“We show that if the prevalence of positive samples is greater than 30% it is never worth pooling. From 30% down to 1% pools of size 4 are close to optimal. Below 1% substantial gains can be made by pooling, especially if the samples are pooled twice. However, with large pools the sensitivity of the test will fall correspondingly and this must be taken into consideration. We derive simple expressions for the optimal pool size and for the corresponding proportion of samples tested.”
I think it may be possible to do even better than the algorithm in this paper if your 2nd round of pooling is allowed to cut across multiple pools from your first round.
This article provides a helpful look at optimal pooling strategies: https://arxiv.org/pdf/1007.4903.pdf
“We show that if the prevalence of positive samples is greater than 30% it is never worth pooling. From 30% down to 1% pools of size 4 are close to optimal. Below 1% substantial gains can be made by pooling, especially if the samples are pooled twice. However, with large pools the sensitivity of the test will fall correspondingly and this must be taken into consideration. We derive simple expressions for the optimal pool size and for the corresponding proportion of samples tested.”
I think it may be possible to do even better than the algorithm in this paper if your 2nd round of pooling is allowed to cut across multiple pools from your first round.