Abstract

The study of adaptive designs has received impetus over the past 20 years, mainly because of its potential in applications to clinical trials, and a large number of these designs is now available in the statistical and biomedical literature, starting from simple ones like Efrons Biased Coin Design and Zelens Play-the-Winner, to the more sophisticated ones: D_A-optimum Biased Coin designs, Doubly-Adaptive designs, ERADE , Randomly Reinforced Urns, Reinforced Doubly-Adaptive Biased Coins, etc., not forgetting covariates (Covariate-Adjusted Response-Adaptive, Covariate-Adaptive Biased Coin, Covariate-adjusted Doubly-adaptive Biased Coin designs, etc.).

A complicating factor is that nowadays adaptive experiments are in general multipurpose: they try to simultaneously achieve inferential efficiency, bias avoidance, and utilitarian or ethical gains. Another is the very nature of an adaptive design, which is a random experiment that may or may not converge to a fixed treatment allocation.

This talk does not intend to be a survey of the existing literature, rather it is an effort to highlight potentially critical points: inference after an adaptive experiment, combined versus constrained optimization, speed of convergence to a desired target, possible misuse of simulations. Each of these points will be discussed with reference to one or more specific adaptive designs.