Multi-state Models Used in Oncology Trials

Among the surrogate endpoints for overall survival (OS) in oncological trials, progression-free survival (PFS) is used as an important endpoint especially in first or second line of cancer therapies. Basic formulae for the determination of sample sizes based on time to event data can be found in the literature. Assumptions about the distributions of the survival time for OS and PFS, the accrual time and the censoring time are of key importance. Most often only uniformly distributed patient accrual and no censoring are mentioned, whereas the event time is assumed to be exponentially distributed. Considering the dependence between PFS and OS, we will investigate how a three-state model that includes states of progression/response and death can be used for a joint modelling of progression-free survival and overall survival. Sample size/power calculations are discussed for the three-state model and compared to the estimations based on exponentially distributed OS times. These sample size calculations are based on the assumption of piecewise uniformly accrual and exponentially distributed censoring time. The new three-state model approach results in a 10–30 % lower sample size and a corresponding higher power. An application to a Phase III lung cancer trial illustrates how the new approach can be successfully applied to the planning of a trial and to the monitoring of the needed events for the PFS and OS analyses.