Using Urn Models for the Design of Clinical Trials

The essential feature of controlled clinical trials is the random assignment of subjects to two or more treatment groups under investigation. The principle of randomization provides a protection against hidden biases and thus increases the validity of the trial’s findings. Another fundamental aspect of clinical trials is the incorporation into the design and/or analysis those prognostic factors (e.g. gender, age, study center) which are known or thought to affect a patient’s response to treatment. Ignoring such explanatory information may result in the trial yielding wrong conclusions, either by falsely claiming one treatment superior, or by obscuring true treatment differences. Typically, eligible subjects arrive at an experimental site sequentially and must be treated immediately. The complete randomization scheme, which, for two treatment arms, determines treatment membership by tossing a fair coin independently each time a patient arrives, reduces or eliminates different kinds of experimental bias, and also provides a basis for statistical inference (Lehmann, 1975). However, in small-sized experiments, (less than 200 patients) complete randomization may result in a severe imbalance in the final number of patients assigned to each treatment group (Lachin, 1988b). As a result, inference about treatment effect may suffer from a loss in precision. Assigning an equal number of patients to each treatment group increases the accuracy of the inference concerning no treatment difference, result-