| In most analyses of medical expenditure data, the focus is upon the total costs that play a crucial role in policy and decision-making. The mean is the location parameter of interest because other location parameters lack its relation to the total. Mean estimation is complicated by the skewness most medical cost distributions.;In this thesis, we examine three simple problems in medical cost analysis: the estimation of the mean medical cost from a small to moderate size sample; the construction of a valid confidence interval for the mean cost; and comparison of the mean costs between two groups.;The sample mean is the optimal mean estimator when data are normally distributed but it is sensitive to the largest observations. Parametric mean estimators can be extremely sensitive to violation of the distributional assumption. We proposed a novel estimator, the smooth spacings mean, which is robust to the change in the distributional assumption. The smooth spacings mean allows the distribution of the medical cost data to deviate smoothly from its reference distributions, taken here to be the lognormal and the Weibull distributions.;Performance of mean estimators and confidence intervals are examined through simulation studies. The sample mean has larger mean squared error than other mean estimators. However, its mean squared error is greatly reduced when the underlying distribution is bounded from above, such as the empirical Medicare payment distribution.;The lower and upper coverage errors of the normal-theory interval for the mean medical costs can be reduced by using theoretically more accurate bootstrap intervals. We propose combining the BCa lower confidence limit and the upper limit of the bootstrap-t interval to construct two-sided equal-tailed confidence interval.;When the cost distribution of both groups are identical, the estimator formed by taking the difference between two once-Winsorized means has the best performance. However, both bootstrap-t and BCa intervals have larger coverage error than the normal-theory interval. The relative shapes of the two cost distributions play a major role in choosing a better confidence interval procedure. |
