A marginalized two-part model with heterogeneous variance for semicontinuous data

Semicontinuous data, characterized by a point mass at zero followed by a positive, continuous distribution, arise frequently in medical research. These data are typically analyzed using two-part mixtures that separately model the probability of incurring a positive outcome and the distribution of positive values among those who incur them. In such a conditional specification, however, standard two-part models do not provide a marginal interpretation of covariate effects on the overall population. We have previously proposed a marginalized two-part model that yields more interpretable effect estimates by parameterizing the model in terms of the marginal mean. In the original formulation, a constant variance was assumed for the positive values. We now extend this model to a more general framework by allowing non-constant variance to be explicitly modeled as a function of covariates, and incorporate this variance into two flexible distributional assumptions, log-skew-normal and generalized gamma, both of which take the log-normal distribution as a special case. Using simulation studies, we compare the performance of each of these models with respect to bias, coverage, and efficiency. We illustrate the proposed modeling framework by evaluating the effect of a behavioral weight loss intervention on health care expenditures in the Veterans Affairs health system.