A Flexible Model for the Mean and Variance Functions, with Application to Medical Cost Data

• Activity Number: 283
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Health Policy Statistics Section
• Author(s): Lei Liu*+ and Jinsong Chen and Daowen Zhang and Tina Shih
• Companies: Northwestern University and Northwestern University and North Carolina State University and The University of Chicago
• Keywords: Generalized linear model ; semiparametric regression ; health econometrics ; smoothing parameter ; generalized cross validation

Abstract

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 the generalized linear models by assuming nonlinear covariate effects 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 (CDR) at the University of Virginia Hospital System.