Bayesian sample size determination using robust commensurate priors with interpretable discrepancy weights

Randomized controlled clinical trials provide the gold standard for evidence generation in relation to the effectiveness of a new treatment in medical research. Relevant information from previous studies may be desirable to incorporate in the design of a new trial, with the Bayesian paradigm providing a coherent framework to formally incorporate prior knowledge. Many established methods involve the use of a discounting factor, sometimes related to a measure of `similarity' between historical sources and the new trial. However, it is often the case that the sample size is highly nonlinear in those discounting factors. This hinders communication with subject-matter experts to elicit sensible values for borrowing strength at the trial design stage. Focusing on a sample size formula that can incorporate historical data from multiple sources, we propose a linearization technique such that the sample size changes evenly over values of the discounting factors (hereafter referred to as `weights'). Our approach leads to interpretable weights that directly represent the dissimilarity between historical and new trial data on the probability scale, and could therefore facilitate easier elicitation of expert opinion on their values. Inclusion of historical data in the design of clinical trials is not common practice. Part of the reason might be difficulty in interpretability of discrepancy parameters. We hope our work will help to bridge this gap and encourage uptake of these innovative methods. Keywords: Bayesian sample size determination; Commensurate priors; Historical borrowing; Prior aggregation; Uniform shrinkage.