Increased SARS-CoV-2 Testing Capacity with Pooled Saliva Samples

We analyzed feasibility of pooling saliva samples for severe acute respiratory syndrome coronavirus 2 testing and found that sensitivity decreased according to pool size: 5 samples/pool, 7.4% reduction; 10 samples/pool, 11.1%; and 20 samples/pool, 14.8%. When virus prevalence is >2.6%, pools of 5 require fewer tests; when <0.6%, pools of 20 support screening strategies.

and 400 µl extraction conditions. This equation was used, separately, for both pre-extraction saliva and post-extraction RNA pooling. Ratio in this model can be interchanged with "condition" for the model of the 1/20 PBS and water dilution data.
We found that the change in Ct value post-pooling was independent of the Ct value of the undiluted sample (Pearson's, r=-0.004; 95% CI: -0.240, 0.233), thus it was not included in the model. Confidence intervals were generated by simulating from the covariance matrix of the parameters from the fitted model using the mvrnorm function in the R package "MASS" (4), and quantile functions.
Modeling the resource-saving benefit of sample pooling for SARS-CoV-2 testing The problem of pooling can be approached modularly. We model pooling based on the expected prevalence in a test population of known size at a given time. By approaching the problem this way, we abstract from the problem of estimating prevalence in the sampled population at a given time. Nevertheless, our approach can be plugged into broader population level models with epidemiological dynamics.
If samples are independent of each other, pulled from the same well-mixed population (identically distributed), and that anyone in a test-positive pool needs to be re-tested individually, then binomial sampling theory provides the tool to compute the number of tests needed, which has been used for over half a century (5,6). The number of positive groups is = [1 − (1 − ( ) ) ]( / ), given a total test population of size that is divided into groups of size yield (N/g) groups, with a prevalence of infection in the sampled population equal to and a test sensitivity ( ), where sensitivity can be a function of group size. The total number of tests need is = ( / ) + . The R script to implement these calculations are available at https://github.com/efenichel/pooled-saliva-testing.
To calculate the total number of tests and the number of test positive groups, we assume the expected prevalence is computed with error or that any error is orthogonal to the sampling error associated with the estimates of sensitivity. Therefore, to propagate the uncertainty associated with sensitivity sampling error, we make the calculations for the number of positive groups and total tests using a single predefined, conservative cut-off value. This mimics the existence of an established protocol. Variation in the cycle thresholds used would increase the sampling uncertainty for sensitivity, and would expect the point estimate of the sensitivity, Page 3 of 7 conditional on pool size, to be a convex combination of the estimates using individual cycle thresholds.
In practice, those coordinating testing need to consider what constitutes a single, wellmixed sampled population. For example, demographic or socio-economic information may be used to group samples into distinct subpopulations prior to pooling and testing. This would be called stratifying the population. If these subpopulations have different expected prevalences, then different sized pools may be optimal for the different subpopulations. However, stratification requires population specific data that is invariant to the test itself or stronger assumptions. The possibility of embedding an adaptive pooling approach into a model of a system that brings population level data to bear is a strength of the approach.
Another consideration that the model does not directly address is selection into the sampled population. If there is selection, then the well-mixed assumption is violated. There are two reasons to be concerned about this in practice. First, if people who are more likely to test positive are also more likely to get tested when there is a binding test capacity constraint, then as the constraint is relaxed with pooling, the expected prevalence in the population is likely to fall. This is a reason why stratifying the sample based on observable features, e.g., self-assessed probability of infection prior to pooling might be important. Conversely, consider a segment of the population that tries to avoid testing and engages in high risk behaviors (i.e., people who believe COVID-19 is a hoax). These people select out of testing. If it is easier to include these people in a testing regime with greater capacity due to pooling, then expected prevalence may actually rise. This can also be addressed with stratification of the population.
Further statistical analyses were conducted in GraphPad Prism 8.0.0 as described in the text and figure legends.

Results
When pooling saliva samples, the effect on the sensitivity of detection was independent of the Ct value of the undiluted sample (Pearson's, r=-0.004; 95% CI: -0.240, 0.233), i.e. the sensitivity loss in a sample with a higher Ct value (lower viral load) was not more than that of a sample with a lower Ct value (higher viral load).

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We also evaluated the effect of pooling post-RNA extraction and pooled RNA templates extracted from undiluted saliva samples by 5 and by 10 (n=10). While we observed a similar decrease in sensitivity (pool: of 5, +2.2 Ct, 95% CI: 1.7-2.6; pool of 10, +3.1 Ct, 95% CI: 2.6-3.6) as to when pooled prior to RNA extraction, the degree to which each sample varied was less with less overall variation as compared to pre-extraction pooling (F test, pools: of 5, p = 0.061; pools of 10, p = 0.009, Appendix Figure 3).