Comparison Between Individual Testing and Sample Pooling for Whole Populations

The Demo

This interactive demonstration compares individual sample testing to sample pooling for whole population testing. The idea is that nonscientists, e.g. policy makers, can sit and play with the sliders and get a feel for which variables have the most influence on outcomes of interest, comparing individual testing to sample pooling, a method in which samples from multiple people are mixed and tested using a single test.

Usage

This demo compares individual testing with sample pooling for COVID-19. See it live here:

https://www.robertjacobson.dev/BayesTesting/BayesTesting.html

It is possible to set default values with parameters in the URL:

https://www.robertjacobson.dev/BayesTesting/BayesTesting.html?specificity=0.99&infection_rate=0.01&people_count=1500&pool_size=25

The variables available to set from the URL are as follows:

const DEFAULT_VALUES = {
    'pool_size'      : 15,
    'cost_per_test'  : 100,
    'people_count'   : 10000,
    'infection_rate' : 0.05,
    'sensitivity'    : 0.85,
    'specificity'    : 1.0,
    'select_stats'   : 'naive',
    'stats_panel'    : 'closed'
}

The Sample Pooling Testing Scheme

The sample pooling scheme pools samples from n individuals and uses a single test to test the pool. If the result is negative, the samples are assumed to be negative. If the result is positive, the individual (unpooled) samples are retested individually. (It is assumed a portion of the original individual samples are retained.) The model uses the counter-factual but simplifying assumption that the sensitivity and specificity for a pool is identical as for individual samples. It would be easy to include a feature that attenuates the sensitivity as an infected sample is increasingly diluted with larger pool sizes. Users can also account for dilution by lowering sensitivity.

Technical Notes

It includes a feature I have not seen elsewhere in the literature: it computes the optimal pool size using a closed-form formula (if we include the Lambert-W function as "closed form"). Using the optimal pool size, we easily compute the minimum number of tests possible for the modeled testing scheme.

I had to write my own Lambert-W implementation, because the only Javascript version I could find online cannot handle input less than $$e$$. The function uses the well-known Halley's method, which is just Newton's method but with one more term of the Taylor series. I use an initial guess of $$w=1$$ regardless of the value of the input. This and similar simple algorithms are easily found online. Far more sophisticated algorithms are described in the literature, but most applications are better served by one of the simple algorithms. My point is, if you are looking for a Javascript Lambert-W function, just copy&paste it from this repo.

MIT License

MIT License Copyright (c) 2020 Robert Jacobson

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The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

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