Approximate independent structure
EVENTS, RECRUITMENT
In stage 2, data are collected from two sets of patients namely (i) the stage 2 patients and (ii) the stage 1 patients without events prior to the interim analysis. To have independent increment structure, for each of the two sets of patients, we aim that data collected from them in stage 2 are independent of stage 1 data. Stage 2 patients are new patients recruited after the interim analysis. Therefore, their data are independent of stage 1 data if the number of stage 2 patients and either the number of events from them or calendar length of how long to follow them are set independent of stage 1 data. This is what we have proposed in Section Patients in the other set, that is, stage 1 patients without events up to the interim analysis that are followed in stage 2, contribute to both stage 1 data and stage 2 data. Furthermore, these patients are followed in stage 2 because of the selection made using stage 1 data. Consequently, following in stage 2 patients without events during the interim analysis can induce correlation between stage 1 and stage 2 data. This corresponds to the second complexity with TTE data stated in the introduction. To approximately achieve independence between data collected in stage 1 and stage 2, we will use the strategy by Jenkins et al.We have set conditions for when the interim analysis is performed, how long to follow patients recruited in stage 2 and how long to follow stage 1 patients after the interim analysis. This is a practical design to achieve approximate independent increment structure. The bias adjusted estimators we will consider are appropriate for any design where independent increment structure can be assumed. The correlation between stage 1 and stage 2 data depends on several factors such as the true hazard functions, the recruitment rate and the true log hazard ratios. In simulations, the Jenkins et al approach achieved approximate independence between stage 1 and stage 2 estimates when these factors were varied in two‐stage clinical trials with subpopulation selection.