{"paper":{"title":"Nonparametric inference for sublevel-set probabilities of conditional average treatment effect functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The probability that a conditional average treatment effect falls below a given threshold produces a monotone curve summarizing treatment heterogeneity.","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Anders Munch, Thomas A. Gerds","submitted_at":"2026-05-14T20:01:21Z","abstract_excerpt":"The average treatment effect can obscure important heterogeneity when individuals respond differently to a treatment. While the conditional average treatment effect (CATE) function captures such heterogeneity, it is difficult to communicate when it depends on many covariates. Sublevels sets of a multivariate CATE function are equally complicated objects, but the probability of a sublevel set of a CATE function is a single number with a simple interpretation as the proportion of individuals whose expected treatment effect does not exceed a prespecified threshold. By varying the threshold, a uni"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The probability of a sublevel set of a CATE function is a single number with a simple interpretation as the proportion of individuals whose expected treatment effect does not exceed a prespecified threshold. By varying the threshold, a univariate monotone curve appears which can be used to visualize the overall type and degree of heterogeneity in a population. We formalize this curve as a target parameter and show that it is not pathwise differentiable under a nonparametric model.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The CATE function is identifiable from observed data under randomized treatment assignment, allowing the sublevel-set probabilities to be targeted and estimated via monotone function techniques combined with machine learning, as used in the numerical studies based on synthesized randomized trial data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Develops Grenander-type and debiased machine learning estimators for the sublevel-set probability curve of the CATE function, shown to be non-pathwise differentiable, along with its piecewise linear approximation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The probability that a conditional average treatment effect falls below a given threshold produces a monotone curve summarizing treatment heterogeneity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f1b8615aa20373a341b9f791e53533917e1ab5a9f3b7f6c12cbb9ce11868e170"},"source":{"id":"2605.15373","kind":"arxiv","version":1},"verdict":{"id":"d17e324e-ea83-4eb8-b14d-e702e3d1769a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T15:22:24.254666Z","strongest_claim":"The probability of a sublevel set of a CATE function is a single number with a simple interpretation as the proportion of individuals whose expected treatment effect does not exceed a prespecified threshold. By varying the threshold, a univariate monotone curve appears which can be used to visualize the overall type and degree of heterogeneity in a population. We formalize this curve as a target parameter and show that it is not pathwise differentiable under a nonparametric model.","one_line_summary":"Develops Grenander-type and debiased machine learning estimators for the sublevel-set probability curve of the CATE function, shown to be non-pathwise differentiable, along with its piecewise linear approximation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The CATE function is identifiable from observed data under randomized treatment assignment, allowing the sublevel-set probabilities to be targeted and estimated via monotone function techniques combined with machine learning, as used in the numerical studies based on synthesized randomized trial data.","pith_extraction_headline":"The probability that a conditional average treatment effect falls below a given threshold produces a monotone curve summarizing treatment heterogeneity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15373/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T15:31:17.878883Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:30:47.442164Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.184111Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.734431Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6f4de12924b6a0ef4145800e6eafde2bc122d7c8e6ed3b83e2952ed3668691d3"},"references":{"count":64,"sample":[{"doi":"","year":2007,"title":"J.-Y. 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