  Debiased estimation has long been an area of research in the group testing
literature. This has led to the development of several estimators with the goal
of bias minimization and, recently, an unbiased estimator based on sequential
binomial sampling. Previous research, however, has focused heavily on the
simple case where no misclassification is assumed and only one trait is to be
tested. In this paper, we consider the problem of unbiased estimation in these
broader areas, giving constructions of such estimators for several cases. We
show that, outside of the standard case addressed previously in the literature,
it is impossible to find any proper unbiased estimator, that is, an estimator
giving only values in the parameter space. This is shown to hold generally
under any binomial or multinomial sampling plans
