{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T03:09:30Z","timestamp":1779246570428,"version":"3.51.4"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2024,11,9]],"date-time":"2024-11-09T00:00:00Z","timestamp":1731110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100004191","name":"Novo Nordisk","doi-asserted-by":"publisher","award":["NNF22OC0076595"],"award-info":[{"award-number":["NNF22OC0076595"]}],"id":[{"id":"10.13039\/501100004191","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In instrumental variable (IV) settings, such as imperfect randomized trials and observational studies with Mendelian randomization, one may encounter a continuous exposure, the causal effect of which is not of true interest. Instead, scientific interest may lie in a coarsened version of this exposure. Although there is a lengthy literature on the impact of coarsening of an exposure with several works focusing specifically on IV settings, all methods proposed in this literature require parametric assumptions. Instead, just as in the standard IV setting, one can consider partial identification via bounds making no parametric assumptions. This was first pointed out in Alexander Balke\u2019s PhD dissertation. We extend and clarify his work and derive novel bounds in several settings, including for a three-level IV, which will most likely be the case in Mendelian randomization. We demonstrate our findings in two real data examples, a randomized trial for peanut allergy in infants and a Mendelian randomization setting investigating the effect of homocysteine on cardiovascular disease.<\/jats:p>","DOI":"10.1093\/biostatistics\/kxae042","type":"journal-article","created":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T07:16:38Z","timestamp":1727421398000},"source":"Crossref","is-referenced-by-count":1,"title":["The impact of coarsening an exposure on partial identifiability in instrumental variable settings"],"prefix":"10.1093","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0504-8404","authenticated-orcid":false,"given":"Erin E","family":"Gabriel","sequence":"first","affiliation":[{"name":"Section of Biostatistics, Department of Public Health, University of Copenhagen , \u00d8ster Farimagsgade 5 , 1353 K\u00f8benhavn K, Copenhagen,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1279-8676","authenticated-orcid":false,"given":"Michael C","family":"Sachs","sequence":"additional","affiliation":[{"name":"Section of Biostatistics, Department of Public Health, University of Copenhagen , \u00d8ster Farimagsgade 5 , 1353 K\u00f8benhavn K, Copenhagen,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5226-6685","authenticated-orcid":false,"given":"Arvid","family":"Sj\u00f6lander","sequence":"additional","affiliation":[{"name":"Department of Medical Epidemiology and Biostatistics, Karolinska Institutet , Nobels v\u00e4g 12A , 17177, Stockholm,","place":["Sweden"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,11,9]]},"reference":[{"key":"2026031108011570200_kxae042-B1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1111\/1468-0262.00114","article-title":"Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space","volume":"68","author":"Andrews","year":"2000","journal-title":"Econometrica"},{"key":"2026031108011570200_kxae042-B2","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1080\/01621459.1995.10476535","article-title":"Two-stage least squares estimation of average causal effects in models with variable treatment intensity","volume":"90","author":"Angrist","year":"1995","journal-title":"J Am Stat Assoc"},{"key":"2026031108011570200_kxae042-B3","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1080\/01621459.1997.10474074","article-title":"Bounds on treatment effects from studies with imperfect compliance","volume":"92","author":"Balke","year":"1997","journal-title":"J Am Stat Assoc"},{"key":"2026031108011570200_kxae042-B4","author":"Balke","year":"1995"},{"key":"2026031108011570200_kxae042-B5","first-page":"967","article-title":"On the choice of m in the m out of n bootstrap and confidence bounds for extrema","volume":"18","author":"Bickel","year":"2008","journal-title":"Stat Sin"},{"key":"2026031108011570200_kxae042-B6","first-page":"48","volume-title":"Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence","author":"Bonet","year":"2001"},{"key":"2026031108011570200_kxae042-B7","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1007\/s10654-018-0424-6","article-title":"Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates","volume":"33","author":"Burgess","year":"2018","journal-title":"Eur J Epidemiol"},{"key":"2026031108011570200_kxae042-B8","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1177\/0962280206077743","article-title":"Mendelian randomization as an instrumental variable approach to causal inference","volume":"16","author":"Didelez","year":"2007","journal-title":"Stat Methods Med Res"},{"key":"2026031108011570200_kxae042-B9","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1056\/NEJMoa1414850","article-title":"Randomized trial of peanut consumption in infants at risk for peanut allergy","volume":"372","author":"Du Toit","year":"2015","journal-title":"N Engl J Med"},{"key":"2026031108011570200_kxae042-B10","doi-asserted-by":"crossref","DOI":"10.1093\/biomet\/asae020","article-title":"Sharp symbolic nonparametric bounds for measures of benefit in observational and imperfect randomized studies with ordinal outcomes","author":"Gabriel","year":"2024","journal-title":"Biometrika"},{"key":"2026031108011570200_kxae042-B11","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1080\/01621459.2021.1950734","article-title":"Nonparametric bounds for causal effects in imperfect randomized experiments","volume":"118","author":"Gabriel","year":"2023","journal-title":"J Am Stat Assoc"},{"key":"2026031108011570200_kxae042-B12","doi-asserted-by":"crossref","first-page":"2244","DOI":"10.1214\/aos\/1176348396","article-title":"Ignorability and coarse data","volume":"19","author":"Heitjan","year":"1991","journal-title":"Ann Stat"},{"key":"2026031108011570200_kxae042-B13","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1093\/ije\/dyab208","article-title":"Interpreting Mendelian-randomization estimates of the effects of categorical exposures such as disease status and educational attainment","volume":"51","author":"Howe","year":"2022","journal-title":"Int J Epidemiol"},{"key":"2026031108011570200_kxae042-B14","doi-asserted-by":"crossref","first-page":"53","DOI":"10.32614\/RJ-2023-083","article-title":"Accessible computation of tight symbolic bounds on causal effects using an intuitive graphical interface","volume":"15","author":"Jonzon","year":"2023","journal-title":"R J"},{"key":"2026031108011570200_kxae042-B15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1093\/pan\/mpw007","article-title":"Coarsening bias: how coarse treatment measurement upwardly biases instrumental variable estimates","volume":"24","author":"Marshall","year":"2016","journal-title":"Politic Anal"},{"key":"2026031108011570200_kxae042-B16","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1093\/ajcn\/77.1.63","article-title":"Thermolabile methylenetetrahydrofolate reductase, homocysteine, and cardiovascular disease risk: the European Concerted Action Project","volume":"77","author":"Meleady","year":"2003","journal-title":"Am J Clin Nutrition"},{"key":"2026031108011570200_kxae042-B17","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1177\/1536867X1101100302","article-title":"Nonparametric bounds for the causal effect in a binary instrumental-variable model","volume":"11","author":"Palmer","year":"2011","journal-title":"Stata J"},{"key":"2026031108011570200_kxae042-B18","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1080\/10618600.2022.2071905","article-title":"A general method for deriving tight symbolic bounds on causal effects","volume":"32","author":"Sachs","year":"2023","journal-title":"J Comput Graph Stat"},{"key":"2026031108011570200_kxae042-B19","first-page":"264","author":"Stitelman","year":"2010"},{"key":"2026031108011570200_kxae042-B20","doi-asserted-by":"crossref","first-page":"2523","DOI":"10.1002\/sim.9368","article-title":"Nonparametric bounds in two-sample summary-data Mendelian randomization: some cautionary tales for practice","volume":"41","author":"Trane","year":"2022","journal-title":"Stat Med"},{"key":"2026031108011570200_kxae042-B21","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1002\/gepi.22376","article-title":"Mendelian randomisation with coarsened exposures","volume":"45","author":"Tudball","year":"2021","journal-title":"Genet Epidemiol"},{"key":"2026031108011570200_kxae042-B22","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1214\/11-STS360","article-title":"On instrumental variables estimation of causal odds ratios","volume":"26","author":"Vansteelandt","year":"2011","journal-title":"Stat Sci"},{"key":"2026031108011570200_kxae042-B23","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1080\/01621459.2018.1469993","article-title":"Inverse probability weighted estimation of risk under representative interventions in observational studies","volume":"114","author":"Young","year":"2019","journal-title":"J Am Stat Assoc"}],"container-title":["Biostatistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biostatistics\/advance-article-pdf\/doi\/10.1093\/biostatistics\/kxae042\/60576154\/kxae042.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biostatistics\/article-pdf\/26\/1\/kxae042\/60576154\/kxae042.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biostatistics\/article-pdf\/26\/1\/kxae042\/60576154\/kxae042.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:01:25Z","timestamp":1773230485000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biostatistics\/article\/doi\/10.1093\/biostatistics\/kxae042\/7888835"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,9]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,12,31]]}},"URL":"https:\/\/doi.org\/10.1093\/biostatistics\/kxae042","relation":{},"ISSN":["1468-4357"],"issn-type":[{"value":"1468-4357","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025]]},"published":{"date-parts":[[2024,11,9]]},"article-number":"kxae042"}}