  The primary benefit of identifying a valid surrogate marker is the ability to
use it in a future trial to test for a treatment effect with shorter follow-up
time or less cost. However, previous work has demonstrated potential
heterogeneity in the utility of a surrogate marker. When such heterogeneity
exists, existing methods that use the surrogate to test for a treatment effect
while ignoring this heterogeneity may lead to inaccurate conclusions about the
treatment effect, particularly when the patient population in the new study has
a different mix of characteristics than the study used to evaluate the utility
of the surrogate marker. In this paper, we develop a novel test for a treatment
effect using surrogate marker information that accounts for heterogeneity in
the utility of the surrogate. We compare our testing procedure to a test that
uses primary outcome information (gold standard) and a test that uses surrogate
marker information, but ignores heterogeneity. We demonstrate the validity of
our approach and derive the asymptotic properties of our estimator and variance
estimates. Simulation studies examine the finite sample properties of our
testing procedure and demonstrate when our proposed approach can outperform the
testing approach that ignores heterogeneity. We illustrate our methods using
data from an AIDS clinical trial to test for a treatment effect using CD4 count
as a surrogate marker for RNA.
