  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.
