Modelling of overall survival by an association between progression-free and post-progression survival using a conditional distribution

Abstract

In oncology, overall survival (OS) is the optimal endpoint for measuring the clinical benefit. However, and contrary to progression-free survival (PFS) which represents a potential surrogate endpoint of OS in clinical trials, OS often requires a long follow-up where the effect of the studied treatment may be diluted by subsequent therapies. In the literature, the relationship between PFS and OS was investigated more analytically than theoretically. We propose a new statistical modelling for OS based on the two survival times: PFS and post-progression survival (PPS) which we assumed to be linked using a conditional exponential distribution. This model allows us to test the existence of an association between PFS and PPS to better understand the process of improvement or decrement of OS. We found a closed form of the correlation coefficient between PFS and both PPS and OS. We expressed them as simple formulas in function of model parameters. One of the model parameters proved to be a correlation indicator between these survival times. We also defined the likelihood of the model in order to use the maximum likelihood estimator to estimate the model parameters from Phase III randomized clinical trial data, involving patients with locally advanced non-small cell lung cancer. The results showed a significant link between PFS and PPS and a strong association between improvements in PFS and OS.

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

“…Multi-state modeling approaches provide a useful framework for design and analysis when there are potentially intermediate disease states (e.g., a progressed state) experienced prior to death (Andersen et al (2002); Putter et al (2007); Farewell and Tom (2014)). These models have been applied, implicitly or explicitly, to the situation we are considering in this paper, but not generally as a formal design tool (Broglio and Berry (2009); Fleischer et al (2009); Dejardin et al (2010); Redman et al (2013); Zhang et al (2013); Belkacemi et al (2014); Jönsson et al (2014)). …”