SUMMARY. In this article, we analyze the coronary artery calcium (CAC) score in the Multi-Ethnic Study of Atherosclerosis (MESA), where about half of the CAC scores are zero and the rest are continuously distributed. When the observed data has a mixture distribution, two-part models can be the natural choice. With a two-part model, there are two covariate effects, with one in each part of the model. Determination of whether the two covariate effects are proportional can provide more insights into the process underlying development and progression of CAC. In this study, we model the CAC score using a semiparametric two-part model, and investigate the determination of proportionality of the covariate effects. We propose penalized maximum likelihood estimation and using thin plate splines in practical data analysis, and establish asymptotic estimation properties. We propose a step-wise hypothesis testing based approach to determine proportionality. Simulation studies suggest satisfactory finite-sample performance of the proposed approach. Analysis of the MESA data suggests that proportionality holds for all covariates except the LDL and HDL.



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