| This dissertation provides solutions to problems in the analysis of skewed data. It consists of four parts.; The first part studies the theoretical performance of normal based confidence intervals for the one- and two-sample problems for skewed data via Edgeworth expansion. We evaluate several existing techniques and propose new methods to improve coverage accuracy of confidence intervals. Our study shows that our new intervals and the bootstrap-t intervals give the best coverage accuracy and have shorter interval lengths.; The second part studies the theoretical performance of normal based confidence intervals for the incremental cost-effectiveness ratio and the net health benefit, which are often used in cost-effectiveness analysis. We evaluate several existing techniques and propose new methods based on Edgeworth expansion to improve coverage accuracy of confidence intervals. Our new intervals give good coverage accuracy and are narrower than the currently recommended intervals.; The third part adopts missing data methodologies to the cost-effectiveness analysis framework. In existing cost-effectiveness literature, missing data have been either ignored or simple ad hoc methods (like mean substitution) have been used. We provide a concise description of proper methods for handling missing data in the cost-effectiveness analysis framework. The methods include maximum likelihood estimation using the Expectation-Maximization (EM) algorithm (Little and Rubin, 1987, chap. 8) and multiple imputation via data augmentation (Little and Rubin, 1987, chap. 10). The maximum likelihood approach using EM algorithm and multiple imputation using Rubin's combination rule provide consistent and best coverage of confidence intervals.; The fourth part examines the Box-Cox transformation model for handling skewed data. The Box-Cox transformation has the following form: hy;l= yl-1l ,whenl≠0 logy,when l=0. In this section, we assume that there exists a hyperparameter lambda that, after transformation, the outcome of interest will be linear in the covariates hYi;l =XTib+gZi ;gei where epsiloni, i=1,..., n, are independent and identically distributed from some unknown distribution Fepsilon. In this part of the dissertation, we provide a procedure for estimating E(Y|X), which is of interest in many health care costs studies. |
