A unifying approach for surrogate marker validation based on Prentice's criteria.
Part of the recent literature on the evaluation of surrogate endpoints starts from a multi-trial approach which leads to a definition of validity in terms of the quality of both trial-level and individual-level association between a potential surrogate and a true endpoint, Buyse et al. These authors proposed their methodology based on the simplest cross-sectional case in which both the surrogate and the true endpoint are continuous and normally distributed. Different variations to this theme have been implemented for binary responses, times to event, combinations of binary and continuous endpoints, etc. However, a drawback of this methodology is that different settings have led to different definitions to quantify the association at the individual-level. In the longitudinal setting; Alonso et al. defined a class of canonical correlation functions that can be used to study surrogacy at the trial and individual-level. In the present work, we propose a new approach to evaluate surrogacy in the repeated measurements framework, we also show the connection between this proposal and the previous ones reported in the literature. Finally, we extend this concept to the non-normal case using the so-called 'likelihood reduction factor' (LRF) a new validation measure based on some of the Prentice's criteria. We apply the previous methodology using data from two clinical studies in psychiatry and ophthalmology.