Bayesian sample size re-estimation using power priors

Abstract

The sample size of a randomized controlled trial is typically chosen in order for frequentist operational characteristics to be retained. For normally distributed outcomes, an assumption for the variance needs to be made which is usually based on limited prior information. Especially in the case of small populations, the prior information might consist of only one small pilot study. A Bayesian approach formalizes the aggregation of prior information on the variance with newly collected data. The uncertainty surrounding prior estimates can be appropriately modelled by means of prior distributions. Furthermore, within the Bayesian paradigm, quantities such as the probability of a conclusive trial are directly calculated. However, if the postulated prior is not in accordance with the true variance, such calculations are not trustworthy. In this work we adapt previously suggested methodology to facilitate sample size re-estimation. In addition, we suggest the employment of power priors in order for operational characteristics to be controlled.