Conditional Estimations for Seamless Phase II/III Clinical Trials Involving Multi-Stage Early Stopping.

To avoid unnecessary resource expenditure resulting from the sample size overestimation in seamless phase II/III designs, multi-stage early stopping may be incorporated in the phase III component. However, existing estimation methods for seamless phase II/III designs are primarily developed for two-stage settings and do not directly accommodate designs with multi-stage early stopping in phase III. In this paper, we develop a Score-statistics-based framework for point and interval estimation in this specific class of designs. The framework provides a design-specific formulation of conditional bias adjustment, conditional median-unbiased estimation, and Rao-Blackwellization for seamless phase II/III designs with multi-stage early stopping. Conditional on the trial continuing to phase III, the proposed framework targets valid and efficient estimation of the treatment effect for the selected arm and is applicable to a range of common endpoint distributions. Within this framework, we formulate and evaluate several representative conditional estimation procedures: the multiple iterations-based conditional bias-adjusted estimator (CBAE-MI), the single iteration-based conditional bias-adjusted estimator (CBAE-SI), the conditional median unbiased estimators with the unselected treatment group effects be estimated by their maximum likelihood estimators (CMUE-MLE) or set as zero (CMUE-ZERO), and the Rao-Blackwellized (RB) estimator. In addition, to properly quantify uncertainty around the point estimates, we derive confidence intervals based on CMUE-MLE, CMUE-ZERO, and RB. Through simulation under various endpoint types and parameter configurations, we recommend employing RB for point estimation and confidence interval, as it demonstrates superior robustness and conservative coverage probability across treatment selection and trial design settings.