Covariate-Adaptive Sample Size Re-estimation for Population-Standardized Historical Control Designs in Single-Arm Trials

2026-07-27

AI Summary

This study addresses estimation bias and sample size planning challenges in single-arm trials arising from baseline imbalances between enrolled participants and historical controls. The authors propose a population standardization design framework that maps historical control outcomes to the actual trial population using a prespecified balancing score. For the first time, this approach integrates a population-standardized target estimand with blinded covariate-adaptive sample size reassessment, enabling dynamic sample size adjustments based solely on accumulating baseline covariates without requiring interim outcome data from the experimental arm. The proposed algorithm combines a scenario-driven initial design, sequential updates of covariate distributions, and prespecified stopping rules to effectively accommodate population shifts while rigorously controlling Type I error. Simulations demonstrate that the method maintains target power under population drift, achieving performance close to an ideal oracle design, and successfully captures dynamic sample size adjustments across different covariate adjustment sets in an ADCS case study.

Abstract

Externally controlled single-arm trials are increasingly considered when randomized controls are infeasible, but baseline imbalance between the active-arm trial and historical controls complicates both estimation and sample size planning. We propose a population-standardized design framework in which the target estimand is defined for the actually enrolled active-arm population and historical-control outcomes are standardized to that population through a pre-specified balancing score. Building on this estimand, we develop an outcome-blinded, covariate-adaptive sample size re-estimation (SSR) procedure that updates the required sample size using only accumulating baseline covariates, without using active-arm outcomes during enrollment. The method combines an initial scenario-based design with sequential updates of the enrolled-population score distribution, standardized control parameters, and target sample size under pre-specified stopping rules. We give conditional and unconditional power interpretations and sufficient conditions for approximate type I error control under repeated blinded SSR. In simulation studies with distributional shifts between planned and true active-arm populations, fixed designs based only on planning assumptions lost power, whereas the proposed SSR maintained power near the target level and performed similarly to an oracle design. In an illustrative ADCS-based example, the proposed procedures yielded different final sample sizes across adjustment sets, reflecting evolving enrolled-population covariate profiles. These results support covariate-adaptive, outcome-blinded SSR as a practical design strategy for externally controlled single-arm trials that target population-standardized treatment effects.

Problem

• externally controlled trials
• baseline imbalance
• sample size re-estimation
• population-standardized estimand
• single-arm trials

Innovation

• covariate-adaptive
• sample size re-estimation
• population-standardized
• outcome-blinded
• historical control