Treatment allocation for nonlinear models in clinical trials: the logistic model

Many clinical trials have a binary outcome variable. If covariate adjustment is necessary in the analysis, the logistic-regression model is frequently used. Optimal designs for allocating treatments for this model, or for any nonlinear or heteroscedastic model, are generally unbalanced with regard to overall treatment totals and totals within strata. However, all treatment-allocation methods that have been recommended for clinical trials in the literature are designed to balance treatments within strata, either directly or asymptotically. In this paper, the efficiencies of balanced sequential allocation schemes are measured relative to sequential Ds-optimal designs for the logistic model, using as examples completed trials conducted by the Eastern Cooperative Oncology Group and systematic simulations. The results demonstrate that stratified, balanced designs are quite efficient, in general. However, complete randomization is frequently inefficient, and will occasionally result in a trial that is very inefficient.