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We propose methods for incorporating overrunning data, either balanced or unbalanced, into the final analysis of a sequential clinical trial comparing an experimental arm with a control arm. We consider inference on the primary endpoint for which the sequential test is designed and a correlated secondary endpoint. By separating the monitoring process into arm-specific processes, we derive the sufficient statistics and show how the independent overrunning data can be combined with the trial data at stopping and thus allow the likelihood-based inference to be conducted.