Predictively Consistent Prior Effective Sample Sizes

Determining the sample size of an experiment can be challenging, even more so when incorporating external information via a prior distribution. Such information is increasingly used to reduce the size of the control group in randomized clinical trials. Knowing the amount of prior information, expressed as an equivalent prioreffective sample size (ESS), clearly facilitates trial designs. Various methods to obtain a prior'sESShave been proposed recently. They have been justified by the fact that they give the standardESSfor one-parameter exponential families. However, despite being based on similar information-based metrics, they may lead to surprisingly differentESSfor nonconjugate settings, which complicates many designs with prior information. We show that current methods fail a basic predictive consistency criterion, which requires the expected posterior-predictiveESSfor a sample of sizeNto be the sum of the priorESSandN. Theexpected local-information-ratioESSis introduced and shown to be predictively consistent. It corrects theESSof current methods, as shown for normally distributed data with a heavy-tailed Student-t prior and exponential data with a generalized Gamma prior. Finally, two applications are discussed: the priorESSfor the control group derived from historical data and the posteriorESSfor hierarchical subgroup analyses.