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**Extra info for Quantitative Evaluation of Safety in Drug Development : Design, Analysis and Reporting**

**Sample text**

19) partial borrowing power priors. 5 Sampling Priors We now discuss how to specify the sampling priors. Under the random effects model, for the sampling prior, π(Rs) (ΨR ), ℓ = 0, 1, we take π(Rs) (ΨR ) ∝ π(Rs) ( γ 0 ) π(Rs) (θ) π(Rs) (τ2 ) π( s) ( γ 1 ). 20) ⎪⎩Δ { γ 1 = 0} for = 1, where Δ { γ1 = γ10 } denotes a degenerate distribution at γ1 = γ10, that is, P(γ1 = γ10) = 1. We note that under the random effects model, 1 − exp{− exp(γ0)} corresponds to the annualized event rate for a subject with high CV risk and 1 − exp{− exp(γ0 + θ)} corresponds to the annualized event rate for a subject with low CV risk in the control group.

5), the models for the historical data and the current data share the common parameter γ0 under the fixed effects model, while the fixed effects parameters θ and θ 0 are different in these two models. Thus, the strength of the historical data is borrowed through the common parameters γ0 and τ2 with different parameters θ and θ 0 under the random effects model, and only a single common parameter γ0 with different fixed effects parameters θ and θ 0 under the fixed effects model provides us with greater flexibility in accommodating different CV risk effects in the current and historical data.

3. Those posterior estimates will be used as the guide values of the model parameters in specifying the sampling priors. 18) where 0 ≤ a0 ≤ 1 and π(Rf0) (θ0 ) and π(Rf0) (ΨR ) are initial priors. 18), we further specify independent initial priors for (γ0, γ1, θ, θ 0, τ2) as follows: (a) a normal prior N (0, τ02 f ) is assumed for each of γ0, γ1, θ, and θ 0, where τ02 f > 0 is a prespecified hyperparameter, and (b) we specify an inverse gamma prior for d0 f 1 + 1 ⎤ exp{−d0 f 2 / τ2 }, where d > 0 and τ2, which is given by π(0f ) (τ2 ) ∝ ⎢⎡1 (τ2 ) 0f1 ⎣ ⎦⎥ d0f2 > 0 are prespecified hyperparameters.