title: Weibull mixture regression for marginal inference in zero-heavy continuous outcomes.
abstract: Continuous outcomes with preponderance of zero values are ubiquitous in data that arise from biomedical studies, for example studies of addictive disorders. This is known to lead to violation of standard assumptions in parametric inference and enhances the risk of misleading conclusions unless managed properly. Two-part models are commonly used to deal with this problem. However, standard two-part models have limitations with respect to obtaining parameter estimates that have marginal interpretation of covariate effects which are important in many biomedical applications. Recently marginalized two-part models are proposed but their development is limited to log-normal and log-skew-normal distributions. Thus, in this paper, we propose a finite mixture approach, with Weibull mixture regression as a special case, to deal with the problem. We use extensive simulation study to assess the performance of the proposed model in finite samples and to make comparisons with other family of models via statistical information and mean squared error criteria. We demonstrate its application on real data from a randomized controlled trial of addictive disorders. Our results show that a two-component Weibull mixture model is preferred for modeling zero-heavy continuous data when the non-zero part are simulated from Weibull or similar distributions such as Gamma or truncated Gauss.
authors.affiliation: 1 Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC, USA.|2 Health Equity and Rural Outreach Innovation Center, Ralph H. Johnson Department of Veterans Affairs Medical Center, Charleston, SC, USA.
authors.forename: Mulugeta
authors.initials: M
authors.lastname: Gebregziabher
authors.affiliation: 1 Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC, USA.
authors.forename: Delia
authors.initials: D
authors.lastname: Voronca
authors.affiliation: 1 Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC, USA.
authors.forename: Abeba
authors.initials: A
authors.lastname: Teklehaimanot
authors.affiliation: 2 Health Equity and Rural Outreach Innovation Center, Ralph H. Johnson Department of Veterans Affairs Medical Center, Charleston, SC, USA.
authors.forename: Elizabeth J
authors.initials: EJ
authors.lastname: Santa Ana
mesh_terms: D016739:Behavior, Addictive; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D062405:Motivational Interviewing; D016011:Normal Distribution; D012044:Regression Analysis; D012984:Software; D019966:Substance-Related Disorders / Q000523:psychology / Q000628:therapy*; D016896:Treatment Outcome
keywords: Addictive disorder; Weibull mixture; marginalized inference; two-part model; zero-degenerate; zero-heavy