## Mathematics Dissertations

Fall 12-15-2016

#### Degree Type

Closed Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics and Statistics

Dr. Gengsheng Qin

Dr. Xin Qi

Dr. Xiaoyi Min

Dr. Ruiyan Luo

#### Abstract

Medical cost analysis is an important part of treatment evaluation. Since resources are limited in society, it is important new treatments are developed with proper costconsiderations. The mean has been mostly accepted as a measure of the medical cost analysis. However, it is well known that cost data is highly skewed and the mean could be highly influenced by outliers. Therefore, in many situations the mean cost alone cannot offer complete information about medical costs. The quantiles (e.g., the first quartile, median and third quartile) of medical costs could better represent the typical costs paid by a group of individuals, and could provide additional information beyond mean cost.

For a specified patient population, cost estimates are generally determined from the beginning of treatments until death or end of the study period. A number of statistical methods have been proposed to estimate medical cost. Since medical cost data are skewed to the right, normal approximation based confidence intervals can have much lower coverage probability than the desired nominal level when the cost data are moderately or severely skewed. Additionally, we note that the variance estimators of the cost estimates are analytically complicated.

In order to address some of the above issues, in the first part of the dissertation we propose two empirical likelihood-based confidence intervals for the mean medical costs: One is an empirical likelihood interval (ELI) based on influence function, the other is a jackknife empirical likelihood (JEL) based interval. We prove that under very general conditions, 2log (empirical likelihood ratio) has an asymptotic standard chi squared distribution with one degree of freedom for mean medical cost. Also we show that the log-jackknife empirical likelihood ratio statistics follow standard χ2 distribution with one degree of freedom for mean medical cost.

In the second part of the dissertation, we propose an influence function-based empirical likelihood method to construct a confidence region for the vector of regression parameters in mean cost regression models with censored data. The proposed confidence region can be used to obtain a confidence interval for the expected total cost of a patient with given covariates. The new method has sound asymptotic property (Wilks Theorem).

In the third part of the dissertation we propose empirical likelihood method based on influence function to construct confidence intervals for quantile medical costs with censored data. We prove that under very general conditions,2log (empirical likelihood ratio) has an asymptotic standard chi squared distribution with one degree of freedom for quantile medical cost. Simulation studies are conducted to compare coverage probabilities and interval lengths of the proposed confidence intervals with the existing confidence intervals. The proposed methods are observed to have better finite sample performances than existing methods. The new methods are also illustrated through a real example.

#### DOI

https://doi.org/10.57709/9440047

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