A Bivariate Random-Effects Copula Model for Length of Stay and Cost
Copula models and random effect models are becoming increasingly popular for modeling dependencies or correlations between random variables. Recent applications appear in such fields as economics, finance, insurance, and survival analysis. We give a brief
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Abstract Copula models and random effect models are becoming increasingly popular for modeling dependencies or correlations between random variables. Recent applications appear in such fields as economics, finance, insurance, and survival analysis. We give a brief overview of the principles of construction of copula models from the Farlie-Gumbel-Morgenstern, Gaussian, and Archimedean families to the Frank, Clayton, and Gumbel families. We develop a flexible joint model for correlated errors modeled by copulas and incorporate a cluster level random effect to account for within-cluster correlations. In an empirical application our proposed approach attempts to capture the various dependence structures of hospital length of stay and cost (symmetric or asymmetric) in the copula function. It takes advantage of the relative ease in specifying the marginal distributions and introduction of within-cluster correlation based on the cluster level random effects. Keywords Copula families • Random effects • Joint models • Healthcare cost
1 Introduction Among the challenges in the analysis of multivariate outcomes of mixed types is the specification of a joint distribution that accommodates the different measurement scales and dependencies among the outcomes. In healthcare studies it is common to have multiple patient-level outcomes, some of which are continuous and others are discrete. For example, for hospital resource management and planning studies it is important to consider both length of stay (LOS) and the final disposition of
X. Tang Asthma, Allergy and Autoimmunity Institute, Allegheny Health Network, 4800 Friendship Ave., Pittsburgh, PA 15224, USA e-mail: [email protected] Z. Luo • J.C. Gardiner () Department of Epidemiology and Biostatistics, Michigan State University, 909 Fee Road, B629 West Fee, East Lansing, MI 48824, USA e-mail: [email protected]; [email protected] © Springer International Publishing Switzerland 2016 J. Lin et al. (eds.), Statistical Applications from Clinical Trials and Personalized Medicine to Finance and Business Analytics, ICSA Book Series in Statistics, DOI 10.1007/978-3-319-42568-9_25
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the patient (died in hospital, discharged home, to nursing home, hospice, or other facility). During a hospital stay adverse events such as incident pressure ulcer, fall, or deep-vein thrombosis are regarded as defects in patient-care with the unintended consequences of an increase in LOS and cost. Flexible models that can address multiple outcomes of different types while incorporating covariates have useful application for prediction. Multilevel models (also called hierarchical models, nested models, mixed models, random-effects (RE) models, random-coefficient models, or split-plot designs) are statistical models addressing variations at more than one level (Skrondal et al. 2004). They can be viewed as generalizations of linear models. For an example using LOS and cost, patients share characteristics of the hospital in which they are treated. Therefore, in addition to the patie
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