Quantifying the association between progression-free survival and overall survival in oncology trials using Kendall's τ.

This paper considers methods for estimating the association between progression-free and overall survival in oncology trials. Copula-based, nonparametric, and illness-death model-based methods are reviewed. In addition, the approach based on an underlying illness-death model is generalized to allow general parametric models. The performance of these methods, in terms of bias and efficiency, is investigated through simulation and also illustrated using data from a clinical trial of treatments for colon cancer. The simulations suggest that the illness-death model-based method provides good estimates of Kendall's τ across several scenarios. In some situations, copula-based methods perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios, which might realistically reflect an oncology trial, but the use of copula models in practice is questionable.