[Paper Review] Boosting test-efficiency by pooled testing strategies for SARS-CoV-2

Ricardó A. Hanel, Stefan Thurner|IIASA PURE (International Institute of Applied Systems Analysis)|Mar 22, 2020

SARS-CoV-2 detection and testing30 citations

TL;DR

The paper develops a formulaic framework to optimize pooled testing for SARS-CoV-2, deriving optimal pool sizes, expected efficiency gains, and bounds on missed infections as a function of population infection level and test error rates; it discusses replicates and provides an Austria example.

ABSTRACT

In the current COVID19 crisis many national healthcare systems are confronted with an acute shortage of tests for confirming SARS-CoV-2 infections. For low overall infection levels in the population, pooling of samples can drastically amplify the testing efficiency. Here we present a formula to estimate the optimal pooling size, the efficiency gain (tested persons per test), and the expected upper bound of missed infections in the pooled testing, all as a function of the populationwide infection levels and the false negative/positive rates of the currently used PCR tests. Assuming an infection level of 0.1 % and a false negative rate of 2 %, the optimal pool size is about 32, the efficiency gain is about 15 tested persons per test. For an infection level of 1 % the optimal pool size is 11, the efficiency gain is 5.1 tested persons per test. For an infection level of 10 % the optimal pool size reduces to about 4, the efficiency gain is about 1.7 tested persons per test. For infection levels of 30 % and higher there is no more benefit from pooling. To see to what extent replicates of the pooled tests improve the estimate of the maximal number of missed infections, we present all results for 1, 3, and 5 replicates.

Motivation & Objective

• Motivate pooling to increase testing throughput under limited test availability.
• Derive a mathematical framework to compute optimal pool size, tested persons per test (PPT), and upper bounds on missed infections (FNPT).
• Assess how replicates affect false negatives and efficiency across infection levels.
• Provide practical guidance and an illustrative example for Austria.

Proposed method

• Model assumes infection fraction lambda in the population.
• Pool samples into groups of size omega and test the pooled sample.
• Introduce false positive rate gamma_plus and false negative rate gamma_minus in the pooled test.
• Use r replicates and a majority rule to declare pool positive.
• If pool is positive, test each individual in the group separately.
• Compute P_plus, the probability a pooled test is positive.
• Compute q, the expected number of tests per person, and PPT = 1/q.
• Define FNPT as the upper bound on missed infections per tested person using the majority rule with replicates.
• Derive gamma_minus^* as the binomial majority probability and express FNPT via p, gamma_minus, and gamma_minus^*.
• Note that results depend on infection level, test error rates, pool size, and replicates.

Experimental results

Research questions

• RQ1 What is the optimal pool size omega_opt as a function of population infection level lambda and test error rates (gamma_plus, gamma_minus)?
• RQ2 How much efficiency gain (PPT) can pooled testing achieve under different infection levels and replicates?
• RQ3 What is the upper bound on missed infections (FNPT) for pooled testing and how does it depend on r (replicates) and gamma_minus?
• RQ4 Do multiple replicates meaningfully improve FNPT and PPT, and under what conditions?

Key findings

• Optimal pool size decreases as population infection level increases (e.g., ~32 at 0.1%, 11 at 1%, 4 at 10%, ~3–4 up to 29% before pooling loses benefit).
• Efficiency gains (PPT) are high at low infection levels (≈15 PPT at 0.1%, ≈5.1 PPT at 1%, ≈1.7 PPT at 10%), diminishing to near 1 as infection rises above 30%.
• Replicates reduce FNPT, but overall PPT declines with more replicates (more replicates yield about 4.3 PPT in the presented scenario).
• Taking more than one replicate is not clearly warranted across infection levels; single replication suffices for many practical screening uses.
• An Austria example (≈10 million population) suggests optimal pool size ≈32 at 0.1% infection and ≈11 at 1% infection, with an expected gain of about a factor of 10 using one replicate.
• FNPT increases with gamma_minus and is only modestly improved by replicates; worst-case missed infections remain bounded (e.g., at 0.1% infection, about 1 in 800, or 0.13%, may be missed).