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A flexible model for the mean and variance functions, with application to medical cost data
Author(s) -
Chen Jinsong,
Liu Lei,
Zhang Daowen,
Shih YaChen T.
Publication year - 2013
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5838
Subject(s) - covariate , heteroscedasticity , flexibility (engineering) , nonparametric statistics , econometrics , variance (accounting) , statistics , variance function , computer science , mathematics , function (biology) , extension (predicate logic) , regression analysis , economics , accounting , evolutionary biology , biology , programming language
Medical cost data are often skewed to the right and heteroscedastic, having a nonlinear relation with covariates. To tackle these issues, we consider an extension to generalized linear models by assuming nonlinear associations of covariates in the mean function and allowing the variance to be an unknown but smooth function of the mean. We make no further assumption on the distributional form. The unknown functions are described by penalized splines, and the estimation is carried out using nonparametric quasi‐likelihood. Simulation studies show the flexibility and advantages of our approach. We apply the model to the annual medical costs of heart failure patients in the clinical data repository at the University of Virginia Hospital System. Copyright © 2013 John Wiley & Sons, Ltd.