Selecting a Biased-Coin Design

TL;DR

This paper compares various biased-coin designs for clinical trials, analyzing their balance, bias, and information loss, and introduces a Bayesian rule with favorable properties that minimizes bias with minimal imbalance.

Contribution

It extends existing biased-coin rules to include covariate balance and evaluates their properties through theoretical analysis and simulations.

Findings

Bayesian rule reduces bias with minimal imbalance.

Large-sample theory supports the properties of the rules.

Simulations confirm theoretical results across small samples.

Abstract

Biased-coin designs are used in clinical trials to allocate treatments with some randomness while maintaining approximately equal allocation. More recent rules are compared with Efron's [Biometrika 58 (1971) 403-417] biased-coin rule and extended to allow balance over covariates. The main properties are loss of information, due to imbalance, and selection bias. Theoretical results, mostly large sample, are assembled and assessed by small-sample simulations. The properties of the rules fall into three clear categories. A Bayesian rule is shown to have appealing properties; at the cost of slight imbalance, bias is virtually eliminated for large samples.