In factorial designs, patients are subject to two or more randomizations, but all take place simultaneously. As a consequence, there is no possibility that the outcome of one randomization could influence the decision to take part in another. When designing a trial in which patients may become eligible for further randomizations with respect to some aspect of their treatment, at some time after the initial randomization, some caution is needed, particularly with respect to the impact of subsequent randomizations on the outcome assessments of earlier randomizations. These issues also arise when considering patients for more than one trial. The fundamental question is, is entry into the second trial (or second randomization) more likely amongst patients allocated one arm rather than another? If the answer is yes, then one needs to consider the impact of this on the endpoints of the first trial. For example - suppose the first trial randomizes between chemotherapy and no chemotherapy and the second trial randomizes between radiotherapy and no radiotherapy. If there is a tendency for more patients allocated no chemotherapy to enter the radiotherapy trial, then there is a potential for the two arms in the first trial to differ not just by whether or not they receive chemotherapy, but also in the proportion of patients receiving radiotherapy, i.e. they would be confounded. If radiotherapy was only available, or would only be considered in the context of the trial, and if radiotherapy proves effective, a false negative could arise in your chemotherapy comparison. It is of course always important to consider what happens in the real world. Suppose in this example radiotherapy was freely available; ethical considerations will always permit the use of any additional treatment which is felt to be in the patient's best interest and so patients could receive radiotherapy in an uncontrolled manner. Is this actually any less problematic than a formal randomized comparison?
To illustrate some of the issues, we review the discussions on the design of an MRC trial in advanced colorectal cancer, CR06 , in which the intention was to evaluate two issues. The first was a specific question: which of three chemotherapy regimens is most effective? The second was a more general question: in patients who do not have progressive disease after three months of chemotherapy, should chemotherapy be given continuously until progression is noted, or should chemotherapy stop, recommencing only when progression is noted? Importantly, in both cases, the main outcome measure was survival.
There are three main design options here. The first is to randomize patients between the three chemotherapy options initially, and carry out the second randomization at three months, in the group of patients who do not have progressive disease. The second is to randomize patients with respect to both questions at the same time, as in a factorial design. The third is to conduct two completely separate trials in different groups of patients.
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