Determining whether a surrogate marker can be used to replace a primary outcome in a clinical study is complex. While many statistical methods have been developed to formally evaluate a surrogate marker, they generally do not provide a way to examine potential heterogeneity in the utility of a surrogate marker. Similar to treatment eect heterogeneity, where the eect of a treatment varies based on a patient characteristic, heterogeneity in surrogacy means that the strength or utility of the surrogate marker varies based on a patient characteristic. The small number of methods that have been recently developed to examine such heterogeneity cannot accommodate censored time- to-event outcomes. Studies with a censored time-to-event outcome are typically the studies that could most benet from a surrogate marker because the follow-up time is often quite long. Thus, the development of methods for this setting is essential. In this paper, we develop a robust nonparametric approach to assess heterogeneity in the utility of a surrogate marker with respect to a baseline variable in a censored time-to- event outcome setting. In addition, we propose and evaluate a testing procedure to formally test for heterogeneity. The proposed approach can be used to examine and test for heterogeneity at a single time point or across multiple time points simultane- ously. Finite sample performance of our estimation and testing procedure are examined in a simulation study. We use our proposed method to provide new insight into the complex relationship between change in fasting plasma glucose, diabetes, and sex hor- mones using data from the Diabetes Prevention Program (DPP) study. Specically, we examine the heterogeneity of fasting plasma glucose as a surrogate for time to diabetes with respect to sex hormone binding globulin (SHBG). 2