DOPE: D-Optimal Pooling Experimental design with application for SARS-CoV-2 screening

Testing individuals for the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the pathogen causing the coronavirus disease 2019 (COVID-19), is crucial for curtailing transmission chains. Moreover, rapidly testing many potentially infected individuals is often a limiting factor in controlling COVID-19 outbreaks. Hence, pooling strategies, wherein individuals are grouped and tested simultaneously, are employed. We present a novel pooling strategy that implements D-Optimal Pooling Experimental design (DOPE). DOPE defines optimal pooled tests as those maximizing the mutual information between data and infection states. We estimate said mutual information via Monte-Carlo sampling and employ a discrete optimization heuristic for maximizing it. DOPE outperforms common pooling strategies both in terms of lower error rates and fewer tests utilized. DOPE holds several additional advantages: it provides posterior distributions of the probability of infection, rather than only binary classification outcomes; it naturally incorporates prior information of infection probabilities and test error rates; and finally, it can be easily extended to include other, newly discovered information regarding COVID-19. Hence, we believe that implementation of Bayesian D-optimal experimental design holds a great promise for the efforts of combating COVID-19 and other future pandemics.