Pooling strategies for SARS-CoV-2 -- web calculator v1.0


1. Pooling algorithms to be evaluated
  • D2 --- 2 level hierarchical pools (e.g. 100:1)
  • D3 --- 3 level hierarchical pools (e.g. 100:10:1)
  • A2m --- n x n matrix with a master pool (e.g. 100:10x10:1)
Note that this calculator considers only "square" D3 and A2m algorithms. In the D3 case, this means that the master pool is of size N = n x n, and there are n intermediate pools of n samples each. In the A2m case there is a single master pool of size N = n x n, and there are n rows and n columns, for a total of 2n total intermediate pools.

It is possible that more-efficient combinations of pool sizes may exist.

2. Dilution effects for SARS-CoV-2

Here we assume a 14 day window period inside of which SARS-CoV-2 can be detected with sensitivity Se in individual specimens; that viral load increases by 1 log10 viral copies every day for the first 7 days (so if viral load is 50 copies/unit on day 1, it is 500 on day 2, etc.) and then that viral load decreases by 1 log10 viral copies every day for the last 7 days.

Further assuming that the virus is only detectable within the 14-day window (again, with sensitivity Se), a pool of size 10 (tenfold dilution) would result in non-detectability of virus on days 1 and 14 of that window period - a loss of two days out of 14, and therefore a dilution of individual assay sensitivity of 14%.

A pool size of 100 (hundredfold dilution) would result in non-detectability on days 1-2 and 13-14, a loss of four days out of 14, and a dilution of individual assay sensitivity of 29%. In general, pooling size is related to dilution of individual assay sensitivity by dilution = [log10(pooling size)/7].

In general, then, the user must set the maximum allowable dilution factor (MAD) a priori and then calculate the maximum acceptable pool size as MAPS = 10 (7 x MAD). So if


MAD is 0.1, MAPS is 5;
MAD is 0.2, MAPS is 25;
MAD is 0.3, MAPS is 125;
MAD is 0.4, MAPS is 631;

The user must enter MAPS by hand - we include no default and do not autocalculate MAPS below, because our assumptions (immediately above) for SARS-CoV-2 viral dynamics are preliminary and may change over the next weeks and months (updated: 15 April 2020). WARNING: THIS ALLOWS THE USER TO ENTER INCOMPATIBLE VALUES OF MAD & MAPS.

Finally, note that if the optimal master pool size returned by our code is smaller than the MAPS, there will be less dilution than the maximum allowable dilution.


3. Enter parameters

Parameter Input value Notes
Assay Sensitivity (Se) The sensitivity of the assay on individual samples/specimens, within the detectable window.

Se must be 0 < Se <= 1
Maximum allowable dilution The dilution effects apply in the master pool only and depend on the length of the sensitivity window, and exponential rate of SARS-CoV-2 viral load increase early in acute infection. Typically, maximum allowable dilution will be determined a priori and we multiply (1-dilution) X assay sensitivity for the total sensitivity. See section 2, above.

Maximum allowable dilution must be 0 < MAD <= 1
Maximum Acceptable Pooling Size (MAPS) Typically determined from Maximum allowable dilution, see section 2, above.

MAPS must be an integer greater than 1.
Assay Specificity (Sp) assay specificity is the probabilty an individual, truly negative specimen is correctly categorized as negative when tested individually by the assay.

Specificity must be 0 < specificity <= 1.
Prevalence of SARS-CoV-2 (p) p, the prevalence of acute SARS-CoV-2 individuals in the population being pooled.

Prevalence must be 0 < p < 1.

4. Click this button to calculate optimally efficient master pool size,
and efficiency and positive predictive value for that master pool size:


5. Results:

Algorithm Optimal master pool size Efficiency* Positive predictive value*
D2
D3
A2m

* For a given algorithm/row, efficiency and positive predictive value are both calculated for
the master pool size listed in column 2. Efficiency is measured in test kits per specimen;
individual testing has an efficiency of 1; an efficiency < 1 is better than individual testing.