Boosting test-efficiency by pooled testing for SARS-CoV-2-Formula for optimal pool size

National health systems face a shortage of SARS-CoV-2 diagnostic tests. At low infection rates, pooled testing can increase testing capacity. Prior research has shown that combining samples can reduce test numbers. However, uncertainty remains about optimal pool sizes. This gap motivated the search for a formula to estimate pool sizes. The study addresses how false negative rates affect efficiency. No prior work had resolved the upper bound of missed infections. The authors propose a method to calculate efficiency gains. This paper aims to provide actionable guidance for test allocation.

The study aims to derive a formula for optimal pool sizes in SARS-CoV-2 testing. It seeks to estimate efficiency gains and missed infections at various infection rates. The motivation is to help health systems maximize test use. The authors propose a method based on PCR test characteristics. They consider false negative and false positive rates. The goal is to calculate efficiency gains per test. The study also evaluates the impact of test replicates. This approach allows for adaptive testing strategies.

The researchers used mathematical modeling to estimate pool sizes. They considered population-wide infection levels as a variable. The formula accounts for false negative and false positive rates. Efficiency gain is calculated as tested persons per test. The model includes replicates to assess missed infections. The approach assumes PCR test performance metrics. No experimental testing was conducted. The method provides a framework for optimizing test use.

At 0.1% infection rate, the optimal pool size is 34 with a gain of 15 per test. At 1% infection rate, the optimal pool size is 11 with a gain of 5.1 per test. At 10% infection rate, the optimal pool size is 4 with a gain of 1.7 per test. At 30% infection rate, pooling offers no benefit. The upper bound of missed infections is calculated for each rate. Replicates improve the estimate of missed infections. The model shows diminishing returns at higher infection rates. These results suggest test strategies can be adapted to prevalence.

The authors propose that pool sizes should be adjusted based on infection levels. They suggest that at low prevalence, pooling can increase testing capacity. The study highlights that false negative rates affect efficiency gains. The upper bound of missed infections is a key consideration. The model provides a tool for health systems to optimize test use. The findings suggest replicates can reduce missed infections. The authors emphasize that no benefit occurs at high infection rates. These conclusions are based on the mathematical model presented.