  Sample size derivation is a crucial element of the planning phase of any
confirmatory trial. A sample size is typically derived based on constraints on
the maximal acceptable type I error rate and a minimal desired power. Here,
power depends on the unknown true effect size. In practice, power is typically
calculated either for the smallest relevant effect size or a likely point
alternative. The former might be problematic if the minimal relevant effect is
close to the null, thus requiring an excessively large sample size. The latter
is dubious since it does not account for the a priori uncertainty about the
likely alternative effect size. A Bayesian perspective on the sample size
derivation for a frequentist trial naturally emerges as a way of reconciling
arguments about the relative a priori plausibility of alternative effect sizes
with ideas based on the relevance of effect sizes. Many suggestions as to how
such `hybrid' approaches could be implemented in practice have been put forward
in the literature. However, key quantities such as assurance, probability of
success, or expected power are often defined in subtly different ways in the
literature. Starting from the traditional and entirely frequentist approach to
sample size derivation, we derive consistent definitions for the most commonly
used `hybrid' quantities and highlight connections, before discussing and
demonstrating their use in the context of sample size derivation for clinical
trials.
