  We develop a baseline-adjusted C-index to evaluate fitted Cox proportional
hazard models. This metric is particularly useful in evaluating stratified Cox
models, as well as model selection using cross validation. Our metric is able
to compare all pairs of comparable individuals in strata or cross validation
folds, as opposed to only pairs within the same stratum/folds. We demonstrate
through simulations and real data applications that the baseline adjusted
C-index is more stable and that it selects better model in high-dimensional
$L^1$ penalized Cox regression.
