Generalized Inferences on Problems in Biostatistics

• Main Authors: Hsin-Neng Hsieh, 謝鑫能
• Other Authors: 蘇秀媛
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/13163649452950942511

博士 === 國立臺灣大學 === 農藝學研究所 === 97 === The main objective of this dissertation is to use generalized inference on biostatistics. There are three parts in this dissertation. In vitro dissolution testing has been suggested as a surrogate for assessment of bioequivalence between the test and reference formulations for postapproval changes. First is that we use the concept of generalized p-values (GPVs) to assessment of similarity between dissolution profiles. The often used criteria for assessment of dissolution similarity between general profiles are functions of average squared mean differences and absolute mean difference. Because of the complexity of the distributions of estimators of two functions, it is difficult to obtain a test to test the hypothesis of dissolution similarity. Therefore, in first study, the GPVs is applied to construct a test procedure to assess the similarity of dissolution profiles. Simulation results show that when the numbers of dosage units are large, the GPVs testing procedure yields satisfactory results for size and power with f2 and g1 criteria recommended by the U.S. Food and Drug Administration (FDA). Through this simulation study, with the same f2 and g1 criteria, the performance of empirical sizes and empirical power by using GPVs are as good as by using bootstrap method. The proposed method is illustrated with a real example. The receiver operating characteristic (ROC) curve is a popular statistical tool for the accuracy of diagnostic device. One of primary objectives in a diagnostic test evaluation study is to compare the diagnostic accuracy of the new diagnostic procedure with that of current standard procedure. The second part is that we construct confidence intervals for the difference in paired areas under ROC curves in the absence of a gold standard test. The ROC curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of continuously valued diagnostic tests is the area under the ROC curve. To estimate such a measure, we require the existence of a gold standard test on the presence of disease status. However a gold standard test may sometimes be too expensive or infeasible to obtain. Therefore, in many medical research studies, the true disease status of the subjects may not be known or available. Under the normality assumption on the diagnostic test results from each group of subjects, based on the expectation-maximization (EM) algorithm in conjunction with a bootstrap method, we propose a maximum likelihood based procedure for construction of confidence intervals for the difference in paired areas under ROC curves in the absence of a gold standard test. In addition, we also propose to use the concept of generalized pivotal quantities (GPQs) to construct generalized confidence intervals (GCIs) for the difference in paired areas under ROC curves in the absence of a gold standard test. Simulation results show that the proposed interval estimation procedures yield satisfactory coverage probabilities and expected lengths. The proposed methods are illustrated with two data examples. The last part is that we propose a generalized inference on assessment non-inferiority of a new treatment in a three-arm trial in the presence of heteroscedasticity. In non-inferiority trials, the goal is to show how an experimental treatment is statistically and clinically not inferior to the active control. The three-arm clinical trial usually recommended for non-inferiority trials by the FDA. The three-arm trial consists of a placebo, reference, and an experimental treatment. In this study, under the normality assumption on the placebo, reference, and an experimental treatment, the GPVs is applied to facilitate non-inferiority tests in a three-arm design. In the situation of heterogeneous group variances, through a simulation study, the GPVs will adequately maintain the alpha level than Fieller''s method and bootstrap method. Simulation results also show that the performance of empirical power of GPVs method is as good as that of the Fieller''s method and the bootstrap method. Finally, the proposed method is illustrated with two data examples.