followed by a division of the population arbitrarily into two halves and a pooled test is applied to each half. Every positive result leads to another bisection until we get down to the level of individuals. Exact expressions for the number of tests required seem difficult to obtain. Simulation runs were carried out with N = 256 for the bisection procedure and N = 243 for a similar trisection procedure. Typical results are shown in Table 2 although the variance is appreciable with a coefficient of variation of about 2%.

The bisection results are better than the equivalent results for the single-stage procedure but less good than the two-stage results. The trisection results apparently show it to be the least efficient of the procedures considered.

2.8 Conclusions

Of the procedures examined, the most efficient in terms of minimising the expected total number of tests is the two-stage procedure in which the

Table 2

population is divided into groups each containing K 1 individuals at the first stage and K 2 individuals at the second stage. The optimal values of K 1 and K 2 are independent of the population size N, depending only on the value of P, the incidence of the condition being tested in the population. For small P the saving obtained over the single-stage test is about 50%. It is possible that an improvement could be made using procedures with more than two stages but, in practice, two stages seem likely to be sufficient.