DOPE: D-optimal pooling experimental design with application for SARS-CoV-2 screening

Objective: 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. Here, we present a novel pooling strategy that builds on the Bayesian D-optimal experimental design criterion. Materials and Methods: Our strategy, called DOPE (D-Optimal Pooling Experimental design), is built on a novel Bayesian formulation of pooling. 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 to maximize it. Results: We compare DOPE to other, commonly used pooling strategies, as well as to individual testing. DOPE dominates the other strategies as it yields lower error rates while utilizing fewer tests. We show that DOPE maintains this dominance for a variety of infection prevalence values. Discussion: DOPE has several additional advantages over common pooling strategies: 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. Conclusion: DOPE can substantially improve accuracy and throughput over current pooling strategies. Hence, DOPE can facilitate rapid testing and aid the efforts of combating COVID-19 and other future pandemics.