General Methodology for Bayesian Meta-Design

In this section, we present a general methodology for Bayesian meta-design only for the log-linear random effects or fixed effecfs regression models. We assume thaf the hypotheses for noninferiorify fesfing can be formulated as follows  

The meta-frials are successful if is accepfed. As discussed in Section 2.3, 5 = 1.3 as specified in fhe FDA guidelines. 

Let = (y, 0, denote the collection of parameters for the random effects model and Pp = (y, 0) denote the collection of parameters for the fixed effects model. Following Wang and Gelfand (2002), let Jt5 (VR) and Jtp (Wp) denote the sampling priors under the random and fixed effects models, respectively. Each of fhese sampling priors captures a certain specified portion of the parameter space in achieving a certain level of performance in the Bayesian meta-design. Also, let ity ( Pjj) and ) denote the respec- 

Given the data Dy the fitting posterior distribution of imder the random effects model takes the form 

We note that the fitting priors, and ), may be improper as long 

---