Power and sample size determination for dose finding and multiple endpoints problems

The proposed research considers power and sample size determination for a problem in dose finding and a problem in multiple endpoints. The dose finding problem deals with a stepwise test procedure (SD2PC) proposed in Tamhane, Dunnett, Green and Wetherington (2001) to identify the maximum safe dose (MAXSD) 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. The power and sample size are also considered for a Bayesian formulation in which weighted average priors are put on the MAXSD. Sample size determination is discussed for an alternative definition of power in a similar way as for the former definition of power.The multiple endpoints problem deals with the superiority-equivalence approach (Tamhane and Logan, 2004). A general expression for the power of the Tamhane-Logan (TL) test is derived and its least favorable configuration (LFC) is considered. Numerical method is utilized to evaluate the multiple integral in the power expression. The optimum sample size allocation for the TL test is given and it is used, along with the power expression, to find the minimum sample size to achieve a specified power under different subsets of the alternative hypothesis region (SAHRs). Simulation studies are performed to confirm the validity of the proposed algorithm for evaluating the power expression.