The MESA (Multi-Ethnic Study of Atherosclerosis) is an ongoing study of the prevalence, risk factors, and progression of subclinical cardiovascular disease in a multi-ethnic cohort. It provides a valuable opportunity to examine the development and progression of CAC (coronary artery calcium), which is an important risk factor for the development of coronary heart disease. In MESA, about half of the CAC scores are zero and the rest are continuously distributed. Such data has been referred to as "zero-inflated data" and may be described using two-part models. Existing two-part model studies have limitations in that they usually consider parametric models only, make the assumption of known forms of the covariate effects, and focus only on the estimation property of the models. In this article, we investigate statistical modeling of CAC in MESA. Building on existing studies, we focus on two-part models. We investigate both parametric and semiparametric, and both proportional and nonproportional models. For various models, we study their estimation as well as prediction properties. We show that, to fully describe the relationship between covariates and CAC development, the semiparametric model with nonproportional covariate effects is needed. In contrast, for the purpose of prediction, the parametric model with proportional covariate effects is sufficient. This study provides a statistical basis for describing the behaviors of CAC and insights into its biological mechanisms.