Recent studies show that medical cost data can be heavily censored and highly skewed, which leads to have more complex cost data analysis. In this paper, we propose influence function and empirical likelihood (EL)-based methods to construct confidence regions for regression parameters in median cost regression models with censored data. We further propose confidence intervals for the median cost with given covariates using the proposed EL-based confidence regions. Simulation studies are conducted to compare the proposed EL-based confidence regions with the existing normal approximation-based confidence regions in terms of coverage probabilities. The new EL-based methods are observed to have better finite sample performances than existing methods particularly when the censoring proportion is high. The new methods are also illustrated through a real data example.
Keywords: Censored medical cost; confidence region; empirical likelihood; jackknife; median regression.