Abstract
In recent years, scientists have difficulties to study rare diseases by conventional methods, because the sample size needed in such studies to meet a conventional frequentist power is not adapted to the number of available patients. After systemically searching in literature and characterizing different methods used in the contest of rare diseases, we remarked that most of the proposed methods are deterministic and are globally unsatisfactory because it is difficult to correct the insufficient statistical power.More attention has been placed on Bayesian models which through a prior distribution combined with a current study enable to draw decisionsfrom a posterior distribution. Determination of the prior distribution in a Bayesian model is challenging, we will describe the process of determining the prior including the possibility of considering information from some historical controlled trials and/or data coming from other studies sufficiently close to the subject of interest.First, we describe a Bayesian model that aims to test the hypothesis of the non-inferiority trial based on the hypothesis that methotrexate is more effective than corticosteroids alone.On the other hand, our work rests on the use of the epsilon-contamination method, which is based on contaminating an a priori not entirely satisfactory by a series of distributions drawn from information on other studies sharing close conditions,treatments or even populations. Contamination is a way to include the proximity of information provided bythese studies.