  The development of statistical methods to evaluate surrogate markers is an
active area of research. In many clinical settings, the surrogate marker is not
simply a single measurement but is instead a longitudinal trajectory of
measurements over time, e.g., fasting plasma glucose measured every 6 months
for 3 years. In general, available methods developed for the single-surrogate
setting cannot accommodate a longitudinal surrogate marker. Furthermore, many
of the methods have not been developed for use with primary outcomes that are
time-to-event outcomes and/or subject to censoring. In this paper, we propose
robust methods to evaluate a longitudinal surrogate marker in a censored
time-to-event outcome setting. Specifically, we propose a method to define and
estimate the proportion of the treatment effect on a censored primary outcome
that is explained by the treatment effect on a longitudinal surrogate marker
measured up to time $t_0$. We accommodate both potential censoring of the
primary outcome and of the surrogate marker. A simulation study demonstrates
good finite-sample performance of our proposed methods. We illustrate our
procedures by examining repeated measures of fasting plasma glucose, a
surrogate marker for diabetes diagnosis, using data from the Diabetes
Prevention Program (DPP).
