ABSTRACT
Originally introduced by Efron [24] in the context of sequential trials for comparing two treatments, Biased Coin Designs (BCDs) represent a fundamental device to provide a suitable tradeoff between randomization and balance. Indeed, randomization represents a methodological cornerstone in the statistical
theory, because it neutralizes several forms of bias that could compromise the inferential conclusions, also providing a fundamental requirement of impartiality and a solid basis for inferential methodologies. On the other hand, if the main purpose of the trial is accurate inference without ethical demands on the subject’s health, balance represents another fundamental requirement, since in many circumstances it optimizes inference (in terms of both estimation and testing) about the treatment effects. The demand for balance is particularly cogent for phase III trials, where the experiments evolve sequentially without knowing in advance the total sample size, so that keeping a reasonable degree of balance at each step, even for small or moderate samples, is crucial for stopping the experiment at any time under an excellent inferential setting.
