  Given the long follow-up periods that are often required for treatment or
intervention studies, the potential to use surrogate markers to decrease the
required follow-up time is a very attractive goal. However, previous studies
have shown that using inadequate markers or making inappropriate assumptions
about the relationship between the primary outcome and surrogate marker can
lead to inaccurate conclusions regarding the treatment effect. Currently
available methods for identifying and validating surrogate markers tend to rely
on restrictive model assumptions and/or focus on uncensored outcomes. The
ability to use such methods in practice when the primary outcome of interest is
a time-to-event outcome is difficult due to censoring and missing surrogate
information among those who experience the primary outcome before surrogate
marker measurement. In this paper, we propose a novel definition of the
proportion of treatment effect explained by surrogate information collected up
to a specified time in the setting of a time-to-event primary outcome. Our
proposed approach accommodates a setting where individuals may experience the
primary outcome before the surrogate marker is measured. We propose a robust
nonparametric procedure to estimate the defined quantity using censored data
and use a perturbation-resampling procedure for variance estimation. Simulation
studies demonstrate that the proposed procedures perform well in finite
samples. We illustrate the proposed procedures by investigating two potential
surrogate markers for diabetes using data from the Diabetes Prevention Program.
