Affine analysis for quantitative PCR measurements
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RESEARCH PAPER
Affine analysis for quantitative PCR measurements Paul N. Patrone1
· Erica L. Romsos1 · Megan H. Cleveland1 · Peter M. Vallone1 · Anthony J. Kearsley1
Received: 10 July 2020 / Revised: 26 August 2020 / Accepted: 28 August 2020 © This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2020
Abstract Motivated by the current COVID-19 health crisis, we consider data analysis for quantitative polymerase chain-reaction (qPCR) measurements. We derive a theoretical result specifying the conditions under which all qPCR amplification curves (including their plateau phases) are identical up to an affine transformation, i.e. a multiplicative factor and horizontal shift. We use this result to develop a data analysis procedure for determining when an amplification curve exhibits characteristics of a true signal. The main idea behind this approach is to invoke a criterion based on constrained optimization that assesses when a measurement signal can be mapped to a master reference curve. We demonstrate that this approach: (i) can decrease the fluorescence detection threshold by up to a decade; and (ii) simultaneously improve confidence in interpretations of latecycle amplification curves. Moreover, we demonstrate that the master curve is transferable reference data that can harmonize analyses between different labs and across several years. Application to reverse-transcriptase qPCR measurements of a SARS-CoV-2 RNA construct points to the usefulness of this approach for improving confidence and reducing limits of detection in diagnostic testing of emerging diseases. Keywords qPCR · DNA detection · Measurement sensitivity · Data analysis · SARS-CoV-2
Introduction Quantitative polymerase chain-reaction measurements (qPCR) are the mainstay tool diagnosing COVID-19 [1], since they detect viral RNA up to a week before the formation of antibodies. However, preliminary studies indicate that the rate of false-negatives may be as high as 30% for SARS-CoV-2 testing [2], driven in large part by asymptomatic patients and/or those in the earliest stages of the disease [3]. Methods that can increase the sensitivity of qPCR techniques, improve confidence in measurements, and harmonize results between laboratories are therefore critical for helping to control the outbreak by providing a more accurate picture of infections. The present manuscript addresses this problem by developing a mathematical procedure that enables more robust analysis and interpretation of qPCR measurements. We first derive a new theoretical result that, under general conditions, all qPCR amplification curves (including their
Paul N. Patrone
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plateau phases) are the same up to an affine transformation. Using this, we develop a data analysis approach employing constrained optimization to determine if an amplification curve exhibits characteristics that are representative of a true signal. This decision is made by projecting data onto a master curve, which leverages informa
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