published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Leung Shun-piu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 41-43). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiplicity Problem in Multiple Testing --- p.1 / Chapter 1.2 --- Family --- p.2 / Chapter 1.3 --- Family wise Error Rate --- p.2 / Chapter 1.4 --- Multiple Comparisons with a Control --- p.3 / Chapter 1.5 --- Single-step Procedures vs Stepwise Procedures --- p.4 / Chapter 1.6 --- Dunnett Procedure --- p.5 / Chapter 1.6.1 --- One-way Fixed Effect Model --- p.5 / Chapter 1.6.2 --- Simultaneous Inference and Test Statistics --- p.6 / Chapter 1.6.3 --- Calculation of the Upper and Lower Percentage Points --- p.8 / Chapter 1.7 --- Objectives --- p.10 / Chapter 2 --- Testing Procedures --- p.11 / Chapter 2.1 --- Simultaneous Inference in Mixed Families --- p.11 / Chapter 2.2 --- "Evaluation of C1,α and c2,α" --- p.13 / Chapter 2.3 --- Extension to Mixed Families with 3 Testing Groups --- p.15 / Chapter 3 --- The Calculation of Critical Values --- p.18 / Chapter 3.1 --- Calculation of Critical Values --- p.18 / Chapter 3.2 --- "Tabulation of Critical Values (c-*,α c*,α)" --- p.22 / Chapter 4 --- Numerical Example --- p.30 / Chapter 5 --- Conclusions --- p.34 / Appendix --- p.35 / References --- p.41

Lee Hang Ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 37-39). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple comparison procedures --- p.1 / Chapter 1.2 --- Multiple comparisons with a control (MCC) --- p.2 / Chapter 1.3 --- MCC in two-way designs --- p.3 / Chapter 1.4 --- Directional-mixed families --- p.4 / Chapter 1.5 --- Objectives --- p.6 / Chapter 2 --- MCC with directional-mixed families in one-way designs: a review --- p.8 / Chapter 2.1 --- The model --- p.8 / Chapter 2.2 --- The test statistics --- p.8 / Chapter 2.3 --- The evaluation of critical constants --- p.9 / Chapter 2.4 --- Testing and estimation --- p.11 / Chapter 2.5 --- An example --- p.12 / Chapter 3 --- MCC with directional-mixed families in two-way designs --- p.14 / Chapter 3.1 --- The model --- p.14 / Chapter 3.2 --- The test statistics --- p.15 / Chapter 3.3 --- Testing and estimation --- p.16 / Chapter 4 --- Evaluation and tabulation of critical values --- p.17 / Chapter 4.1 --- Evaluation of critical values --- p.17 / Chapter 4.2 --- Comparisons of computational methods --- p.19 / Chapter 4.3 --- Tabulation of critical values --- p.24 / Chapter 5 --- Power study --- p.30 / Chapter 5.1 --- Objectives --- p.30 / Chapter 5.2 --- Simulation results --- p.30 / Chapter 6 --- Numerical example --- p.33 / Chapter 7 --- Conclusions --- p.36 / Bibliography

Wang Yanhui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 46-48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparisons with a Control --- p.1 / Chapter 1.1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.1.2 --- Multiple Comparisons with a Control --- p.2 / Chapter 1.1.3 --- Single-step and Stepwise Procedures --- p.2 / Chapter 1.2 --- The Dunnett Procedure --- p.4 / Chapter 1.2.1 --- One-way Fixed Effect Model --- p.4 / Chapter 1.2.2 --- Testing Procedure --- p.4 / Chapter 1.3 --- Directional-mixed Families --- p.7 / Chapter 1.3.1 --- Definition of Directional-mixed Families --- p.7 / Chapter 1.3.2 --- Selection between One- and Two-sided Inferences --- p.7 / Chapter 1.4 --- Objectives --- p.8 / Chapter 2 --- Single-step Procedure --- p.10 / Chapter 2.1 --- SSI Procedure --- p.10 / Chapter 2.1.1 --- The Testing Procedure --- p.10 / Chapter 2.1.2 --- Computation of Optimal Critical Values --- p.11 / Chapter 2.2 --- p-value Consistency --- p.17 / Chapter 2.3 --- The SS2 Procedure --- p.18 / Chapter 3 --- Step-down Procedure --- p.24 / Chapter 3.1 --- The Testing Procedure --- p.24 / Chapter 3.2 --- Derivation of Critical p-values for the SD Procedure --- p.26 / Chapter 4 --- Simulation Study of Power --- p.30 / Chapter 5 --- Practical Example --- p.36 / Appendix --- p.39 / References --- p.46

Chan Tat-on. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.2 --- One-step MCCP --- p.2 / Chapter 1.3 --- Stepwise MCCP --- p.7 / Chapter 1.4 --- Thesis Objectives --- p.10 / Chapter Chapter 2 --- One-step MCCP with Heterogeneous Group Variances --- p.11 / Chapter 2.1 --- The Model --- p.11 / Chapter 2.2 --- Test Statistics --- p.12 / Chapter 2.3 --- Testing and Estimation --- p.15 / Chapter Chapter 3 --- Stepwise MCCP with Heterogeneous Group Variances --- p.17 / Chapter 3.1 --- The Model --- p.17 / Chapter 3.2 --- Testing Procedure --- p.17 / Chapter 3.3 --- Simulation Study --- p.18 / Chapter 3.3.1 --- Average power --- p.19 / Chapter 3.3.2 --- Family wise Type I error rate --- p.20 / Chapter 3.3.3 --- Simulation procedures --- p.21 / Chapter 3.3.4 --- Choice of parameter configurations --- p.23 / Chapter 3.3.5 --- Simulation results --- p.24 / Chapter 3.3.6 --- Summary --- p.28 / Chapter Chapter 4 --- Numerical Example --- p.33 / Chapter 4.1 --- SS procedures --- p.34 / Chapter 4.2 --- SW procedures --- p.35 / Chapter Chapter 5 --- Further Research --- p.38 / References --- p.39

Multiple comparisons and selection procedures are commonly studied in research and employed in application. Clinical trial is one of popular fields to which the subject of multiple comparisons is extensively applied. Based on the Federal Food, Drug, and Cosmetic Act, drug manufacturers need to not only demonstrate safety of their drug products but also establish effectiveness by substantial evidence in order to obtain marketing approval. However, the problem of error inflation occurs when there are more than two groups to compare with at the same time. How to design a test procedure with high power while controlling type I error becomes an important issue. The treatment with the largest population mean is considered to be the best one in the study. Potentially the best treatments can receive increased resources and further investigation by excluding clearly inferior treatments. Hence, a small number of possibly the best treatments is preferred. This thesis focuses on the problem of eliminating the less effective treatments among three in clinical trials. The goal is to increase the ability to identify any inferior treatment providing that the probability of excluding any best treatment is guaranteed to be less than or equal to alpha. A step-down procedure is applied to solve the problem. The general step-down procedure with fixed thresholds is conservative in our problem. The test is not efficient in rejecting the less effective treatments. We propose two methods with sharper thresholds to improve current procedures and construct a subset containing strictly inferior treatments. The first method, the restricted parameter space approach, is designed for the scenario when prior information about range of treatment means is known. The second method, the step-down procedure with feedback, utilizes observations to modify the threshold and controls error rate for the whole parameter space. The new procedures have greater ability to detect more inferior treatments than the standard procedure. In addition, type I error is also controlled under mild violation of the assumptions demonstrated by simulation.

Thesis (Ph. D.)--Virginia Polytechnic Institute, 1955. / Vita. Abstract. Includes bibliographical references (leaves 114-119). Also available via the Internet.

Thesis (Ph. D.)--University of Hong Kong, 1993.

Cheung Ching Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 64-65). / Abstracts in English and Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.2 --- Multiple Comparisons with a control --- p.2 / Chapter 1.3 --- Multiple Comparisons with a control in two-way designs --- p.5 / Chapter 1.4 --- Example --- p.12 / Chapter 1.5 --- Thesis Objectives --- p.13 / Chapter 2 --- Evaluation of Power (Homogeneous Variance) --- p.14 / Chapter 2.1 --- Definition and the use of power --- p.14 / Chapter 2.2 --- Setup and Notations --- p.15 / Chapter 2.3 --- Evaluation of power --- p.16 / Chapter 2.4 --- Computational Details --- p.19 / Chapter 2.4.1 --- Algorithm --- p.19 / Chapter 2.4.2 --- Results --- p.20 / Chapter 2.5 --- Numerical Example --- p.39 / Chapter 3 --- Evaluation of Power (Heterogeneous Variances) --- p.42 / Chapter 3.1 --- Setup and Notations --- p.42 / Chapter 3.2 --- Evaluation of power --- p.43 / Chapter 3.3 --- Results --- p.45 / Chapter 3.3.1 --- All-pairs Power --- p.46 / Chapter 3.3.2 --- Any-pair Power --- p.53 / Chapter 3.4 --- Numerical Example --- p.60 / Chapter 4 --- Conclusions --- p.63 / References --- p.64

by Ying-wang Wong. / Year shown on spine: 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 41-44). / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.2 --- Familywise Error Rate --- p.3 / Chapter 1.3 --- One-step Procedures Versus Stepwise Procedures --- p.4 / Chapter 1.4 --- Pairwise Multiple Comparisons --- p.5 / Chapter 1.5 --- Pairwise Multiple Comparisons in Two-Way Designs --- p.6 / Chapter 1.6 --- Objectives --- p.8 / Chapter 2. --- Pairwise Multiple Comparisons in One-Way Designs with Covariates --- p.9 / Chapter 2.1 --- The General ANCOVA Model --- p.9 / Chapter 2.2 --- Pairwise Comparisons --- p.12 / Chapter 3. --- Pairwise Comparisons in Two-Way Layout with Covariates --- p.15 / Chapter 3.1 --- The Model --- p.15 / Chapter 3.2 --- The Test Statistics --- p.16 / Chapter 3.3 --- Computation of Upper Percentage Points --- p.17 / Chapter 3.4 --- Approximation Procedure --- p.21 / Chapter 3.5 --- Two-Way Layout with One Covariate --- p.21 / Chapter 4. --- Numerical Examples --- p.23 / Appendix A - An Algorithm in Solving Equation (3.2.4) for the value of ta --- p.35 / Appendix B - Evaluation of Multivariate Normal Probabilities --- p.38 / References --- p.41