Sample Sizes for Comparisons of k Treatments with a Control Based on Different Definitions of the Power

The determination of sample sizes for the comparison of k treatments against a control by means of the test of Dunnett (1955, 1964) as well as by means of the multiple t-test will be considered. The power in multiple comparisons can be defined in different ways, see Hochberg and Tamhane (1987). We will derive formulas for the per-pair power, the any-pair power and the all-pairs power for both one- and two-sided comparisons. Tables will be provided that allow sample sizes to be determined for preassigned values of the power.     

Sample size determination for testing nonequality under a three‐treatment two‐period incomplete block crossover trial

To reduce the lengthy duration of a crossover trial for comparing three treatments, the incomplete block design has been often considered. A sample size calculation procedure for testing nonequality between either of the two experimental treatments and a placebo under such a design is developed. To evaluate the performance of the proposed sample size calculation procedure, Monte Carlo simulation is employed. The accuracy of the sample size calculation procedure developed here is demonstrated in a variety of situations. As compared with the parallel groups design, a substantial proportional reduction in the total minimum required sample size in use of the incomplete block crossover design is found. A crossover trial comparing two different doses of formoterol with a placebo on the forced expiratory volume is applied to illustrate the use of the sample size calculation procedure.     

A Survey of Sample Size Formulas for Pairwise and Many‐one Multiple Comparisons in the Parametric,Nonparametric and Binomial Case

We present a survey of sample size formulas derived in other papers for pairwise comparisons of k treatments and for comparisons of k treatments with a control. We consider the calculation of sample sizes with preassigned per‐pair, any‐pair and all‐pairs power for tests that control either the comparisonwise or the experimentwise type I error rate. A comparison exhibits interesting similarities between the parametric, nonparametric and binomial case.