A Multi-State Model for Designing Clinical Trials for Testing Overall Survival Allowing for Crossover after Progression

In designing a clinical trial for comparing two or more treatments with respect to overall survival (OS), a proportional hazards assumption is commonly made. However, in many cancer clinical trials, patients pass through various disease states prior to death and because of this may receive treatments other than originally assigned. For example, patients may crossover from the control treatment to the experimental treatment at progression. Even without crossover, the survival pattern after progression may be very different than the pattern prior to progression. The proportional hazards assumption will not hold in these situations and the design power calculated on this assumption will not be correct. In this article, we describe a simple and intuitive multi-state model allowing for progression, death before progression, post-progression survival, and crossover after progression and apply this model to the design of clinical trials for comparing the OS of two treatments. For given values of the parameters of the multi-state model, we simulate the required number of deaths to achieve a specified power and the distribution of time required to achieve the requisite number of deaths. The results may be quite different from those derived using the usual PH assumption. Supplementary materials for this article are available online.