Testing for differences in survival with delayed ascertainment

During the interim stages of most large-scale clinical trials, knowledge th at a patient is alive or dead is usually not up-to-date. This is due to the pattern of patient visits to hospitals as well as the administrative set-u p used by the study to obtain information on vital status. On a two-armed s tudy, if the process of ascertaining vital status is not the same in both t reatment groups, then the standard method of testing based on the logrank s tatistic may not be applicable. Instead, an ad hoc modification to the logr ank test, which artificially truncates follow-up prior to the time of analy sis, is often used. These approaches have not been formally addressed in th e literature. In the early stages of a clinical trial, severe bias or loss of power may result. For this situation, we propose a class of test statist ics that extends the usual class of U statistics. Asymptotic normality is d erived by reformulating the statistics in terms of counting processes and e mploying the theory of U statistics along with martingale techniques. For e arly interim analyses, a numerical study indicates that the new tests can b e more powerful than the current practice when differential ascertainment i s present. To illustrate the potential loss of information when lagging fol low-up to control for ascertainment delays, we reanalyze an AIDS clinical t rial with the truncated logrank and the new statistics.