key: cord-0945195-gh1plurq
authors: Regen, Francesca; Eren, Neriman; Heuser, Isabella; Hellmann-Regen, Julian
title: A Simple Approach to Optimum Pool Size for Pooled SARS-CoV-2 Testing
date: 2020-08-28
journal: Int J Infect Dis
DOI: 10.1016/j.ijid.2020.08.063
sha: 17cf1b02c5d19bd495e5d6ca59822a3f796401c1
doc_id: 945195
cord_uid: gh1plurq

Systematic, large-scale testing of asymptomatic subjects is an important strategy in the management of the SARS-CoV-2 pandemic. In order to increase the capacity of laboratory-based molecular SARS-CoV-2 testing, it has been suggested to combine several samples and jointly measure them in a sample pool. While saving cost and labour at first sight, pooling efficiency depends on the pool size and the presently experienced prevalence of positive samples. Here we address the question of the optimum pool size at a given prevalence. We demonstrate the relation between analytical effort and pool size and delineate the effects of the target prevalence on the optimum pool size. Finally, we derive a simple-to-use formula and table that allows laboratories performing sample pooling to assess the optimum pool size at a presently experienced target prevalence rate.

table that allows laboratories performing sample pooling to assess the optimum pool size at a presently experienced target prevalence rate.

An efficient diagnostic pipeline is crucial in the management of the present SARS-CoV-2 pandemic and of great value for society returning back to normality at confidence (Koo et al., 2020) . Recently, Hogan et al. (Hogan et al., 2020) have demonstrated sample pooling in SARS-CoV2-testing to increase capacities of RT-PCR, which remains gold standard for testing. Despite compromised sensitivity, pooling may be particularly suited for testing of asymptomatic carriers with high viral load, who likely contribute most to the spreading of the disease (Wolfel et al., 2020 , Zou et al., 2020 . However, the decision to setup a pooling strategy with possibly compromising sensitivity must be rational and the benefits must be significant to justify the procedure of sample pooling. Several critical aspects such as the setting (e.g. J o u r n a l P r e -p r o o f hot spot screening), the purpose (e.g. risk assessment), availability of equipment and materials but also local statutory provisions may affect the individual decision of a lab to setup a pooling strategy.

On the other hand, the success of pooling depends on the frequency of positive samples, which also determines the optimum pool-size for a pooling strategy. Positives pools must eventually be resolved which brings about additional workload. Here we provide a simple strategy to estimate the optimum pool size for a two-staged pooling based on a known target prevalence.

All calculations, including deriving the function that defines the required tests at a given prevalence, generation of data matrices and preparation of contour plots were performed using Matlab 2019, Ver. 9.7.0, MathWorks Inc. While the mathematical relation between a target prevalence and the resulting total number of tests required to resolve all positive subjects in a two-step pooling procedure is described in the results section, the differentiation was accomplished using the Matlab "diff" function, which can be used to approximate partial derivatives.

Plotting of the results was achieved by generating grid coordinates as required using the Matlab "meshgrid" function, then generating a matrix by applying the grid coordinates to the respective equation and eventually plotting isolines using the Matlab "contour" function. Intersections of the isolines of the derivative with the x-axis were used for curve fitting using the Matlab curve fitting toolbox and the "Power" fit algorithm.

The most important factor for determining the efficiency of a pooling strategy is the net analyses required per specimen (θ), which may also be considered a proxy of associated analytical efforts and cost. While the probability Pn of a pool of size ps being negative at target prevalence (p) can be described as =

(1 − ) , the probability of a pool being positive (Pp) can be described as This simplifies as

The optimum pool size for a given frequency is defined by the local minima of the isolines in figure 1A and can be more precisely determined by the first derivative of equation 1 

Results from our analysis clearly demonstrate the relation between target prevalence rates and optimum pool sizes in a two staged pooling strategy. The power function (equation 2) derived from the relation between prevalence and optimum pool size ( figure 1D ) provides a simple tool to calculate the optimum pool size at an expected prevalence. Our results suggest that at high target prevalence rates (>0.1), sample pooling can only marginally improve testing capacities, whereas pooling at rather low target frequencies as observed by Hogan and colleagues (Hogan et al., 2020) , may substantially enhance sample throughput and thus lower the effort and cost associated with RT-PCR-based testing strategies.

Rational pooling may thus provide the basis to overcome a shortage of reagents or help with otherwise J o u r n a l P r e -p r o o f limited testing capacities, even with larger pool sizes when used in combination with sensitive assay procedures (Lohse et al.) . While sample pooling can generally increase throughput, reduce analysis time, and cost on the one hand, it may compromise sensitivity for samples with low viral loads. On the other hand, it is widely accepted that subjects with high viral loads contribute most to the spreading of the disease. This suggests pooling as a strategy towards a fast and efficient testing procedure of asymptomatic cohorts and highlights the need to adjust the pool size to an individual testing environment. While our approach can help to determine the most economical pool size at a given prevalence, there are other important aspects including but not limited to reagent availability, local regulations, sampling options and available extraction strategies that may significantly affect the decision to perform pooling in general.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This study received no external funding.

Not applicable.

The authors declare no competing interests.

J o u r n a l P r e -p r o o f

Sample Pooling as a Strategy to Detect Community Transmission of SARS-CoV-2

Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a modelling study

Pooling of samples for testing for SARS-CoV-2 in asymptomatic people

Virological assessment of hospitalized patients with COVID-2019

SARS-CoV-2 Viral Load in Upper Respiratory Specimens of Infected Patients

The relation between the estimated analyses per specimen and a pool size are given for various target prevalence rates as defined by equation 1 (isolines; A). Local minima suggest optimum pool sizes at the respective target prevalence rate (isolines; A). The first derivative of equation 1 allows precise determination of optimum pool sizes from the intersections of the isolines with the x-axis (B). Optimum pool sizes associated with a given target prevalence are summarized for select target prevalence rates (D). The association between prevalence and optimum pool size closely follows a power function = with sufficient precision (R 2 > 0,99) and a=1.24 and b = -0.466, allowing to estimate the optimum pool size by the formula = 1.24 * −0,466 .