title: A marginalized two-part model for semicontinuous data.
abstract: In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero followed by a right-skewed continuous distribution with positive support. Examples include health expenditures, in which the zeros represent a subpopulation of patients who do not use health services, while the continuous distribution describes the level of expenditures among health services users. Semicontinuous data are typically analyzed using two-part mixture models that separately model the probability of health services use and the distribution of positive expenditures among users. However, because the second part conditions on a non-zero response, conventional two-part models do not provide a marginal interpretation of covariate effects on the overall population of health service users and non-users, even though this is often of greatest interest to investigators. Here, we propose a marginalized two-part model that yields more interpretable effect estimates in two-part models by parameterizing the model in terms of the marginal mean. This model maintains many of the important features of conventional two-part models, such as capturing zero-inflation and skewness, but allows investigators to examine covariate effects on the overall marginal mean, a target of primary interest in many applications. Using a simulation study, we examine properties of the maximum likelihood estimates from this model. We illustrate the approach by evaluating the effect of a behavioral weight loss intervention on health-care expenditures in the Veterans Affairs health-care system.
authors.affiliation: Center for Health Services Research in Primary Care, Durham VAMC, Durham, NC, U.S.A.; Department of Biostatistics, University of North Carolina, Chapel Hill, NC, 27599-7420, U.S.A.
authors.forename: Valerie A
authors.initials: VA
authors.lastname: Smith
authors.forename: John S
authors.initials: JS
authors.lastname: Preisser
authors.forename: Brian
authors.initials: B
authors.lastname: Neelon
authors.forename: Matthew L
authors.initials: ML
authors.lastname: Maciejewski
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009765:Obesity / Q000191:economics; D014481:United States; D014728:Veterans; D061217:Weight Reduction Programs / Q000191:economics / Q000592:standards
keywords: health-care expenditures; log-skew-normal distribution; marginalized models; semicontinuous data; two-part model; weight loss intervention