Bivariate Prior Specification for Bayesian Decision Making in Early Phase Clinical Trials
Bayesian Go/No-Go decisions with co-primary endpoints require specifying prior distributions under the Normal-Inverse-Wishart framework; however guidance on how prior hyperparameters influence trial decisions remains limited. We propose a calibrated prior specification framework for bivariate Go/No-Go decisions. Skeptical and enthusiastic priors are calibrated so that each assigns a target probability to a clinically relevant decision region. We prove that for any prior precision $\kappa > 0$, a unique scale parameter $\lambda_0$ achieves the target calibration. Operating characteristics are evaluated across different $\kappa $ via simulation and applied to a phase~3 telitacicept lupus trial.The simulation result indicates $\kappa$ is the primary driver of prior discrimination. At $\kappa = 1$, the go rate difference between priors was 0.07; at $\kappa = 10$ it reached 0.56, with false positive rates below 0.01. Operating characteristics were robust to the degrees of freedom parameter $\nu_0$ and prior correlation $\rho_0$, supporting a default of $\nu_0 = 2$. In the lupus application, prior sensitivity was negligible at $\kappa = 1$ but at $\kappa = 10$ the enthusiastic go rate was three times the skeptical rate at small sample sizes. The framework reduces prior specification to two choices: the prior center and the prior precision $\kappa$. The identification of $\kappa$ as the dominant parameter, together with the cautious choice of $\kappa$ before the trial, motivates adaptive approaches to prior precision.