  Prior information is often incorporated informally when planning a clinical
trial. Here, we present an approach on how to incorporate prior information,
such as data from historical clinical trials, into the nuisance parameter based
sample size re-estimation in a design with an internal pilot study. We focus on
trials with continuous endpoints in which the outcome variance is the nuisance
parameter. For planning and analyzing the trial frequentist methods are
considered. Moreover, the external information on the variance is summarized by
the Bayesian meta-analytic-predictive (MAP) approach. To incorporate external
information into the sample size re-estimation, we propose to update the MAP
prior based on the results of the internal pilot study and to re-estimate the
sample size using an estimator from the posterior. By means of a simulation
study, we compare the operating characteristics such as power and sample size
distribution of the proposed procedure with the traditional sample size
re-estimation approach which uses the pooled variance estimator. The simulation
study shows that, if no prior-data conflict is present, incorporating external
information into the sample size re-estimation improves the operating
characteristics compared to the traditional approach. In the case of a
prior-data conflict, that is when the variance of the ongoing clinical trial is
unequal to the prior location, the performance of the traditional sample size
re-estimation procedure is in general superior, even when the prior information
is robustified. When considering to include prior information in sample size
re-estimation, the potential gains should be balanced against the risks.
