Rapid evaluation and calibration of Bayesian group sequential designs via conjugate-mixture semi-simulation
Bayesian group sequential designs (GSDs) extend frequentist GSDs with interpretable decision-making and external evidence borrowing, but their use is limited by the computational burden of design-stage operating-characteristic evaluation. Conventional methods simulate virtual trials with Markov chain Monte Carlo or approximate analytical posterior updates at each interim look, making joint calibration of decision thresholds and design skeletons impractical on commodity hardware. Here we introduce a semi-simulation framework with two innovations. First, finite conjugate-mixture priors replace the posterior computation for each look (``per-look'') with closed-form conjugate updates and low-dimensional numerical integration for decision-rule tail probabilities. Second, a precomputation strategy caches per-look posterior tail probabilities from a single Monte Carlo pass at the union of all candidate analysis times, and each design in the calibration grid is evaluated against the same cache by a sub-second sweep, with no further simulation cost. The framework supports posterior-probability decision rules with multiple efficacy and futility criteria under either binding or non-binding futility, and derives closed-form per-look updates for binary, continuous, count and time-to-event endpoints, with benchmarking here focused on the binary endpoint. When applied to re-design the ADRENAL trial, with up to nine analyses, the framework reproduces the operating characteristics of BATSS and adaptr within Monte Carlo error while running, per GSD, approximately $7\times$ to $16\times$ faster than adaptr at a matched budget (several hundredfold at the million-trial calibration budget) and $3{,}700\times$ to $6{,}600\times$ faster than BATSS. This brings routine Bayesian GSD calibration within computational reach for confirmatory trials.