THE EFFECT OF INCOMPLETE KNOWLEDGE OF PARAMETER VALUES ON SINGLE-STAGE AND MULTIPLE-STAGE DESIGNS FOR LOGISTIC-REGRESSION

We consider the design of single- and multiple-stage dose-response tri als in which the probability of response is a logistic function of the dose. Knowledge of the parameters of the logistic at the time of plan ning the trial is represented by a Gaussian prior distribution. Method s are presented for determining a design that approximately optimizes a measure of the accuracy of estimation averaged over the prior distri bution. Changes in design due to uncertainty of parameter values are d escribed as well as the changes in sample size required to produce a s pecified precision. In multiple-stage trials, the initial stage is pla nned as if it were the only stage. For succeeding stages, the initial Gaussian prior distribution is updated using outcomes at the previous stages. At each such stage, the design optimizes a chosen criterion av eraged over the updated prior distribution. The effectiveness of this methodology is evaluated by comparing the operating characteristics of two-stage designs with those of single-stage designs.