A nonparametric approach to a survival study with surrogate endpoints

A nonparametric estimator for the joint distribution of a survival time and surrogate response time, which may occur earlier during follow-up, is presented. In the absence of the surrogate response variable, the estimator reduces to the Kaplan Meier nonparametric estimator for the survival time alone. The estimator derived in this paper is done so in a particular novel way using an exchangeable process (reinforced random walks) to model individual observations. The methodology introduced in the paper is readily extended to modelling multiple state processes.