Testing for differences in survival with delayed ascertainment

During the interim stages of most large-scale clinical trials, knowledge that 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-up used by the study to obtain information on vital status. On a two-armed study, if the process of ascertaining vital status is not the same in both treatment groups, then the standard method of testing based on the logrank statistic may not be applicable. Instead, an ad hoc modification to the logrank test, which artificially truncates follow-up prior to the time of analysis, is often used. These approaches have not been formally addressed in the 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 statistics that extends the usual class of U statistics. Asymptotic normality is derived by reformulating the statistics in terms of counting processes and employing the theory of U statistics along with martingale techniques. For early interim analyses, a numerical study indicates that the new tests can be more powerful than the current practice when differential ascertainment is present. To illustrate the potential loss of information when lagging follow-up to control for ascertainment delays, we reanalyze an AIDS clinical trial with the truncated logrank and the new statistics.