The effect of correlation and false negatives in pool testing strategies for COVID-19

During the current COVID-19 pandemic, active testing has risen as a key component of many response strategies around the globe. Such strategies have a common denominator: the limited availability of diagnostic tests. In this context, pool testing strategies have emerged as a means to increase testing capacity. The efficiency gains obtained by using pool testing, derived from testing combined samples simultaneously, vary according to the spread of the SARS-CoV-2 virus in the population being tested. Motivated by the need for testing closed populations, such as long-term care facilities (LTCFs), where significant correlation in infections is expected, we develop a probabilistic model for settings where the test results are correlated, which we use to compute optimal pool sizes in the context of two-stage pool testing schemes. The proposed model incorporates the specificity and sensitivity of the test, which makes it possible to study the impact of these measures on both the expected number of tests required for diagnosing a population and the expected number and variance of false negatives. We use our experience implementing pool testing in LTCFs managed by SENAMA (Chile's National Service for the Elderly) to develop a simulation model of contagion dynamics inside LTCFs, which incorporates testing and quarantine policies implemented by SENAMA. We use this simulation to estimate the correlation of test results among collected samples when following SENAMA's testing guidelines. Our results show that correlation estimates are high in settings representative of LTCFs, which validates the use of the proposed model for incorporating correlation in determining optimal pool sizes for pool testing strategies. Generally, our results show that settings in which pool testing achieves efficiency gains, relative to individual testing, are likely to be found in practice. Moreover, the results show that incorporating correlation in the analysis of pool testing strategies both improves the expected efficiency and broadens the settings in which the technique is preferred over individual testing.