  The increasing interest in subpopulation analysis has led to the development
of various new trial designs and analysis methods in the fields of personalized
medicine and targeted therapies. In this paper, subpopulations are defined in
terms of an accumulation of disjoint population subsets and will therefore be
called composite populations. The proposed trial design is applicable to any
set of composite populations, considering normally distributed endpoints and
random baseline covariates. Treatment effects for composite populations are
tested by combining $p$-values, calculated on the subset levels, using the
inverse normal combination function to generate test statistics for those
composite populations. The family-wise type I error rate for simultaneous
testing is controlled in the strong sense by the application of the closed
testing procedure. Critical values for intersection hypothesis tests are
derived using multivariate normal distributions, reflecting the joint
distribution of composite population test statistics under the null hypothesis.
For sample size calculation and sample size re-calculation multivariate normal
distributions are derived which describe the joint distribution of composite
population test statistics under an assumed alternative hypothesis. Simulations
demonstrate the strong control of the family-wise type I error rate in fixed
designs and re-calculation designs with blinded sample size re-calculation. The
target power after sample size re-calculation is typically met or close to
being met.
