One-step validation method for surrogate endpoints using data from multiple randomized cancer clinical trials with failure-time endpoints

A surrogate endpoint can be used instead of the most relevant clinical endpoint to assess the efficiency of a new treatment. Before being used, a surrogate endpoint must be validated based on appropriate methods. Numerous validation approaches have been proposed with the most popular used in a context of meta-analysis, based on a two-step analysis strategy. For two failure-time endpoints, two association measurements are usually used, Kendall's tau at the individual level and the adjusted coefficient of determination (Rtrial,adj2) at the trial level. However, Rtrial,adj2 is not always available due to model estimation constraints. We propose a one-step validation approach based on a joint frailty model, including both individual-level and trial-level random effects. Parameters have been estimated using a semiparametric penalized marginal log-likelihood method, and various numerical integration approaches were considered. Both individual- and trial-level surrogacy were evaluated using a new definition of Kendall's tau and the coefficient of determination. Estimators' performances were evaluated using simulation studies and satisfactory results were found. The model was applied to individual patient data meta-analyses in gastric cancer to assess disease-free survival as a surrogate for overall survival, as part of the evaluation of adjuvant therapy.