The problem of finding the minimum effective dose (MED) of a drug involves multiple comparisons. In such a problem, generally, family-wise error rate is inflated if multiplicity adjustment is not made appropriately. The sample sizes are also an important issue that we need to consider from the aspect of efficiency, such as costs in studies. In this dissertation, we propose several novel procedures for MED under heteroscedasticity, which control family-wise error rate as well as the accuracy level for identifying MED.
In the literature, Bonferroni adjustment is widely used due to it's simplicity, but it is too conservative. Hsu and Berger (1999) proposed a stepwise confidence intervals procedure for MED using partitioning principle, which controlled the family-wise error rate without multiplicity adjustment. Their method is based on the cases of equal variance assumption. However, equal variance assumption is seldom satisfied in practice. Tao et al. (2002) extended Hsu and Berger's procedure for MED under heteroscedasticity.
When variances in different dose groups are not equal, to determine the minimum effective dose, we have to deal with the Behrens-Fisher problem (comparing means from two normal populations when population variances cannot be assumed equal). Exact solutions to Behrens-Fisher problem can be obtained by using two-stage procedures. For instance, Chapman (1950) extended Stein's (1945) two-stage sampling procedure in two-sample case.
In this dissertation, we examine methods in the comparisons of two populations and innovatively construct three new stepwise procedures that shed new light in the aspect of asymptotic efficiency, power improvement, and accuracy control in the inference of the minimum effective dose of a drug. Simulation studies greatly enhance and confirm the desired theoretical results. The procedures are applied to the analysis of the pharmacologic effect of an experimental compound on relative organ weights in mice.