In comparing k (greater than or equal to 2) treatments for a disease, often only comparisons of the individual treatments with the unknown best treatment are of primary interest. One needs to know more than whether the k treatments are equal or not, so tests of homegenity are inadequate. On the other hand, all pairwise comparisons procedures make too many comparisons; one hardly need to know which of the terrible treatments are more terrible. Consequently, they are less than sensitive in indicating which treatments are good. Recently, a methodology called MCB (multiple comparisons with the best) was developed in Hsu (1981). For comparing with the best treatment, this methodology gives results sharper than all pairwise procedures and in fact sharper than the union of the well known Indifference Zone selection procedure of Bechhofer (1954) and Subset Selection procedure of Gupta (1956, 1965). Thus among the existing methodologies, MCB makes the strongest inference. The existing methodologies, including MCB, assume there is no information on the true response rate. Often partial information is available. For example, if the treatments correspond to different dosages, then we can expect the true response rate to be unimodal (increasing, decreasing, or increasing then decreasing) as dosage increases. We propose to develop both parametric and nonparametric MCB under incomplete order restrictions. By making use of known incomplete ordering restrictions, significant improvement over existing methodologies can be realized.
NIH ExPorter
NIH ExPorter