MULTIPLE TEST PROCEDURES FOR DOSE-FINDING

The problem of identifying the lowest dose level for which the mean re sponse differs from that at the zero dose level is considered. A gener al framework for stepwise testing procedures that use contrasts among the dose level means is proposed. Using this framework, several new pr ocedures are derived. These and some existing procedures, including th at of Williams (1971, Biometrics 27, 103-117; 1972, Biometrics 28, 519 -531), are compared analytically and by an extensive simulation study for the normal theory balanced one-way layout case. It is pointed out that the procedures based on the so-called step and basin contrasts pr oposed by Ruberg (1989, Journal of American Statistical Association 84 , 816-822) have excessively high type I familywise error rates (FWEs) and, hence, they should not be used. Some findings of the simulation s tudy are as follows: For monotone dose mean configurations, Williams' procedure and two step-down test procedures based on Helmert and linea r contrasts offer the best performance. For nonmonotone dose mean conf igurations, the performance of Williams' procedure does degrade somewh at, but the other two procedures are still the best. For more complex designs, a simple step-down test procedure that uses any ct-level test s (not necessarily t-tests) to compare each dose level with the zero d ose level controls the FWE and is the only alternative available, but its power is rather low, especially under nommonotone configurations. Step-up procedures are generally dominated by step-down procedures whe n the same contrasts are used although the differences are not great.