Applications of Bayesian quantile regression and sample size determination.

Abstract

Bayesian statistical methods reverse the philosophy of traditional statistical practice by treating parameters as random, rather than fixed. In so doing, Bayesian methods are able to incorporate uncertainty about parameter values and offer new approaches to problems traditionally viewed through only one lens. One technique that was introduced forty years ago but has only been considered from the Bayesian perspective within the last twenty years is quantile regression (QR). Similarly, sample size determination is a staple of both introductory coursework in statistics and upper-level clinical trial design, but it has historically been presented with little to no mention of its construction under the Bayesian paradigm. With Bayesian research now rapidly building in both of these arenas, we offer two distinct applications of Bayesian QR to count data and present a Bayesian sample size determination scheme for a cost-effectiveness model.