  We consider conditional estimation in two-stage sample size adjustable
designs and the following bias. More specifically, we consider a design which
permits raising the sample size when interim results look rather promising,
and, which keeps the originally planned sample size when results look very
promising. The estimation procedures reported comprise the unconditional
maximum likelihood, the conditionally unbiased Rao-Blackwell estimator, the
conditional median unbiased estimator, and the conditional maximum likelihood
with and without bias correction. We compare these estimators based on
analytical results and by a simulation study. We show in a real clinical trial
setting how they can be applied.
