  Estimation using pooled sampling has long been an area of interest in the
group testing literature. Such research has focused primarily on the assumed
use of fixed sampling plans (i), although some recent papers have suggested
alternative sequential designs that sample until a predetermined number of
positive tests (ii). One major consideration, including in the new work on
sequential plans, is the construction of debiased estimators which either
reduce or keep the mean square error from inflating. Whether, however, under
the above or other sampling designs unbiased estimation is in fact possible has
yet to be established in the literature. In this paper, we introduce a design
which samples until a fixed number of negatives (iii), and show that an
unbiased estimator exists under this model, while unbiased estimation is not
possible for either of the preceding designs (i) and (ii). We present new
estimators under the different sampling plans that are either unbiased or that
have reduced bias relative to those already in use as well as generally improve
on the mean square error. Numerical studies are done in order to compare
designs in terms of bias and mean square error under practical situations with
small and medium sample sizes.
