Assessing temporal agreement between central and local progression-free survival times

In oncology clinical trials, progression-free survival (PFS), generally defined as the time from randomization until disease progression or death, has been a key endpoint to support licensing approval. In the U.S. Food and Drug Administration guidance for industry, May 2007, concerning the PFS as the primary or co-primary clinical trial endpoint, it is recommended to have tumor assessments verified by an independent review committee blinded to study treatments, especially in open-label studies. It is considered reassuring about the lack of reader-evaluation bias if treatment effect estimates from the investigators' and independent review committees' evaluations agree. The agreement between these evaluations may vary for subjects with short or long PFS, while there exist no such statistical quantities that can completely account for this temporal pattern of agreements. Therefore, in this paper, we propose a new method to assess temporal agreement between two time-to-event endpoints, while the two event times are assumed to have a positive probability of being identical. This method measures agreement in terms of the two event times being identical at a given time or both being greater than a given time. Overall scores of agreement over a period of time are also proposed. We propose a maximum likelihood estimation to infer the proposed agreement measures using empirical data, accounting for different censoring mechanisms, including reader's censoring (event from one reader dependently censored by event from the other reader). The proposed method is demonstrated to perform well in small samples via extensive simulation studies and is illustrated through a head and neck cancer trial.