Assessment of Bayesian expected power via Bayesian bootstrap.

The Bayesian expected power (BEP) has become increasingly popular in assessing the probability of success for a future trial. While the traditional power assumes a single value for the unknown effect size Δ and is thus highly dependent on the assumed value, the BEP embraces the uncertainty around Δ given the prior information and is therefore a less subjective measure for the probability of success than the traditional power especially when the prior information is not rich. 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 Δ. The model-based approach can be analytically challenging and computationally costly especially for multivariate data sets, and it also runs the risk of generating misleading BEP if the model is misspecified. We propose an approach based on the Bayesian bootstrap (BBS) technique 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 also circumvents the analytical and computational complexity associated with obtaining the posterior distribution of the Δ. Information from multiple pilot studies is also straightforward to combine. We also propose the double bootstrap technique, a frequentist counterpart to the BBS, that shares similar properties and achieves the same goal as the BBS for BEP assessment. Simulation and case studies are presented to demonstrate the implementation of the BBS technique and the double bootstrap technique and to compare the BEP results with model-based approach.