{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T14:16:48Z","timestamp":1767795408397,"version":"3.49.0"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T00:00:00Z","timestamp":1675728000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100015539","name":"Australian Government","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100015539","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100011779","name":"Brien Holden Vision Institute","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100011779","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Ophthalmic Physiologic Optic"],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Introduction<\/jats:title>\n                    <jats:p>Sampling and describing the distribution of refractive error in populations is critical to understanding eye care needs, refractive differences between groups and factors affecting refractive development. We investigated the ability of mixture models to describe refractive error distributions.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We used key informants to identify raw refractive error datasets and a systematic search strategy to identify published binned datasets of community\u2010representative refractive error. Mixture models combine various component distributions via weighting to describe an observed distribution. We modelled raw refractive error data with a single\u2010Gaussian (normal) distribution, mixtures of two to six Gaussian distributions and an additive model of an exponential and Gaussian (ex\u2010Gaussian) distribution. We tested the relative fitting accuracy of each method via Bayesian Information Criterion (BIC) and then compared the ability of selected models to predict the observed prevalence of refractive error across a range of cut\u2010points for both the raw and binned refractive data.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>We obtained large raw refractive error datasets from the United States and Korea. The ability of our models to fit the data improved significantly from a single\u2010Gaussian to a two\u2010Gaussian\u2010component additive model and then remained stable with \u22653\u2010Gaussian\u2010component mixture models. Means and standard deviations for BIC relative to 1 for the single\u2010Gaussian model, where lower is better, were 0.89\u2009\u00b1\u20090.05, 0.88\u2009\u00b1\u20090.06, 0.89\u2009\u00b1\u20090.06, 0.89\u2009\u00b1\u20090.06 and 0.90\u2009\u00b1\u20090.06 for two\u2010, three\u2010, four\u2010, five\u2010 and six\u2010Gaussian\u2010component models, respectively, tested across US and Korean raw data grouped by age decade. Means and standard deviations for the difference between observed and model\u2010based estimates of refractive error prevalence across a range of cut\u2010points for the raw data were \u22123.0%\u2009\u00b1\u20096.3, 0.5%\u2009\u00b1\u20091.9, 0.6%\u2009\u00b1\u20091.5 and \u22121.8%\u2009\u00b1\u20094.0 for one\u2010, two\u2010 and three\u2010Gaussian\u2010component and ex\u2010Gaussian models, respectively.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>Mixture models appear able to describe the population distribution of refractive error accurately, offering significant advantages over commonly quoted simple summary statistics such as mean, standard deviation and prevalence.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1111\/opo.13105","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T01:13:08Z","timestamp":1675818788000},"page":"445-453","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Improving population\u2010level refractive error monitoring via mixture distributions"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8087-6835","authenticated-orcid":false,"given":"Timothy R.","family":"Fricke","sequence":"first","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"},{"name":"Brien Holden Vision Institute Sydney New\u00a0South Wales Australia"},{"name":"Department of Optometry and Vision Sciences University of Melbourne Melbourne Victoria Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2215-0678","authenticated-orcid":false,"given":"Lisa","family":"Keay","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5866-4446","authenticated-orcid":false,"given":"Serge","family":"Resnikoff","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"},{"name":"Brien Holden Vision Institute Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8856-2483","authenticated-orcid":false,"given":"Nina","family":"Tahhan","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"},{"name":"Brien Holden Vision Institute Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8018-7711","authenticated-orcid":false,"given":"Ornella","family":"Koumbo","sequence":"additional","affiliation":[{"name":"Brien Holden Vision Institute Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9809-9672","authenticated-orcid":false,"given":"Prakash","family":"Paudel","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"},{"name":"Brien Holden Vision Institute Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9907-084X","authenticated-orcid":false,"given":"Lauren N.","family":"Ayton","sequence":"additional","affiliation":[{"name":"Department of Optometry and Vision Sciences University of Melbourne Melbourne Victoria Australia"},{"name":"Department of Surgery (Ophthalmology) University of Melbourne Melbourne Victoria Australia"},{"name":"Centre for Eye Research Australia, Royal Victorian Eye and Ear Hospital Melbourne Victoria Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1101-2870","authenticated-orcid":false,"given":"Alexis Ceecee","family":"Britten\u2010Jones","sequence":"additional","affiliation":[{"name":"Department of Optometry and Vision Sciences University of Melbourne Melbourne Victoria Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8806-5348","authenticated-orcid":false,"given":"Suhyun","family":"Kweon","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Josephine C. H.","family":"Li","sequence":"additional","affiliation":[{"name":"Australian College of Optometry Carlton Victoria Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0908-7280","authenticated-orcid":false,"given":"Ling","family":"Lee","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7835-3357","authenticated-orcid":false,"given":"Peter","family":"Wagner","sequence":"additional","affiliation":[{"name":"School of Optometry and Vision Science University of New South Wales Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8458-4979","authenticated-orcid":false,"given":"Rebecca","family":"Weng","sequence":"additional","affiliation":[{"name":"Brien Holden Vision Institute Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7944-3925","authenticated-orcid":false,"given":"Boris","family":"Beranger","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics University of New South Wales Sydney New\u00a0South Wales Australia"},{"name":"University of New South Wales Data Science Hub (uDASH) University of New South Wales Sydney New South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3144-4507","authenticated-orcid":false,"given":"Jake","family":"Olivier","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics University of New South Wales Sydney New\u00a0South Wales Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,7]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ophtha.2016.01.006"},{"key":"e_1_2_9_3_1","volume-title":"World report on vision","author":"World Health Organization","year":"2019"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1167\/iovs.04-1040"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1167\/iovs.04-1324"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.exer.2013.02.008"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.21500\/20112084.846"},{"key":"e_1_2_9_8_1","article-title":"Mathematical models of refractive distributions suggest different underlying mechanisms in Chinese and Western myopes","volume":"48","author":"Thorn F","year":"2007","journal-title":"Invest Ophthalmol Vis Sci"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1097\/OPX.0000000000000296"},{"key":"e_1_2_9_10_1","unstructured":"FrickeTR KeayL ResnikoffS TahhanN.Global estimates of distance refractive errors and associated vision impairment.Prospero; 2021. 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