Power priors and their use in clinical trials

This article reviews power priors, a class of prior distributions for an unknown parameter that exploits information from results of previous, similar studies, a situation arising often in clinical trials. The article shows that, for independent and identically distributed historical data, a basic formulation of power priors (geometric priors) can be obtained as the result of a prior updating-and-combining process based on training samples of iid historical data. This formulation gives an operational justification to power priors. It also allows us to relate the discount scalar quantity controlling the influence of historical information on final inference to the size of training samples. Properties of power priors and their extension to more complex set-ups are discussed. Then several examples are provided of their use in the analysis of clinical trials data. The approach is shown to be appropriate for handling problems arising when information is combined from different studies, such as lack of exchangeability between preceding and current data, and the risk that prior information overwhelms evidence from the Study in question.