||In a pharmacokinetic (PK) study, to claim a test drug under study as a generic drug, proof of the bioequivalence between the test drug and a comparative reference drug is needed. To do so, some healthy volunteers are recruited and administered with the two drugs in a 2×2 crossover design with a reasonable wash-out time period, where the volunteers in one sequence receive the reference drug and then the test drug in two different periods, while the volunteers in the other sequence take the drugs in reverse order in the two periods. After the drug is administered to each volunteer, the drug concentrations in blood or plasma at different time points are then measured, which is referred to as the drug concentration–time curve or profile. The average bioavailability parameters such as the area under the drug concentration–time curve (AUC) is conventionally of interest for assessing the bioequivalence of the test drug to the reference drug. Conventionally, however, the distribution of the logarithm of individual AUC (denoted by logAUC) is followed the lognormal distribution. In practice, this assumption is violated and hence, in this thesis, we propose an alternative distribution, inverse gamma distribution, to satisfy the assumption of the distribution of individual logAUC. In this thesis, we consider to construct the model of individual logAUC which has subject variation and the error term are distributed by normal distribution and inverse gamma distribution, respectively, under the 2x2 crossover design. We consider using the stochastic approximation expectation- maximization algorithm to find the maximum likelihood estimates of the parameters. Then, the bioequivalence test of two drugs is inducted by estimated mean AUC. We further present some results of a simulation study investigation of the level and power performances of the purposed method and the application of the proposed test is finally illustrated by using a real data.|
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