{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:49:47Z","timestamp":1783039787740,"version":"3.54.6"},"reference-count":27,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2018,10,3]],"date-time":"2018-10-03T00:00:00Z","timestamp":1538524800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MC_UU_12023\/21"],"award-info":[{"award-number":["MC_UU_12023\/21"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["G0800270"],"award-info":[{"award-number":["G0800270"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000274","name":"British Heart Foundation","doi-asserted-by":"publisher","award":["SP\/09\/002"],"award-info":[{"award-number":["SP\/09\/002"]}],"id":[{"id":"10.13039\/501100000274","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2019,2,10]]},"abstract":"<jats:p>Non\u2010linear exposure\u2010outcome relationships such as between body mass index (BMI) and mortality are common. They are best explored as continuous functions using individual participant data from multiple studies. We explore two two\u2010stage methods for meta\u2010analysis of such relationships, where the confounder\u2010adjusted relationship is first estimated in a non\u2010linear regression model in each study, then combined across studies. The \u201cmetacurve\u201d approach combines the estimated curves using multiple meta\u2010analyses of the relative effect between a given exposure level and a reference level. The \u201cmvmeta\u201d approach combines the estimated model parameters in a single multivariate meta\u2010analysis. Both methods allow the exposure\u2010outcome relationship to differ across studies. Using theoretical arguments, we show that the methods differ most when covariate distributions differ across studies; using simulated data, we show that mvmeta gains precision but metacurve is more robust to model mis\u2010specification. We then compare the two methods using data from the Emerging Risk Factors Collaboration on BMI, coronary heart disease events, and all\u2010cause mortality (&gt;80 cohorts, &gt;18\u2009000 events). For each outcome, we model BMI using fractional polynomials of degree 2 in each study, with adjustment for confounders. For metacurve, the powers defining the fractional polynomials may be study\u2010specific or common across studies. For coronary heart disease, metacurve with common powers and mvmeta correctly identify a small increase in risk in the lowest levels of BMI, but metacurve with study\u2010specific powers does not. For all\u2010cause mortality, all methods identify a steep U\u2010shape. The metacurve and mvmeta methods perform well in combining complex exposure\u2010disease relationships across studies.<\/jats:p>","DOI":"10.1002\/sim.7974","type":"journal-article","created":{"date-parts":[[2018,10,5]],"date-time":"2018-10-05T15:17:44Z","timestamp":1538752664000},"page":"326-338","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Meta\u2010analysis of non\u2010linear exposure\u2010outcome relationships using individual participant data: A comparison of two methods"],"prefix":"10.1002","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6718-7661","authenticated-orcid":false,"given":"Ian R.","family":"White","sequence":"first","affiliation":[{"name":"MRC Clinical Trials Unit University College London  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephen","family":"Kaptoge","sequence":"additional","affiliation":[{"name":"Department of Public Health and Primary Care University of Cambridge  Cambridge UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick","family":"Royston","sequence":"additional","affiliation":[{"name":"MRC Clinical Trials Unit University College London  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Willi","family":"Sauerbrei","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Medical Center \u2013 University of Freiburg  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"name":"The Emerging Risk Factors Collaboration","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2018,10,3]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10654-009-9412-1"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1160"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1097\/00001648-199507000-00025"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2331"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470770771"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-19425-7"},{"key":"e_1_2_9_8_1","volume-title":"Practical Guide to Splines: Revised Edition","author":"De Boor CA","year":"2001"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010404"},{"key":"e_1_2_9_10_1","volume-title":"Generalized Additive Models","author":"Hastie T","year":"1990"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4333"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1177\/1536867X0900900103"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.5471"},{"issue":"12","key":"e_1_2_9_14_1","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/s10654-007-9165-7","article-title":"The emerging risk factors collaboration: analysis of individual data on lipid, inflammatory and other markers in over 1.1 million participants in 104 prospective studies of cardiovascular diseases","volume":"22","author":"Emerging Risk Factors Collaboration","year":"2007","journal-title":"Eur J Epidemiol"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1001\/jama.2009.1619"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(11)60105-0"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(16)30175-1"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4380-9_37"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.2307\/2986270"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949650108812083"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-985X.2008.00552.x"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.3102\/10769986010002075"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280215611702"},{"key":"e_1_2_9_24_1","unstructured":"World Health Organization.Obesity: Preventing and managing the global epidemic (WHO Technical Report Series 894).Geneva Switzerland:World Health Organization;2000. 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