Title: Kendalls tau for survival endpoints in meta-analysis: A general definition and a conditional copula approach
Authors: Takeshi Emura - Chang Gung University (Taiwan) [presenting]
Virginie Rondeau - University of Bordeaux INSERM (France)
Sofeu Casimir - University of Bordeaux (France)
Abstract: Measuring dependence between survival endpoints is an essential process to understand the effect of treatments in clinical trials. In particular, an individual-patient data (IPD) meta-analysis for validating a surrogate endpoint requires the estimation of individual-level dependence between the surrogate endpoint and the true endpoint. Copula models and frailty models have been suggested as promising tools to compute Kendall's tau between the surrogate endpoint and the true endpoint. However, these model-based approaches for computing Kendall's tau seem to impose a simplifying assumption: That is, Kendall's tau does not depend on treatment arms. We propose a general definition of Kendall's tau that allows different values of tau across different treatment arms. We argue that the simplifying assumption in the existing models is questionable for measuring dependence between progression-free survival and overall survival. Motivated by these findings, we propose a frailty-conditional copula model for the IDP meta-analysis with two survival endpoints. We examine the performance of the proposed methods via simulations. The proposed method is implemented in an R package joint.Cox available in CRAN.