Design and monitoring of survival trials in complex scenarios

This paper proposes an approach to design and monitor survival trials accounting for complex scenarios such as delayed treatment effect, treatment dilution, and treatment crossover. These scenarios often lead to non-proportional hazards, making study design and monitoring more difficult. We demonstrate that, with event times following piecewise exponential distributions, the log-rank statistic as well as its variance-covariance structure can be easily computed, which greatly simplifies study design and monitoring. As the number of pieces in the exponential distributions can be arbitrary, this approach can handle a wide range of scenarios. Three hypothetical examples are used to demonstrate its potential use.