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

Benjamin Glemain (1) , Xavier de Lamballerie (2) , Marie Zins (3, 4) , Gianluca Severi (5, 6) , Mathilde Touvier (7) , Jean-François Deleuze (8) , Fabrice Carrat (1) , Pierre-Yves Ancel , Marie-Aline Charles , Gianluca Severi , Mathilde Touvier , Marie Zins , Sofiane Kab , Adeline Renuy , Stephane Le-Got , Celine Ribet , Mireille Pellicer , Emmanuel Wiernik , Marcel Goldberg , Fanny Artaud , Pascale Gerbouin-Rérolle , Mélody Enguix , Camille Laplanche , Roselyn Gomes-Rima , Lyan Hoang , Emmanuelle Correia , Alpha Amadou Barry , Nadège Senina , Julien Allegre , Fabien Szabo de Edelenyi , Nathalie Druesne-Pecollo , Younes Esseddik , Serge Hercberg , Mélanie Deschasaux , Marie-Aline Charles , Valérie Benhammou , Anass Ritmi , Laetitia Marchand , Cecile Zaros , Elodie Lordmi , Adriana Candea , Sophie de Visme , Thierry Simeon , Xavier Thierry , Bertrand Geay , Marie-Noelle Dufourg , Karen Milcent , Delphine Rahib , Nathalie Lydie , Clovis Lusivika-Nzinga , Gregory Pannetier , Nathanael Lapidus , Isabelle Goderel , Céline Dorival , Jérôme Nicol , Olivier Robineau , Cindy Lai , Liza Belhadji , Hélène Esperou , Sandrine Couffin-Cadiergues , Jean-Marie Gagliolo , Hélène Blanché , Jean-Marc Sébaoun , Jean-Christophe Beaudoin , Laetitia Gressin , Valérie Morel , Ouissam Ouili , Jean-François Deleuze , Laetitia Ninove , Stéphane Priet , Paola Mariela Saba Villarroel , Toscane Fourié , Souand Mohamed Ali , Abdenour Amroun , Morgan Seston , Nazli Ayhan , Boris Pastorino , Xavier de Lamballerie , Nathanaël Lapidus , Fabrice Carrat

1 iPLESP - Institut Pierre Louis d'Epidémiologie et de Santé Publique
2 IHU Marseille - Institut Hospitalier Universitaire Méditerranée Infection
3 Université Paris-Saclay
4 UVSQ - Université de Versailles Saint-Quentin-en-Yvelines
5 CESP - Centre de recherche en épidémiologie et santé des populations
6 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence
7 EREN [CRESS - U1153 / UMR_A 1125] - Nutritional Epidemiology Research Team | Equipe de Recherche en Epidémiologie Nutritionnelle
8 CEPH - Fondation Jean Dausset - Centre d’Etudes du Polymorphisme Humain [Paris]

The individual results of SARS-CoV-2 serological tests measured after the first pandemic wave of 2020 cannot be directly interpreted as a probability of having been infected. Plus, these results are usually returned as a binary or ternary variable, relying on predefined cut-offs. We propose a Bayesian mixture model to estimate individual infection probabilities, based on 81,797 continuous anti-spike IgG tests from Euroimmun collected in France after the first wave. This approach used serological results as a continuous variable, and was therefore not based on diagnostic cut-offs. Cumulative incidence, which is necessary to compute infection probabilities, was estimated according to age and administrative region. In France, we found that a “negative” or a “positive” test, as classified by the manufacturer, could correspond to a probability of infection as high as 61.8% or as low as 67.7%, respectively. “Indeterminate” tests encompassed probabilities of infection ranging from 10.8 to 96.6%. Our model estimated tailored individual probabilities of SARS-CoV-2 infection based on age, region, and serological result. It can be applied in other contexts, if estimates of cumulative incidence are available.

Mots clés: SARS-CoV-2; COVID-19; Bayes' theorem; Mixture model

Domaines: Sciences du Vivant [q-bio]; Statistiques [stat]

Benjamin Glemain, Xavier de Lamballerie, Marie Zins, Gianluca Severi, Mathilde Touvier, et al.. Estimating SARS-CoV-2 infection probabilities with serological data and a Bayesian mixture model. Scientific Reports, 2024, 14 (1), pp.9503. ⟨10.1038/s41598-024-60060-3⟩. ⟨hal-04561282⟩