Repeated confidence intervals for a scale change in a sequential survival study

This note considers the problem of comparing the survival distributions of two treatment groups in a clinical trial where the treatment difference is measured in terms of a time-scale change. Patients enter the study sequentially and may be subject to random loss to follow-up. The survival data are reviewed periodically for early evidence of the treatment difference. An approach to constructing repeated confidence intervals for the scale-change parameter is described. These intervals provide useful information about the magnitude of the treatment difference in interim analyses. An example taken from an AIDS clinical trial is given.