Generalized Semiparametric Models with Unknown Variance Function, with Application to Medical Cost Data
Jinsong Chen, University of Virginia 
*Lei Liu, University of Virginia 
Ya-Chen Tina Shih, University of Chicago 
Daowen Zhang, North Carolina State University 

Keywords: health economics, health services research, quasi-likelihood, GEE

Medical cost data are often skewed to the right and heteroscedastic, and are non-linearly related to covariates. To tackle these issues, we consider an extension to 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 assumption on the distributional form. The unknown functions are described by penalized splines, and the estimation is carried out using nonparametric quasi-likelihood. We suggest a criterion for selecting an optimal smoothing parameter. Simulation studies show the flexibility and advantages of our approach. We apply the model to the study of annual medical cost of heart failure patients in the clinical data repository (CDR) at the University of Virginia Hospital System.