# Assessment of Bayesian Expected Power via Bayesian Bootstrap

## TL;DR

This paper introduces a model-free Bayesian bootstrap method to estimate Bayesian expected power for future trials, offering a computationally efficient and robust alternative to traditional model-based approaches, with demonstrated effectiveness through simulations and case studies.

## Contribution

The paper proposes a Bayesian bootstrap approach for BEP estimation that avoids model assumptions and simplifies computation, also introducing a frequentist double bootstrap method.

## Key findings

- BBS provides accurate BEP estimates comparable to model-based methods.
- BBS is computationally simpler and more robust to model misspecification.
- Double bootstrap (BS2) offers a frequentist alternative with similar properties.

## Abstract

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.