  The sample size of a clinical trial relies on information about nuisance
parameters such as the outcome variance. When no or only limited information is
available, it has been proposed to include an internal pilot study in the
design of the trial. Based on the results of the internal pilot study, the
initially planned sample size can be adjusted. In this paper, we study blinded
sample size re-estimation in the 'gold standard' design for normally
distributed outcomes. The 'gold standard' design is a three-arm clinical trial
design which includes an active and a placebo control in addition to an
experimental treatment. We compare several sample size re-estimation procedures
in a simulation study assessing operating characteristics including power and
type I error. We find that sample size re-estimation based on the popular
one-sample variance estimator results in overpowered trials. Moreover, sample
size re-estimation based on unbiased variance estimators such as the Xing-Ganju
variance estimator results in underpowered trials, as it is expected since an
overestimation of the variance and thus the sample size is in general required
for the re-estimation procedure to eventually meet the target power. Moreover,
we propose an inflation factor for the sample size re-estimation with the
Xing-Ganju variance estimator and show that this approach results in adequately
powered trials. Due to favorable features of Xing-Ganju variance estimator such
as unbiasedness and a distribution independent of the group means, the
inflation factor does not depend on the nuisance parameter and, therefore, can
be calculated prior to a trial.
