ABSTRACT
In clinical trials, the traditional approach to demonstrate that a new drug is superior to a placebo uses a fixed sample size design. The number of subjects needed are calculated prior to the start of the study based on a targeted treatment difference δ0 as well as the estimated variation of the response variable. As an example, consider a two arm clinical trial comparing a new test drug with a placebo. Assume that the outcomes of the primary efficacy measurement X for the placebo and Y for the new treatment follow the normal distributions with means μ0 and μ1, respectively, and a common variance 0.5σ2. The corresponding one-sided hypothesis then is
H vs H0 10 0: = . : > ,δ δ (7.1)
where δ = μ1 – μ0 is the treatment difference. Assuming that σ is known, for usual fixed sample size design, the number of subjects per treatment group needed to detect the treatment difference δ based on Z-test with the power 1 – β at the significance level α is calculated as
N z z
( )( ) ( )
(7.2)
Here z is the upper percentile of the standard normal distribution. Write the Z statistic as
N = ∑ ,=1σ
where Zi = Yi – Xi and N = N(1-β) (δ). For simplicity we further assume σ = 1. In practice σ can often be estimated using historical data at the time of study design, or using blinded data during the trial (Gould 1992; Gould and Shi 1992; Shi 1993).
