Estimation After Selection in Seamless Phase II/III Drop-the-Losers Trials with Time-to-Event Endpoints

Under a scaled squared error loss, we establish the minimaxity of the generalized Bayes estimator and provide conditions for inadmissibility of scale-equivariant estimators.</p> <p>To ensure practical utility, we extend the framework to accommodate relaxed foundational assumptions. The generalized Bayes estimator maintains its superior risk profile even when the shape parameter is unknown and estimated from data. Furthermore, the proposed estimators demonstrate robustness under model misspecification (Weibull, log-normal, piecewise exponential) and adapt to unequal shape parameters across arms.

Crucially, we expand the design for right-censored data using conditional maximum likelihood and MCMC-driven Bayesian approaches. Supported by extensive simulations, the methodology is illustrated using uncensored leukemia and right-censored lung cancer datasets.</p>