ABSTRACT
Outcome adaptive randomization (AR) in a clinical trial uses both the assigned treatments and observed outcomes of previous patients to compute randomization probabilities for newly accrued patients. In this chapter, we will focus on two types of AR. The scientific goal of a randomized comparative trial (RCT) of two treatments is to decide whether one treatment is substantively better than the other. Fair (also called 50:50, 1:1, or coin flip) randomization in a RCT fixes the treatment assignment probabilities at .50 throughout in order to obtain data that provide unbiased estimators of the pa-
rameters used for this comparison. While fair randomization serves the needs of future patients, flipping a coin to decide a patient’s treatment looks strange to many non-statisticians, and may seem at odds with maximizing benefit to the patients in the trial and hence ethically undesirable. It also may appear to imply that the patient’s physician is unduly ignorant. Many physicians refuse to participate in trials with fair randomization because they have strong beliefs about which treatment is superior. At the other extreme is a “greedy” algorithm wherein each new patient simply is given the treatment having the currently larger empirical success rate or mean survival time. It is well known that greedy sequential decision algorithms that always choose the next action to maximize a given optimality criterion are “sticky” in that they have a non-trivial risk of getting stuck at a locally optimal action that is globally suboptimal. See, for example, Sutton and Barto [19]. In RCTs, a competitor to fair randomization is AR, which intentionally unbalances the sample sizes by interimly assigning patients to the empirically superior arm with higher probability (cf. Cornfield, Halperin and Greenhouse [7]; Berry and Eick [3]; Hu and Rosenberger [9]). For RCTs, AR provides a compromise between greedy and fairly randomized treatment assignment. For treatment assignment in a RCT with binary outcomes, Thompson [25] first conceived AR using a Bayesian framework.
