In recent years various schemes for allocating treatments to patients in sequential clinical trials have been proposed. These schemes are generally designed to improve efficiency and to create better balance among relevent covariates than complete randomization. All such schemes pursue the goal of balancing treatment totals, and also balancing within strata. Such a goal is consistent with optimal design theory for a homoscedastic linear model. However, it is uncertain that balanced designs are efficient for trials in which a nonlinear model is appropriate or in which the variance is not homoscedastic. Nonlinear models are almost exclusively used, for example, in cancer clinical trials in which the primary outcomes are survival data and categorical response data. We propose to study the relative efficiency of balanced schemes for common non-linear models e.g. logistic model, proportional hazards survival model, using data from the Eastern Cooperative Oncology Group as examples. We shall examine various optimality schemes for comparison with balanced schemes, and we shall develop rules for prospectively identifying trials likely to be substantially inefficient if balanced schemes are used.
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