Smoothing Estimation for Rate Function of Occurrence Medical Cost

Most of recent research into medical cost analysis has focused on developing appropriate models and statistical inferences for the accumulated cost up to the end of study or the pre-determined times within the study period. However, the time of medical cost occurrence was not fully characterized in the total cost. In this thesis, we consider the model for the rate function of occurrence medical cost which uses the information of cost and occurrence times. To explore the association of the covariates with the rate function, a more flexible and easily explained time-varying coefficient generalized linear model is established to account for the heteroscedasticity. Based on censored data, a smoothing estimation method is proposed to estimate the parameter functions. Moreover, a consistent estimator for the asymptotic variance matrix of the estimators is provided. The limiting distribution of estimated functions and the estimator of variance matrix enable us to construct approximated regions. To investigate the finite sample properties of the estimators and the performance of procedure for the construction of confidence intervals, a class of simulations is conducted. An application to the colorectal cancer data retrieved from the Surveillance, Epidemiology, and End Results (SEER) Medicare database is further presented.