Design and sample size estimation in clinical trials with clustered survival times as the primary endpoint

Many clinical trials involve the collection of data on the time to occurrence of the same type of multiple events within sample units, in which ordering of events is arbitrary and times are usually correlated. To design a clinical trial with this type of clustered survival times as the primary endpoint, estimating the number of subjects (sampling units) required for a given power to detect a specified treatment difference is an important issue. In this paper we derive a sample size formula for clustered survival data via Lee, Wei and Amato's marginal model. It can be easily used to plan a clinical trial in which clustered survival times are of primary interest. Simulation studies demonstrate that the formula works very well. We also discuss and compare cluster survival time design and single survival time design (for example, time to the first event) in different scenarios.