Determination of proportionality in two-part models and analysis of Multi-Ethnic Study of Atherosclerosis (MESA)

In MESA (Multi-Ethnic Study of Atherosclerosis), it is of interest to model the development and progression of CAC (coronary artery calcium). With about half of the CAC scores equal to zero and the rest continuously distributed, semiparametric two-part models are needed. Our main interest lies in determining the (partial) proportionality between the two covariate effects in two-part models. Such an investigation can provide important information on the mechanisms underlying CAC development. We propose a novel approach, which consists of penalized maximum likelihood estimation and a step-wise hypothesis testing procedure to determine proportionality. Simulation shows satisfactory performance of the proposed approach. Analysis of MESA suggests that proportionality holds for all covariates except LDL and HDL.