An alternative trial-level measure for evaluating failure-time surrogate endpoints based on prediction error

Abstract

To validate a failure-time surrogate for an established failure-time clinical endpoint such as overall survival, the meta-analytic approach is commonly used. The standard correlation approach considers two levels: the individual level, with Kendall's τ measuring the rank correlation between the endpoints, and the trial level, with the coefficient of determination R2 measuring the correlation between the treatment effects on the surrogate and on the final endpoint. However, the estimation of R2 is not robust with respect to the estimation error of the trial-specific treatment effects.The alternative proposed in this article uses a prediction error based on a measure of the weighted difference between the observed treatment effect on the final endpoint and a model-based predicted effect. The measures can be estimated by cross-validation within the meta-analytic setting or external validation on a set of trials. Several distances are presented, with varying weights, based on the standard error of the observed treatment effect and of its predicted value. A simulation study was conducted under different scenarios, varying the number and the size of the trials, Kendall's τ and R2. These measures have been applied to individual patient data from a meta-analysis of trials in advanced/recurrent gastric cancer (20 randomized trials of chemotherapy, 4069 patients).The distance-based measures appeared to be robust with respect to different values of simulation parameters in several scenarios (such as Kendall's τ, size and number of clinical trials). The absolute prediction error can be an alternative to the trial-level R2 for evaluation of candidate time-to-event surrogates. Keywords: Survival analysis, Surrogate endpoint evaluation, Bivariate models, Copula models, Cox model, Simulation studies. 2010 MSC: 00–01, 99–00