interest (ROI) for feature calculation (@rodiger_pcredux_2022 Figure 5). Typical for qPCR, baseline, exponential/linear and plateau phases are located at the left, middle and right tail region of the curve, respectively (@rodiger_pcredux_2022 Figure 5).

PCRedux's algorithms, published by others and ourselves (qpcR [@ritz_qpcr:_2008], MBmca [@rodiger_surface_2013], chipPCR [@rodiger_chippcr:_2015]), were adapted for qPCR analysis. The PCRedux dependencies include packages for preprocessing (chipPCR, MBmca), fitting of non-linear models and calculation of Cq and E (qpcR). pcrfit_single() is the workhorse function for single ACs that generates a data.frame with 90 descriptors. All output values are of type numeric, even if boolean. Among others, we included autocorrelation analyses, (Bayesian) change-point analyses (bcp [@erdman_bcp:_2007], ecp [@james_ecp_2015]), area determinations (pracma [@pracma]), regression (multi-parametric non-linear & robust local & regression models with segmented relationships: (robustbase [@todorov_object-oriented_2009], stats [@stats], segmented [@muggeo_interval_2017]) and hook effect detection (PCRedux [@burdukiewicz_algorithms_2018]).

encu() is an extension of pcrfit_single(), where meta information such as detection chemistry and platform is included, and is suitable for large data sets. Both functions are error-proof and utilize, among others, the following descriptor-generating functions:

• earlyreg(), calculates features by regression analysis in the background region,
• head2tailratio(), compares the ratio of head and tail,
• hookregNL() and hookreg(), try to detect a hook effect [@burdukiewicz_algorithms_2018],
• mblrr(), performs a local robust regression analysis,
• winklR(), calculates the angle based on the first, and the second derivative and
• autocorrelation_test(), tests for autocorrelation.

Auxiliary preprocessing and analysis functions of the package are:

• armor(), catches errors and creates the output,
• decision_mode(), calculates the frequency of classes in a dataset,
• qPCR2fdata(), converts AC data to the fdata format for Hausdorff distance analysis [@fda.usc] and
• performeR(), performs power analyses (e.g., sensitivity, specificity, Cohen's $\kappa$) for binary classification.

Application examples in the context of machine learning can be found in @rodiger_pcredux_2022 or the current @PCRedux vignette.

Graphical User Interface:

run_PCRedux() invokes a graphical user interface (\autoref{fig:fig_2}) based on the Shiny technology [@shiny], providing features as a downstream accessible table.

Datasets and Data Labeling

PCRedux contains class-labeled ACs (n = 14360; label: negative, positive, ambiguous) from various qPCR instruments and detection methods, as determined by the majority vote of four experienced researchers (@rodiger_pcredux_2022). Class labels were derived from the humanrater2() function, which uses tReem() for shape similarity calculation [@fda.usc].

Conclusion

Manual classification of ACs is time-consuming and error-prone, especially with large data sets where a significant proportion of curves deviate from sigmoidal shape, and where the results are influenced by subjective perception. An automated system for analyzing qPCR curves offers objectification and generalization of the decision-making process.

Here, training neural networks poses a viable option. The question is what the resulting network considers relevant, especially in a diagnostic scenario. To avoid these 'black box' situations, PCRedux enables a fast and computer-assisted classification of ACs based on 90 statistically and analytically founded descriptors, aiming to improve the quality and reproducibility of qPCR data analysis.

Acknowledgments

Grateful thanks belong to the R community.

Funding

None

References

devSJR/PCRedux documentation built on Aug. 3, 2022, 1:34 p.m.