  Biomarker measurements can be relatively easy and quick to obtain and they
are useful to investigate whether a compound works as intended on a
mechanistic, pharmacological level. In some situations, it is realistic to
assume that patients, whose post-baseline biomarker levels indicate that they
do not sufficiently respond to the drug, are also unlikely to respond on
clinically relevant long term outcomes (such as time-to-event). However the
determination of the treatment effect in the subgroup of patients that
sufficiently respond to the drug according to their biomarker levels is not
straightforward: It is unclear which patients on placebo would have responded
had they been given the treatment, so that naive comparisons between treatment
and placebo will not estimate the treatment effect of interest. The purpose of
this paper is to investigate assumptions necessary to obtain causal conclusions
in such a setting, utilizing the formalism of causal inference. Three
approaches for estimation of subgroup effects will be developed and illustrated
using simulations and a case-study.
