Inference following biased coin designs in clinical trials.

Abstract

Randomization schemes for two-treatment clinical trials are studied. Theoretical expressions for the power are derived under both complete randomization and Efron’s biased coin design for normal and binary responses. The better the scheme is at balancing the numbers of patients across treatments, the higher the power is. Efron’s biased coin design is more powerful than complete randomization. Normal approximations to the powers are obtained. The power of the adjustable biased coin design is also investigated by simulation. Covariate-adaptive randomization schemes are analysed when either global or marginal balance across cells is sought. By considering a fixed-effects linear model for normal treatment responses with several covariates, an analysis of covariance t test is carried out. Its power is simulated for global and marginal balance, both in the absence and in the presence of interactions between the covariates. Global balancing covariate-adaptive schemes are more efficient when there are interactions between the covariates. Restricted randomization schemes for more than two treatments are then considered. Their asymptotic properties are provided. An adjustable biased coin design is introduced for which assignments are based on the imbalance across treatments. The finitesample properties of the imbalance under these randomization schemes are studied by simulation. Assuming normal treatment responses, the power of the test for treatment differences is also obtained and is highest for the new design. Imbalance properties of complete randomization and centre-stratified permuted block randomization for several treatments are investigated. It is assumed that the patient recruitment process follows a Poisson-gamma model. When the number of centres is large, the imbalance for both schemes is approximately multivariate normal. The power of a test for treatment differences is simulated for normal responses. The loss of power can be compensated for by a small increase in sample size.