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

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

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International audience. 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.

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