Impact of copula directional specification on multi-trial evaluation of surrogate end points

Evaluation of surrogate end points using patient-level data from multiple trials is the gold standard, where multi-trial copula models are used to quantify both patient-level and trial-level surrogacy. While limited consideration has been given in the literature to copula choice (e.g., Clayton), no prior consideration has been given to direction of implementation (via survival vs. distribution functions). We demonstrate that even with the "correct" copula family, directional misspecification leads to biased estimates of patient-level and trial-level surrogacy. We illustrate with a simulation study and a reanalysis of disease-free survival as a surrogate for overall survival in early stage colon cancer.