The relative concentration index is a widely used measure for assessing relative differences in health across all socioeconomic population groups. We extend its usage to individual-level data collected through complex surveys by deriving its variance using the Taylor linearization (TL) method. Two existing plug-in variance estimators that only require grouped data are also compared. We discuss sources of uncertainty that each variance estimator considers and present simulation studies to compare the performance of the three estimators under various sampling designs. The proposed TL variance estimator consistently produces valid results; however, it requires the access to individual-level data. Both plug-in variance estimators are biased because of failure to account for certain error sources. However, when only grouped data is available, one of the plug-in estimators can be valid as long as the socioeconomic groups are treated equally sized, a commonly used analytic strategy to emphasize group's instead of individual's burden of disease in health disparity assessment. We illustrate the three variance estimators by applying them to assessing socioeconomic disparities in child and adolescent obesity using complex survey sampled drawn from the National Health and Nutrition Examination Survey.