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Proquest Dissertations INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy subm itted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. 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Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 UMI EVALUATION OF THE DISTRIBUTIONS OF COST-EFFECTIVENESS RATIOS AND COMPARISON OF METHODS TO CONSTRUCTING CONFIDENCE INTERVALS FOR SUCH RATIOS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By Hyunsun-Sunny Kim, M.S. ***** The Ohio State University 2000 Dissertation Committee: Approved by Professor Melvin Moeschburger, Adviser Professor Deborah Burr Adviser Professor Dev Pathak School of Public Health UMI Number 9971580 UMI UMI Microform9971580 Copyright 2000 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Leaming Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Copyright by Hyunsun-Sunny Kim 2000 ABSTRACT Health economic evaluation is the comparative analysis of alternative interventions (i.e.. therapies, treatments, or drugs) in terms of both their costs and effects in health care. Economic evaluation systematically analyzes all inputs and outputs of treatment, and suggests the most effective alternatives for given resources. Results of a cost-effectiveness analysis are summarized in a series of cost-effectiveness (C/E) ratios. Understanding of the distribution of the ratio is limited. Hence, there is a lack of statistical tests for the C/E ratios. As with other statistics, the C/E ratio is subject to sampling variation. However, constructing a confidence interval for the cost- effectiveness ratio is complicated because both numerator and denominator of the ratio are stochastic in nature. A closed form for the variability calculation is not readily available. Several statistical methods have been proposed lately, yet, the systematic method of handling uncertainty is generally underdeveloped in economic evaluation. Proposed statistical methods include the box confidence interval, Taylor’s methods, Fieller’s method, and non-parametric bootstrapping. This study has two objectives; description of the ratio distribution, and comparison of statistical methods proposed in constructing confidence intervals for the u ratio. The ratio distributions are formed from the combinations of normal, lognormal, and gamma distributions, which frequently arise in cost-effective studies. Based on the results of this study, the ratio distributions take on a variet>' of shapes depending on the coefficient of variation of their denominator distribution. Most of the time, the ratio distributions have the bell shape with, or without, a heavy right tail. However, the ratio distribution could even be bimodal if the coefficient of variation was very large. None of the statistical methods yield the valid confidence interval if the mean of the denominator of the ratio is close to zero so that the coefficient of variation is large. This result suggests that comparing the Incremental Cost Effectiveness Ratio (ICER) using a statistical test may not be appropriate unless the net effect (denominator) is significantly big. Although, the coefficient of variation is very important, it is the nature of the data and it is beyond what an investigator can control. From a practical point of view, the large sample size is an important way to improve the validity of the statistical tests. Because costs and effects are generally skewed to the right, the numerator and denominator will be skewed to the right. For samples of size 15, accordingly, the results of this study showed that the distributions of cost-effectiveness ratios are skewed to the right for those distributions investigated. The Box method overestimated the level of confidence seriously. Since Taylor’s method, the normal approximated bootstrap method, and the jackknife method assume normality of the ratio distribution, they did not construct the valid confidence intervals. Fieller’s method can not construct valid confidence intervals either because the bivariate normal assumption is violated. Ill For samples of size 50 or 250, all methods, except the box method, constructed the confidence interval well, and they incorporate the correlation between numerator and denominator. Among them, Fieller’s method is the first choice of selection for the estimation of the confidence interval. This may be true because only Fieller’s method provides the exact solution where all other methods provide an approximation, if the numerator and denominator are bivariate normal. IV To my husband, Sangsoo Kim, who give me the unlimited support and courage; to my sons, Dennis and Elliot, who inspire me with endless smiles. ACKNOWLEDGMENTS I wish to thank my adviser. Dr. Melvin Moeschberger, for his guidance and support extended to the details of dissertation writing. I am grateful for his patience in correcting both my stylistic and scientific errors. Also, I thank Dr. Dev Pathak and Dr. Deborah Burr for their expertise in simulation and cost-effectiveness studies. I could not have finished this dissertation without their help. I thank my parents who taught me the value of education. I also thank my grandmother, Hak Lee who prayed every morning for me. Every moment when I was frustrated, I remembered their prayer. I thank my Lord who walked with me throughout my long journey. VI VITA Mar 6. 1963 ................................... Bom — ChungJoo, Korea 1986 ............................................... B.S., Nursing Seoul National University Seoul, Korea 1991 -1994 ..................................... Graduate Research Associate Nursing Research Center University of Wyoming 1994 ............................................... M.S., Nursing University of Wyoming 1994-1996 ..................................... Graduate Teaching Associate University of Wyoming 1996-present................................. Graduate Reserarch Associate Biostatistics Program Ohio State University PUBLICATIONS 1. Zadnik K. Mannis MJ, Kim HS, Miller M. Marquez M. Inter-clinician agreement on clinical data abstracted from patients’ medical charts. Optometry and Vision Science 1998;75(II):813-816. 2. Zadnik K, Mutti DO, Kim HS, Jones LA, Qiu P, Moeschberger ML. Tonic accommodation, age, and refractive error in children. Investigative Ophthalmology & Visual Science 1999:40(6): 1050-1060. j . Zadnik K, Mutti DO, Friedman NE, Qualley PA, Jones LA, Qiu P, Kim HS, Hsu JC. Moeschberger ML. Prediction of the onset of juvenile myopia. Investigative Ophthalmology & Visual Science 1999:40(9): 1936-1943. V ll FIELDS OF STUDY Major Field : Public Health Research Focuses : Biometrics and Epidemiology vm TABLE OF CONTENTS Pages Abstract............................................................................................................................... ii Dedication .......................................................................................................................... v Acknowledgements .............................................................................................................vi V ita......................................................................................................................................vii List of Tables ....................................................................................................................xii List of Figures .....................................................................................................................xv Chapters 1. Introduction .................................................................................................................. 1 1.1 Problem statement ............................................................................................2 1.2 Objective of study .......................................................................................... 4 1.3 Specific aim s.....................................................................................................5 1.3.1 Investigation of the distribution of ratios for various numerator and denominator distributions ................................. 5 (1) Normal numerator and denominator (2) Lognormal numerator and denominator (3) Gamma numerator and denominator
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