Marginal Inference for Positive Continuous Outcomes with a Point Mass at Zero

Positive continuous outcomes with a point mass at zero, usually referred to as semi-continuous out- comes, are prevalent in biomedical research. Two-part models are currently the preferred method to analyze this type of data. However, the two-part models lead to a conditional interpretation of the regression coefficients (i.e., conditional that the observed value is non-zero) which often does not answer the main question of a research investigation. To model the point mass at zero and to provide marginalized covariate effect estimates, marginalized two-part models have been recently developed but only for outcomes with lognormal and log skew normal distributions. Moreover, missing data can further complicate the analysis of these outcomes. Methods for semi-continuous data with missingness have not yet been explored in the context of marginalized inference. To ad- dress these issues we propose the following: 1) marginalized two-part models for generalized gamma family of distributions; 2) two-stage multiple imputation for marginal inference in semi-continuous outcomes with missingness and 3) a unified SAS Macro and Stata programs for fitting marginalized two-part models