Methods and Applications of Statistics in Clinical Trials, Volume 1: Concepts, Principles, Trials, and Designs

Chapter 9

Biased Coin Randomization

Mike D. Smith

9.1 Randomization Strategies for Overall Treatment Balance

In a “simple” or “complete” randomization (CR) scheme, subjects are allocated to treatment groups based on a fixed probability without any regard to previous allocation of subjects or level of current imbalance. In the case of equal randomization to two groups, this procedure is equivalent to tossing a coin. Because it is based on the inability to predict or guess the treatment for future patients, this procedure is free from selection bias [1], which is the bias introduced into a trial from awareness of a patient’s treatment allocation.

The CR procedure does not guarantee overall treatment balance at the end of the trial, and there is a potential during the trial for a long run of one treatment versus another. For these reasons, the CR procedure is rarely used. Avoiding imbalance at specific time points during the trial is particularly important in the implementation of adaptive designs based on interim analysis of data.

An early alternative to CR that addressed the issue of potential treatment imbalance is the nonrandom systematic design (e.g., ABBAABBAA), which is not discussed here as it contains no element of randomization.

An alternative randomization procedure that aims to limit imbalance throughout the trial is “permuted block randomization” (PBR) [2]. For a fixed number of treatments groups, fixed-sized blocks are generated that contain all possible treatment permutations. ...