PROPERTIES OF BIOEQUIVALENCE TESTS UNDER RANKED SET SAMPLING (RSS) AND SIMPLE RANDOM SAMPLING (SRS)
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Mathematics and Statistics
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Statistics
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Abstract
Bioequivalence test procedure is used in clinical trials and environmental studies. In clinical trials testing equivalence is used to assess the different formulations of two treatment drugs and the relevance of this is to determine the equivalence of two or more treatment groups. In environmental studies bioequivalence tests are used to determine environmental effects and changes between two locations. This thesis is aimed at analyzing the properties of bioequivalence tests under two commonly used sampling designs, namely, simple random sampling (SRS) and a ranked set sampling (RSS); for this study, we consider a one sample t-test. The thesis includes background information on bioequivalence tests, a description of test procedures used to determine bioequivalence, illustrations comparing ranked set sampling (RSS) to simple random sampling (SRS), the properties of bioequivalence tests, with emphasis on the two-one sided test (TOST), under SRS and RSS. We also explore the advantages of a variety of estimates of population variance in constructing TOST. In addition, we provide a comprehensive assessment of two methods of variance estimation with a ranked set sample, given by Stokes (1980) and Bose & Neerchal (1996). The Mean squared error (MSE) of these estimators is evaluated in a simulation study. An investigation is done on the distributional properties of the t-statistic data, under the RSS design using the different variance estimators; Quantile-Quantile plots and other statistics such as the goodness-of-fit, percentile and target values are generated. It was shown that the normal distribution was the best fit for the t-statistics used in the TOST procedure. It was also shown that Boss and Neerchal (1996) variance estimator is a better unbiased estimator for the variance of a RSS than Stokes (1986) variance estimator. We concluded that the two-one sided test (TOST), a bioequivalence test procedure, is a reasonable test to analyze a ranked set sample design.