A marginalized two‐part model for semicontinuous data. (9th July 2014) - Smith, Valerie A.; Preisser, John S.; Neelon, Brian; Maciejewski, Matthew L.
<x xml:space="preserve">Abstract</x> 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. Copyright © 2014 John Wiley & Sons, Ltd.