Estimating the treatment effect in a subgroup defined by an early post-baseline biomarker measurement in randomized clinical trials with time-to-event endpoint

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.