On some sample size formulae for controlling both size and power in clinical trials

Abstract

Suppose that observations are taken from a population with normal distribution N(μ, σ 2 ) where both μ and σ 2 are unknown parameters. Our goal is to design a two-sided test of H 0 : μ = 0 against H a : μ ¬= 0 which has, at least approximately, size a and power β at |μ| = d > 0, where a, β and d are three preassigned constants. The classical solution is Stein's two-stage procedure, which tends to oversampling, however. Three new procedures are proposed and studied in this paper. They all have both size and power very close to the target values α and β and require only a few more observations than the necessary sample size to achieve our goal if σ 2 had been completely known.