  The Bayesian expected power (BEP) has become increasingly popular in sample
size determination and assessment of the probability of success (POS) for a
future trial. The BEP takes into consideration the uncertainty around the
parameters assumed by a power analysis and is thus more robust compared to the
traditional power that assumes a single set of parameters. Current methods for
assessing BEP are often based in a parametric framework by imposing a model on
the pilot data to derive and sample from the posterior distributions of the
parameters. Implementation of the model-based approaches can be analytically
challenging and computationally costly especially for multivariate data sets;
it also runs the risk of generating misleading BEP if the model is
mis-specified. We propose an approach based on the Bayesian bootstrap technique
(BBS) to simulate future trials in the presence of individual-level pilot data,
based on which the empirical BEP can be calculated. The BBS approach is
model-free with no assumptions about the distribution of the prior data and
circumvents the analytical and computational complexity associated with
obtaining the posterior distribution of the parameters. Information from
multiple pilot studies is also straightforward to combine. We also propose the
double bootstrap (BS2), a frequentist counterpart to the BBS, that shares
similar properties and achieves the same goal as the BBS for BEP assessment.
Simulation studies and case studies are presented to demonstrate the
implementation of the BBS and BS2 techniques and to compare the BEP results
with model-based approaches.
