Abstract:

"From bench to bedside," a maxim of translational medical research reflects the sequential nature of the experiments involved. However, despite the sequential nature of Phase I-III trials in drug development, these trials are often planned separately, treating each trial as an independent study whose design depends on results from studies in previous phases. In recent years, adaptive designs such as seamless Phase II-III designs and adaptive randomization for testing biomarker-guided personalized therapies have attracted much interest in the pharmaceutical industry. Their advantage in using the information acquired during the course of the trial to update important design features that one lacks at the planning stage is widely recognized. The Bayesian approach is at the forefront of this development because of its "flexibility in both design and analysis" since Bayesian inference is based on the posterior distribution and therefore does not need adjustments for early stopping or adaptive randomization; see Berry et al. (2011). Acknowledging that the statistical benchmark to gain regulatory approval of a new treatment is "to get a statistically significant result at a specified type I error," Bayesian adaptive designs for Phase III trials rely on Monte Carlo simulations, under a chosen parameter configuration belonging to the null hypothesis, to adjust the rejection threshold of the Bayesian test. We show, however, that there is no guarantee that the type I error is maintained by this approach at other parameter configurations for a composite null hypothesis. Hybrid resampling is a versatile and accurate method that was originally developed for frequentist inference in group sequential designs; see Bartroff, Lai and Shih (2013, Chapter 7). After a brief review of the method, we show how it can be applied to construct valid frequentist tests and confidence intervals in Bayesian and other adaptive designs of clinical trials.

Hybrid resampling is also useful for statistical inference in other complex experiments, and we illustrate with the recent example of the Large Hadron Collider at CERN to create and study Higgs bosons. We also give a novel application of hybrid resampling to the long-standing problem of constructing valid confidence intervals following variable selection in regression models.