Zero-inflated outcomes are commonly observed in biomedical studies. Some of such examples can be found in the NOrthern MAnhattan Study (NOMAS), an cohort study on cardiovascular diseases and associated risk factors in the Northern Manhattan community. One of the key variables of interest is atherosclerotic plaque burden. Its phenotypes (area or average number cross carotid artery segments) take non-negative values, with a point mass at zero. Quantile-based inference, an alternative of the traditional mean-based one, is able to comprehensively analyze the associations between risk factors and those phenotypes, and robust to heavy-tailed outcome distributions. However, direct quantile regression cannot handle zero-inflated outcomes. The associations between covariates and quantiles of the outcome are no longer linear as the proportion of zero's changes with covariates. Therefore, we proposed a compound quantile regression framework to flexibly accommodate such heterogeneity. We studied asymptotic properties of the proposed estimator, confirmed its accuracy in estimation by finite samples simulation study, finally applied it to the NOMAS data and obtained useful inference.