Optimal response and covariate-adaptive biased-coin designs for clinical trials with continuous multivariate or longitudinal responses

Adaptive randomization of the sequential construction of optimum experimental designs is used to derive biased-coin designs for longitudinal clinical trials with continuous responses. The designs, coming from a very general rule, target pre-specified allocation proportions for the ranked treatment effects. Many of the properties of the designs are similar to those of well understood designs for univariate responses. A numerical study illustrates this similarity in a comparison of four designs for longitudinal trials. Designs for multivariate responses can likewise be found, requiring only the appropriate information matrix. Some new results in the theory of optimum experimental design for multivariate responses are presented.