We present research on clinical trials with a sensitive subpopulation of patients, that is, a subgroup that is more likely to benefit from the treatment than the overall population. Given a sensitive subgroup defined by a prespecified classifier, for example, a clinical marker or pharmacogenomic marker, the trial’s outcome is declared positive if the treatment effect is established in the overall population or in the subgroup. We provide a summary of key considerations in clinical trials with a sensitive subgroup, including multiplicity and enrichment adjustments as well as optimality considerations in the analysis strategy. The methodology proposed in this article is illustrated using a neuroscience clinical trial and its operating characteristics are accessed via a simulation study. Key Words: Clinical trials; Enriched clinical trials; Sensitive population; Type I error rate control; Weighted power.