Harrell’s concordance (C) index is a widely used non-parametric measure of discrimination ability. However, the estimate of C depends on study-specific characteristics, such as the length of follow-up, the censoring distribution, and the population representativeness of the data. In addition to bias issues, even for simple random samples, some commonly used softwares for estimating C provide overly conservative variance estimates. Building upon previously published work, we propose a modified concordance index that measures overall discriminatory ability up to a time tau and that converges to a censoring-independent quantity. This modified C-index can be applied to interval- or right-censored event time data or to complex survey data, allowing for more meaningful comparison of concordance statistics estimated from different data sets. We derive closed-form variance for the modified C-index and for the difference between 2 correlated C indices, using Taylor linearization methods that can be easily implemented with available software. Results from our simulation studies suggest that the modified C-index and proposed variance methods will perform well in finite samples.