Group Testing: A New Weapon in the Fight Against Syphilis

blog.shriphani.com

27 points·shriphani··5 comments

Why test everyone if the group is tainted? A binary search (subdividing into two groups) would seem more efficient. Perhaps they had to call everyone back in for a second sample and thought that three times would seem silly.

fegu,

That was precisely the reason. The paper mentions that they only collected enough for the group-level and subsequent exhaustive search.

The largest possible n is the total number of population, and if the expected number of infected soldiers is == 0 the largest n is also the optimal one. Since we know the percentage of infections is a lot more than 0, the largest n isn't optimal. Otherwise if 1 person is infected, you'd be back to square one and your initial test of a cocktail of your entire populations' samples was fruitless.

The second largest n one could choose is half the population by dividing into two groups. It's the most optimal n if the expected number of infected soldiers is around 1. Since we know the percentage of infections is a lot more than 1, the largest n isn't optimal. Otherwise, if 1 person in each group is infected, you'd be back to square one and your initial test of two cocktails of each half of the populations' samples was fruitless.

...etc...

At p = 0.01, the optimal n is, according to this article, around 20-25.

A O(log(n)) approach to syphilis testing by using the physical equivalent of search trees. Very interesting.

It only works well if a small percentage of the population is infected.

Really enjoyed this. Great applications to both cost reduction and privacy. I've seen pooling strategies like this for monitoring cars.

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