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https://www.nist.gov/itl/math/acmd-chalkboard-talk-optimal-decision-theory-sars-cov-2-antibody-testing

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# ACMD Chalkboard Talk: Optimal Decision Theory for SARS-CoV-2 Antibody Testing

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Paul Patrone*Applied and Computational Mathematics Division, NIST*

Tuesday, November 16, 2021, 3:00 PM EST (1:00 PM MST)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**Abstract:**The COVID-19 pandemic has highlighted the importance of antibody testing for tracking the spread of pathogens such as the SARS-CoV-2 virus. Significant resources have been devoted to the biological and manufacturing aspects of assay development, while less attention has been paid to data analysis.  

In this (virtual) chalkboard talk, I survey our recent work borrowing from optimal decision theory to address such issues.  I begin with a brief historical review of conventional methods for interpreting diagnostic data based on 80-year-old techniques for radar operation and bomber detection.  Importantly, these analyses fail to account for phenomena such as disease *prevalence when applied to serology data*.  This leads to an alternative description of epidemiological phenomena in terms of conditional probability models and suggests an optimization framework for classifying diagnostic samples.

We use this framework to derive several new results for diagnostic testing.  In particular, we demonstrate that when conditional probability models for positive and negative samples are available, it is possible to construct unbiased estimators of disease prevalence *without the need to classify samples*.  Given these estimates, we construct optimal (i.e. minimum error) classification schemes which generalize to the situation where prevalence is uncertain, leading to the notion of a third class of *holdout samples*.  Time permitting, I will discuss connections between holdout classes, constrained optimization, and measure theory.  I will also present examples of our analyses applied to real-world SARS-CoV-2 antibody assays highlighting improvement gains relative to traditional methods. 

**Bio:**Paul Patrone is a physicist and staff scientist in the Applied and Computational Mathematics Division at NIST.

**Note:**This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Mathematics and statistics

## Contacts

                -  Paul Patrone  paul.patrone@nist.gov      (301) 975-5551   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   

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