Power and sample size determination for a stepwise test procedure for finding the maximum safe dose

This paper addresses the problem of power and sample size calculation for a stepwise multiple test procedure (SD2PC) proposed in Tamhane et al. [2001. Multiple test procedures for identifying the maximum safe dose. J. Amer. Statist. Assoc. 96, 835-843] to identify the maximum safe dose of a compound. A general expression for the power of this procedure is derived. It is used to find the minimum overall power and minimum power under the constraint that the dose response function is bounded from below by a linear response function. It is shown that the two minima are attained under step and linear response functions, respectively. The sample sizes necessary on the zero dose control and each of the positive doses to guarantee a specified power requirement are calculated under these two least favorable configurations. A technique involving a continuous approximation to the sample sizes is used to reduce the number of quantities that need to be tabled, and to derive the asymptotically optimal allocation of the total sample size between the zero dose and the positive doses. An example is given to illustrate use of the tables. Extensions of the basic formulation are noted.