{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T22:17:33Z","timestamp":1768947453926,"version":"3.49.0"},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Regulations of chemical exposures often focus on individual substances, neglecting the amplified toxicity that can arise from multiple concurrent exposures. We propose a novel methodology to identify critical thresholds in multivariate exposure spaces and estimate the effects of policy interventions that limit exposures within these thresholds. Our approach employs a recursive partitioning algorithm integrated with targeted maximum likelihood estimation (TMLE) to discover regions in the exposure space where the expected outcome is minimized or maximized. To address potential overfitting bias from using the same data for threshold discovery and effect estimation, we utilize cross-validated TMLE (CV-TMLE), which ensures asymptotic unbiasedness and efficiency. Simulation studies demonstrate convergence to the optimal exposure region and accurate estimation of intervention effects. We apply our method to synthetic mixture data, successfully identifying true interactions, and to NHANES data, discovering harmful metal exposures affecting telomere length. Our approach provides a flexible and interpretable framework for policy-makers to assess the impact of exposure regulations, and we offer an open-source implementation in the\n                    <jats:monospace>CVtreeMLE<\/jats:monospace>\n                    R package.\n                  <\/jats:p>","DOI":"10.1515\/jci-2024-0056","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T16:43:10Z","timestamp":1767976990000},"source":"Crossref","is-referenced-by-count":0,"title":["Discovery of critical thresholds in mixed exposures and estimation of policy intervention effects"],"prefix":"10.1515","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5515-6307","authenticated-orcid":false,"given":"David B.","family":"McCoy","sequence":"first","affiliation":[{"name":"Division of Biostatistics , University of California , Berkeley , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan","family":"Hubbard","sequence":"additional","affiliation":[{"name":"Division of Biostatistics , University of California , Berkeley , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"van der Laan","sequence":"additional","affiliation":[{"name":"Division of Biostatistics , University of California , Berkeley , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4853-6130","authenticated-orcid":false,"given":"Alejandro","family":"Schuler","sequence":"additional","affiliation":[{"name":"Division of Biostatistics , University of California , Berkeley , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2026,1,9]]},"reference":[{"key":"2026012009030699183_j_jci-2024-0056_ref_001","unstructured":"Landrigan, PJ, Goldman, LR. Children\u2019s health and the environment: public health implications of exposures to neurotoxic chemicals in early childhood. Pediatrics 2006;118:259\u201367."},{"key":"2026012009030699183_j_jci-2024-0056_ref_002","unstructured":"Vrijheid, M, Slama, R, van den Brandt, PA. Mixtures of environmental exposures and health: challenges and opportunities for environmental epidemiology. Int J Environ Res Publ Health 2009;6:205\u201323."},{"key":"2026012009030699183_j_jci-2024-0056_ref_003","unstructured":"Kortenkamp, A. Low-dose mixture effects of endocrine disrupters: implications for risk assessment and human health. Environ Health Perspect 2014;122:A10\u201315."},{"key":"2026012009030699183_j_jci-2024-0056_ref_004","unstructured":"Braun, JM, Gennings, C. The emerging science of environmental mixtures and the future of risk assessment. Environ Health Perspect 2018;126:128\u201334."},{"key":"2026012009030699183_j_jci-2024-0056_ref_005","unstructured":"National Research Council. Cumulative environmental risks: building an integrated framework to better inform decision-making. Washington, DC: National Academies Press; 2018."},{"key":"2026012009030699183_j_jci-2024-0056_ref_006","unstructured":"NRC. Phthalates and cumulative risk assessment: the tasks ahead. Washington, DC: National Academies Press; 2008."},{"key":"2026012009030699183_j_jci-2024-0056_ref_007","doi-asserted-by":"crossref","unstructured":"Carlin, DJ, Rider, CV, Woychik, R, Birnbaum, LS. Unraveling the health effects of environmental mixtures: an niehs priority. Environ Health Perspect 2013;121:A6\u20138. https:\/\/doi.org\/10.1289\/ehp.1206182.","DOI":"10.1289\/ehp.1206182"},{"key":"2026012009030699183_j_jci-2024-0056_ref_008","doi-asserted-by":"crossref","unstructured":"Keil, AP, Buckley, JP, O\u2019Brien, KM, Ferguson, KK, Zhao, S, White, AJ. A quantile-based g-computation approach to addressing the effects of exposure mixtures. arXiv 2019;128:1\u201310. https:\/\/doi.org\/10.1097\/01.ee9.0000606120.58494.9d.","DOI":"10.1289\/EHP5838"},{"key":"2026012009030699183_j_jci-2024-0056_ref_009","doi-asserted-by":"crossref","unstructured":"De Vocht, F, Cherry, N, Wakefield, J. A Bayesian mixture modeling approach for assessing the effects of correlated exposures in case-control studies. J\u00a0Expo Sci Environ Epidemiol 2012;22:352\u201360. https:\/\/doi.org\/10.1038\/jes.2012.22.","DOI":"10.1038\/jes.2012.22"},{"key":"2026012009030699183_j_jci-2024-0056_ref_010","doi-asserted-by":"crossref","unstructured":"Bobb, JF, Valeri, L, Henn, BC, Christiani, DC, Wright, RO, Mazumdar, M, et al.. Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures. Biostatistics 2014;16:493\u2013508. https:\/\/doi.org\/10.1093\/biostatistics\/kxu058.","DOI":"10.1093\/biostatistics\/kxu058"},{"key":"2026012009030699183_j_jci-2024-0056_ref_011","doi-asserted-by":"crossref","unstructured":"van der Laan, MJ, Rose, S. Targeted learning: causal inference for observational and experimental data. Springer Series in Statistics. Springer New York; 2011. Available from: https:\/\/books.google.com\/books?id=RGnSX5aCAgQC.","DOI":"10.1007\/978-1-4419-9782-1"},{"key":"2026012009030699183_j_jci-2024-0056_ref_012","doi-asserted-by":"crossref","unstructured":"van der Laan, MJ, Rose, S. Targeted learning in data science: causal inference for complex longitudinal studies. Springer Series in Statistics. Springer International Publishing; 2018. Available from: https:\/\/books.google.com\/books?id=vKFTDwAAQBAJ.","DOI":"10.1007\/978-3-319-65304-4"},{"key":"2026012009030699183_j_jci-2024-0056_ref_013","doi-asserted-by":"crossref","unstructured":"Zheng, W, van der Laan, MJ. Asymptotic theory for cross-validated targeted maximum likelihood estimation. U.C. Berkeley Division of Biostatistics Working Paper Series, (273); 2010. Available from: http:\/\/biostats.bepress.com\/ucbbiostat\/paper273\/.","DOI":"10.2202\/1557-4679.1181"},{"key":"2026012009030699183_j_jci-2024-0056_ref_014","doi-asserted-by":"crossref","unstructured":"Hubbard, AE, Kherad-Pajouh, S, Van Der Laan, MJ. Statistical inference for data adaptive target parameters. Int J Biostat 2016;12:3\u201319. https:\/\/doi.org\/10.1515\/ijb-2015-0013.","DOI":"10.1515\/ijb-2015-0013"},{"key":"2026012009030699183_j_jci-2024-0056_ref_015","doi-asserted-by":"crossref","unstructured":"McCoy, D, Hubbard, A, Van der Laan, M. Cvtreemle: efficient estimation of mixed exposures using data adaptive decision trees and cross-validated targeted maximum likelihood estimation in r. J\u00a0Open Source Softw 2023;8:4181. https:\/\/doi.org\/10.21105\/joss.04181.","DOI":"10.21105\/joss.04181"},{"key":"2026012009030699183_j_jci-2024-0056_ref_016","doi-asserted-by":"crossref","unstructured":"Li, H, Rosete, S, Coyle, J, Phillips, RV, Hejazi, NS, Malenica, I, et al.. Evaluating the robustness of targeted maximum likelihood estimators via realistic simulations in nutrition intervention trials. Stat Med 2022;41:2132\u201365. https:\/\/doi.org\/10.1002\/sim.9348.","DOI":"10.1002\/sim.9348"},{"key":"2026012009030699183_j_jci-2024-0056_ref_017","unstructured":"Breiman, L, Friedman, J, Olshen, R, Stone, C. Classification and regression trees. Belmont, CA: Wadsworth International Group; 1984."},{"key":"2026012009030699183_j_jci-2024-0056_ref_018","doi-asserted-by":"crossref","unstructured":"Hothorn, T, Hornik, K, Zeileis, A. Unbiased recursive partitioning: a conditional inference framework. J\u00a0Comput Graph Stat 2006;15:651\u201374. https:\/\/doi.org\/10.1198\/106186006X133933.","DOI":"10.1198\/106186006X133933"},{"key":"2026012009030699183_j_jci-2024-0056_ref_019","doi-asserted-by":"crossref","unstructured":"Athey, S, Imbens, GW. Recursive partitioning for heterogeneous causal effects. Proc Natl Acad Sci 2016;113:7353\u201360. https:\/\/doi.org\/10.1073\/pnas.1510489113.","DOI":"10.1073\/pnas.1510489113"},{"key":"2026012009030699183_j_jci-2024-0056_ref_020","doi-asserted-by":"crossref","unstructured":"Wager, S, Athey, S. Estimation and inference of heterogeneous treatment effects using random forests. J\u00a0Am Stat Assoc 2018;113:1228\u201342. https:\/\/doi.org\/10.1080\/01621459.2017.1319839. First posted as arXiv:1510.04342 [stat.ME] in 2015.","DOI":"10.1080\/01621459.2017.1319839"},{"key":"2026012009030699183_j_jci-2024-0056_ref_021","doi-asserted-by":"crossref","unstructured":"Hubbard, AE, Kennedy, CJ, van der Laan, MJ. Data-adaptive target parameters. In: van der Laan, MJ, Rose, S, editors. Targeted learning in data science, Springer Series in Statistics. Cham, Switzerland: Springer; 2018:125\u201342 pp.","DOI":"10.1007\/978-3-319-65304-4_9"},{"key":"2026012009030699183_j_jci-2024-0056_ref_022","doi-asserted-by":"crossref","unstructured":"Bertsimas, D, Dunn, J. Optimal classification trees. Mach Learn 2017;106:1039\u201382. https:\/\/doi.org\/10.1007\/s10994-017-5633-9. First posted as arXiv:1702.01761 [cs.LG].","DOI":"10.1007\/s10994-017-5633-9"},{"key":"2026012009030699183_j_jci-2024-0056_ref_023","doi-asserted-by":"crossref","unstructured":"Hu, B, Rudin, C, Seltzer, M. Optimal decision trees. Oper Res 2020;68:1517\u201337. https:\/\/doi.org\/10.1287\/opre.2019.1918. First posted as arXiv:1810.05041 [cs.LG].","DOI":"10.1287\/opre.2019.1918"},{"key":"2026012009030699183_j_jci-2024-0056_ref_024","unstructured":"Lage, IJ, Sudjianto, A, Zeng, X, Hooker, G. A general framework for globally and locally optimal decision trees. In: Proceedings of the 39th international conference on machine learning (ICML); 2022:11942\u201359 pp. First posted as arXiv:2204.10053 [cs.LG]."},{"key":"2026012009030699183_j_jci-2024-0056_ref_025","doi-asserted-by":"crossref","unstructured":"van der Vaart, AW. Asymptotic statistics. Cambridge, UK: Cambridge University Press; 1998.","DOI":"10.1017\/CBO9780511802256"},{"key":"2026012009030699183_j_jci-2024-0056_ref_026","doi-asserted-by":"crossref","unstructured":"van der Laan, MJ, Polley, EC, Hubbard, AE. Super learner. Stat Appl Genet Mol Biol 2007;6:1\u201323. https:\/\/doi.org\/10.2202\/1544-6115.1309.","DOI":"10.2202\/1544-6115.1309"},{"key":"2026012009030699183_j_jci-2024-0056_ref_027","doi-asserted-by":"crossref","unstructured":"Silver, D, Huang, A, Maddison, CJ, Guez, A, Sifre, L, Van Den Driessche, G, et al.. Mastering the game of go with deep neural networks and tree search. Nature 2016;529:484\u20139. https:\/\/doi.org\/10.1038\/nature16961.","DOI":"10.1038\/nature16961"},{"key":"2026012009030699183_j_jci-2024-0056_ref_028","unstructured":"Silver, D, Schrittwieser, J, Simonyan, K, Antonoglou, I, Huang, A, Guez, A, et al.. Mastering chess and shogi by self-play with a general reinforcement learning algorithm. arXiv preprint arXiv:1712.01815 2017."},{"key":"2026012009030699183_j_jci-2024-0056_ref_029","doi-asserted-by":"crossref","unstructured":"Silver, D, Schrittwieser, J, Simonyan, K, Antonoglou, I, Huang, A, Guez, A, et al.. Mastering the game of go without human knowledge. Nature 2017;550:354\u20139. https:\/\/doi.org\/10.1038\/nature24270.","DOI":"10.1038\/nature24270"}],"container-title":["Journal of Causal Inference"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jci-2024-0056\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jci-2024-0056\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T09:03:23Z","timestamp":1768899803000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jci-2024-0056\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,1]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]},"published-print":{"date-parts":[[2026,1,23]]}},"alternative-id":["10.1515\/jci-2024-0056"],"URL":"https:\/\/doi.org\/10.1515\/jci-2024-0056","relation":{},"ISSN":["2193-3685"],"issn-type":[{"value":"2193-3685","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,1]]},"article-number":"20240056"}}