Option 1 Randomize patients between the three chemotherapy options initially and carry out the second randomization at three months

This option follows the clinical course of events most closely, and ensures that only those patients to whom the question is relevant are randomized. The 'stop or continue' question was relevant to all the chemotherapy regimens, and any difference in survival in the two arms was not expected to differ across the chemotherapy arms (i.e. no interaction between chemotherapy regimen and duration was anticipated). Thus there appear no obstacles to the planned analysis of survival time (measured from the date of the second randomization) according to stop or continue. In fact this is generally true of the last randomization in any trial involving multiple randomizations. The potential problems are generally limited to the interpretation of the earlier randomizations. Here, entry to the second randomization would depend upon response to the initial chemotherapy regimen. As response rates associated with the different regimens might well vary, the proportion of patients in each chemotherapy arm who proceed to the second randomization could also vary. Even if response rates did not vary across the three chemotherapy arms, patients' willingness to be randomized might, particularly if one regimen was found to be more toxic or inconvenient than the others, and the prospect of being randomized to (potentially) continue did not appeal. To assess whether differences across the chemotherapy arms in the proportion of patients being randomized to stop or continue causes any problems in the interpretation of the comparison of survival by chemotherapy arms, we need to consider a number of'what if's.

The first, and most straightforward, scenario is to assume that there is no difference in survival according to stopping versus continuing. Here, there is no concern about the impact of the second randomization on the first. However, if continuing does indeed improve survival, there is a potential impact; to consider the degree, one needs to consider what happens to patients who do not have progressive disease at three months in practice, out of the trial. If they routinely stop treatment, then randomizing introduces an inequality in the proportion of patients continuing treatment in the trial and this will be highest in the chemotherapy arm with the best response rate, hence the survival of this whole group of patients will be further improved, compared with the other chemotherapy arms. It may not, however, be possible to determine whether the improvement is due to the initial chemotherapy regimen or its duration or both. If on the other hand patients without progressive disease routinely continue treatment out of the trial, then the proportion of patients continuing treatment in the trial will still be highest on the arm with the best response rate, but the absolute difference in the proportions continuing will have been reduced by the randomization. Consequently, the impact of the second randomization will be less.

This may seem a serious limitation to this design. However, it is possible to perform numerical sensitivity analyses, (see Box 4.5) to attempt to determine the impact that a range of differences in the proportion of patients being randomized in the three arms could have on the survival comparison, under the assumption that there is a survival difference according to stop or continue (the size of this difference could also vary, but it would be reasonable to take the size anticipated in the trial design).

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