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We introduce a computationally feasible approach for subgroup selection in the context of multivariate isotonic regression based on martingale tests and multiple testing procedures for logically structured hypotheses. Our proposed procedure satisfies a non-asymptotic, uniform Type I error rate guarantee with power that attains the minimax optimal rate up to poly-logarithmic factors. Extensions cover classification, isotonic quantile regression, and heterogeneous treatment effect settings. Numerical studies on both simulated and real data confirm the practical effectiveness of our proposal, which is implemented in the R package ISS.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae083","type":"journal-article","created":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T15:41:10Z","timestamp":1722526870000},"page":"132-156","source":"Crossref","is-referenced-by-count":5,"title":["Isotonic subgroup selection"],"prefix":"10.1093","volume":"87","author":[{"given":"Manuel M","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"Statistical Laboratory, University of Cambridge , Cambridge ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Henry W J","family":"Reeve","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol , Bristol ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Timothy I","family":"Cannings","sequence":"additional","affiliation":[{"name":"School of 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