ABSTRACT
Patients arrive sequentially and are to be allocated one of K treatments. Each patient has a vector of prognostic factors, or covariates, which should be allowed for in the allocation of treatment. It is not known how many patients will receive treatment, so efficient parameter estimation is required for all sample sizes. This chapter describes the application of the methods of
optimum experimental design to such trials. The sequential construction of optimum designs leads to efficient parameter estimation, whenever the trial is stopped, but without randomization. In the absence of some randomness in treatment allocation, there is a potential for bias arising from the ability to guess the next treatment to be allocated. The chapter describes methods that can be used to provide randomness and so reduce potential bias, but with a slight loss of efficiency in parameter estimation, which is measured by the loss described in §6.3.1. Bias and loss are in opposition; designs with high loss typically have low bias, and conversely. The chapter uses the two characteristics of loss and bias to assess the proposed allocation rules.
