Refining COVID-19 retrospective diagnosis with continuous serological tests: a Bayesian mixture model

COVID-19 serological tests with a “positive”, “intermediate” or “negative” result according to predefined thresholds cannot be directly interpreted as a probability of having been infected with SARS-CoV-2. Based on 81,797 continuous anti-spike tests collected in France after the first wave, a Bayesian mixture model was developed to provide a tailored infection probability for each participant. Depending on the serological value and the context (age and administrative region), a negative or a positive test could correspond to a probability of infection as high as 61.9% or as low as 68.0%, respectively. In infected individuals, the model estimated a proportion of “non-responders” of 14.5% (95% CI, 11.2-18.1%), corresponding to a sub-group of persons who exhibited a weaker serological response to SARS-CoV-2. This model allows for an individual interpretation of serological results as a probability of infection, depending on the context and without any notion of threshold. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement The SAPRIS-SERO study was funded by the ANR (Agence Nationale de la Recherche, #ANR-10-COHO-06), Fondation pour la Recherche Médicale (#20RR052-00), Inserm (Institut National de la Santé et de la Recherche Médicale, #C20-26). The sponsor and funders facilitated data acquisition but did not participate in the study design, analysis, interpretation or drafting. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The Sud-Mediterranée III ethics committee gave ethical approval for this work (approval 20.04.22.74247). I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced in the present study can be made available upon reasonable request to fabrice.carrat{at}iplesp.upmc.fr, after a consultation with the steering committee of the SAPRIS-SERO study.