Evaluation and Inference of Pool Testing Costs Using a Probabilistic Perspective

Pool Testing is a strategy introduced by Robert Dorfman in 1943 to address a common problem in pandemics: the high cost of large-scale testing. This two-phase pool test strategy consists of dividing the initial sample into smaller subsamples of equal size (pools) and conducting a combined test on the individuals within each pool. Given a positive result, all individuals in the pool are individually tested. Otherwise, all individuals in the pool will be considered healthy without further testing. Consequently, for the same sample, the number of tests (testing cost) performed is a random variable, which depends on the proportion of infected individuals and their allocation in the pools. We propose a probabilistic way to evaluate the performance of the two-phase Dorfman's pool testing, obtaining the distribution for its relative cost. We consider the prior knowledge about disease prevalence to build the prior distribution of the probability of a pool testing positive. We also obtain the sensitivity and specificity of the overall (full) pool testing procedure. The relative cost for the pool testing is evaluated for populations experiencing different prevalences, pool of different sizes, and also assuming gold-standard tests with different specificity and sensitivity. The proposed approach is applied to estimate the cost of Pool Testing on real data. We obtained the probability that the relative cost is higher than one, providing a tool to assess the risk of the adopted strategies.