Designing and Analyzing Clinical Trials Which Allow Institutions to Randomize Patients to a Subset of the Treatments under Study

When patients have been randomized between different sets of treatments the treatment groups are not strictly comparable. However, if one can assume that biases which are introduced affect the outcome additively, then one can compare treatments across these institutional options. This is illustrated for dichotomous response data and censored survival data. We show how the sample size must be increased to allow for this analysis and how the randomization should be weighted to obtain the best power. These results have application to simultaneous trials by different cooperative groups which have one or more common treatment arms.