Marginalized Two-Part Models for Generalized Gamma Family of Distributions
*Delia Codruta Voronca, MUSC
Keywords: Generalized gamma; Marginal effect; Point mass at zero; Two-part models
Positive continuous outcomes with a point mass at zero are prevalent in biomedical research. To model the point mass at zero and to provide marginalized covariate effect estimates, marginalized two part models (MTP) have been developed for outcomes with log-normal and log-skew-normal distributions (Smith et al 2014). In this paper, we propose MTP models for outcomes from a generalized gamma (GG) family of distributions. In the proposed MTP-GG model, the conditional mean from a two-part model is parameterized to provide regression coefficients that have marginal interpretation. MTP-Gamma and MTP-Weibull are developed as special cases of MTP-GG. We derive marginal effect estimators from each model and assess their finite sample operating characteristics via a simulation study in terms of bias, standard errors, 95% coverage, and rate of convergence. We also demonstrate the applications of these models in a real data set from a randomized trial of addictive disorders and we provide SAS code for implementation. The simulation results show that when the true distribution of data is unknown, which is usually the case in real data sets, MTP-GG is preferable over other models.