Abstract
This paper introduces a two-stage selection rule to compare several experimental treatments with a control when the variances are common and unknown. The selection rule integrates the indifference zone approach and the subset selection approach in multiple-decision theory. Two mutually exclusive subsets of the parameter space are defined, one is called the preference zone (PZ) and the other, the indifference zone (IZ). The best experimental treatment is defined to be the experimental treatment with the largest population mean. The selection procedure opts to select only the experimental treatment which corresponds to the largest sample mean when the parameters are in the PZ, and selects a subset of the experimental treatments and the control when the parameters fall in the IZ. The concept of a correct decision is defined differently in these two zones. A correct decision in the preference zone (CD1) is defined to be the event that the best experimental treatment is selected. In the indifference zone, a selection is called correct (CD2) if the selected subset contains the best experimental treatment. Theoretical results on the lower bounds for P(CD1) in PZ and P(CD2) in IZ are developed. A table is computed for the implementation of the selection procedure.
Highlights
This study is motivated by the current clinical trials involving protease inhibitors
Using Lemma 4.1, we evaluate the lower bounds of the P(CD1|Pc) in the preference zone (PZ) and the P(CD2|Pc) in the indifference zone (IZ)
Multivariate procedures are seldom used in clinical trials because of the strict conditions they impose
Summary
This study is motivated by the current clinical trials involving protease inhibitors. The different combinations include zidovudine plus lamivudine, zidovudine plus didanosine, zidovudine plus zalcitabine, stavudine plus didanosine, lamivudine plus stavudine, and didanosine plus lamivudine Many of these treatments are better than the traditional treatments (AZT, AZT, and ddI, or AZT and ddC, etc.), the best treatment is still unknown. We further assume that the best experimental treatment is better than the control (i.e., μ[k] > μ0) This assumption is reasonable for HIV clinical trials. Many studies have shown that some regimens involving protease inhibitors are better than the traditional treatment. The two-stage selection rule proposed in this paper satisfies any given probability requirement (P1∗, P2∗) by allocating a sufficiently large sample size Since this procedure combines selection and screening, the required sample size will be larger than either the indifference zone approach or the subset selection approach. From this point of view, our procedure is more efficient
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