Statistica Sinica 16(2006), 1213-1232

INFERENCES IN CENSORED COST REGRESSION MODELS

WITH EMPIRICAL LIKELIHOOD

X. H. Zhou$^{1,2}$, G. S. Qin$^3$, H. Z. Lin$^{1,4}$ and G. Li$^5$

$^1$VA Puget Sound Health Care System, $^2$University of Washington,

$^3$Georgia State University, $^4$Sichuan University

and $^5$University of California at Los Angeles

Abstract: In many studies of health economics, we are interested in the expected total cost over a certain period for a patient with given characteristics. Problems can arise if cost estimation models do not account for distributional aspects of costs. Two such problems are (1) the skewed nature of the data, and (2) censored observations. In this paper we propose an empirical likelihood (EL) method for constructing a confidence region for the vector of regression parameters, and a confidence interval for the expected total cost of a patient with the given covariates. We show that this new method has good theoretical properties and we compare its finite-sample properties with those of the existing method. Our simulation results demonstrate that the new EL-based method performs as well as the existing method when cost data are not so skewed, and outperforms the existing method when cost data are highly skewed. Finally, we illustrate the application of our method to a data set.

Key words and phrases: Censored data, empirical likelihood, health care costs, prediction.