Guarantees for Comprehensive Simulation Assessment of Statistical Methods

Abstract: Simulation can evaluate a statistical method for properties such as Type I Error, FDR, or bias on a grid of hypothesized parameter values. But what about the gaps between the grid-points? Continuous Simulation Extension (CSE) is a proof-by-simulation framework which can supplement simulations with (1) confidence bands valid over regions of parameter space or (2) calibration of rejection thresholds to provide rigorous proof of strong Type I Error control. CSE extends simulation estimates at grid-points into bounds over nearby space using a model shift bound related to the Renyi divergence, which we analyze for models in exponential family or canonical GLM form. CSE can work with adaptive sampling, nuisance parameters, administrative censoring, multiple arms, multiple testing, Bayesian randomization, Bayesian decision-making, and inference algorithms of arbitrary complexity. As a case study, we calibrate for strong Type I Error control a Phase II/III Bayesian selection design with 4 unknown statistical parameters. Potential applications include calibration of new statistical procedures or streamlining regulatory review of adaptive trial designs. Our open-source software implementation imprint is available athttps://github.com/Confirm-Solutions/imprint