Efficient sample pooling strategies for COVID-19 data gathering

Istvan Szapudi

To measure the infection rate in a particular age bracket, samples should be pooled based on the results of Table 1 . For final results, the a full maximum likelihood analysis of the data is recommended. If there is no reasonable estimate of the infection rate is available to guide the design of the pooled survey, one case start with large pool, i.e. n = 64. If after N tests, all measurements are positive, it means that the infection rate is too large for this pool. If N = N + , the most likely value for q = 0, therefore Eq. 5 cannot be used to estimate confidence intervals. In that case the likelihood function is (1 − q n ) N , and one has to integrate it directly to obtain a confidence interval for q. This can be done numerically, as an example, assuming that 10 measurements produced positive results with n = 64 sampling, there is a 94% chance that q ≤ 0.9, i.e. one should try n = 16 next. Thus a simple strategy would be to determine the optimal pooling rate with preliminary measurements of higher pooling rate than necessary, and design the survey with the closest rate found in Table 1 . Note also that when the rates are low, individuals can be pinpointed with a binary search with log n extra measurements, but when the infection rate is high, individual measurements are more efficient (5) . Note that realistic protocols realising the idea will have false positives and negatives. These should be calibrated and taken into account when an actual measurement is translated into IFRs. These issues are straightforward fold into the likelihood function in a forward Bayesian analysis, as proposed here. On the other hand, the conclusions are robust enough to be useful for survey design.