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Updated: Jun 27, 2025

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Estimating SARS-CoV-2 infection probabilities with serological data and a Bayesian mixture model.

Benjamin Glemain1,2, Xavier de Lamballerie3, Marie Zins4,5

  • 1Sorbonne Université, Inserm, Institut Pierre-Louis d'épidémiologie et de santé publique, Paris, France. benjamin.glemain@inserm.fr.

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Interpreting SARS-CoV-2 serological tests requires caution, as results are often binary. A new Bayesian model estimates individual infection probabilities using continuous test data, offering more accurate insights into COVID-19 exposure.

Keywords:
Bayes’ theoremCOVID-19Mixture modelSARS-CoV-2

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Immunology

Background:

  • SARS-CoV-2 serological test results are typically binary or ternary, limiting direct interpretation as infection probabilities.
  • Predefined diagnostic cut-offs can lead to misclassification and hinder accurate individual risk assessment.

Purpose of the Study:

  • To develop and validate a Bayesian mixture model for estimating individual SARS-CoV-2 infection probabilities.
  • To utilize continuous anti-spike IgG serological data, bypassing manufacturer-defined cut-offs.

Main Methods:

  • A Bayesian mixture model was applied to 81,797 continuous anti-spike IgG Euroimmun test results from France.
  • Individual infection probabilities were calculated using continuous serological data and estimated cumulative incidence stratified by age and region.

Main Results:

  • Standard "negative" or "positive" test classifications corresponded to infection probabilities as high as 61.8% and as low as 67.7%, respectively.
  • "Indeterminate" test results showed a wide range of infection probabilities, from 10.8% to 96.6%.
  • The model provided tailored individual infection probabilities based on age, region, and serological result.

Conclusions:

  • The proposed Bayesian model offers a more nuanced estimation of individual SARS-CoV-2 infection probabilities than traditional cut-off based methods.
  • This approach enhances the interpretation of serological test results, particularly when continuous data is available.
  • The model is adaptable for use in other geographical contexts with accessible cumulative incidence data.