Group sequential tests for delayed responses

Group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect, a lack of an effect or concerns about patient safety. In many studies, the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond. We formulate a new form of group sequential test which gives a proper treatment of these 'pipeline' subjects; these tests can be applied even when the continued accrual of data after the decision to stop the trial is unexpected. We illustrate our methods through a series of examples. We define error spending versions of these new designs which handle unpredictable group sizes and provide an information monitoring framework that can accommodate nuisance parameters, such as an unknown response variance. By studying optimal versions of our new designs, we show how the benefits of lower expected sample size that are normally achieved by a group sequential test are reduced when there is a delay in response. The loss of efficiency for larger delays can be ameliorated by incorporating data on a correlated short-term end point, fitting a joint model for the two end points but still making inferences on the original, longer-term end point. We derive p-values and confidence intervals on termination of our new tests.