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Although the relationship between structural and functional progression in glaucoma is well established, there is disagreement on how this association evolves over time. In addressing this issue, we propose a new class of non\u2010Gaussian linear\u2010mixed models to estimate the correlations among subject\u2010specific effects in multivariate longitudinal studies with a skewed distribution of random effects, to be used in a study of glaucoma. This class provides an efficient estimation of subject\u2010specific effects by modeling the skewed random effects through the log\u2010gamma distribution. It also provides more reliable estimates of the correlations between the random effects. To validate the log\u2010gamma assumption against the usual normality assumption of the random effects, we propose a lack\u2010of\u2010fit test using the profile likelihood function of the shape parameter. We apply this method to data from a prospective observation study, the Diagnostic Innovations in Glaucoma Study, to present a statistically significant association between structural and functional change rates that leads to a better understanding of the progression of glaucoma over time.<\/jats:p>","DOI":"10.1002\/bimj.201300001","type":"journal-article","created":{"date-parts":[[2015,6,15]],"date-time":"2015-06-15T11:11:57Z","timestamp":1434366717000},"page":"766-776","source":"Crossref","is-referenced-by-count":7,"title":["Log\u2010gamma linear\u2010mixed effects models for multiple outcomes with application to a longitudinal glaucoma study"],"prefix":"10.1002","volume":"57","author":[{"given":"Peng","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics Zhejiang University  86 Zheda Road Hangzhou Zhejiang 310012 China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dandan","family":"Luo","sequence":"additional","affiliation":[{"name":"Bank of Montreal  Toronto M5X 1A1 Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengfei","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Statistics and Actuarial Science University of Waterloo  Waterloo Ontario N2L 3G1 Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucie","family":"Sharpsten","sequence":"additional","affiliation":[{"name":"Hamilton Glaucoma Center Department of Ophthalmology, University of California  San Diego La Jolla, CA 92093 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Felipe A.","family":"Medeiros","sequence":"additional","affiliation":[{"name":"Hamilton Glaucoma Center Department of Ophthalmology, University of California  San Diego La Jolla, CA 92093 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2015,6,15]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2983618"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2667"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.preteyeres.2010.02.001"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(01)00080-3"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ophtha.2006.05.061"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1442-9071.2012.02770.x"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2010.01435.x"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1167\/iovs.12-10345"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531989"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/61.3.539"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1984.10478064"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2000.01047.x"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000240"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478472"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10474030"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1167\/iovs.05-1584"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-2607(02)00017-2"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1973.10482448"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2007.00824.x"}],"container-title":["Biometrical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fbimj.201300001","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.201300001","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T01:49:44Z","timestamp":1696556984000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/bimj.201300001"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,15]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1002\/bimj.201300001"],"URL":"https:\/\/doi.org\/10.1002\/bimj.201300001","archive":["Portico"],"relation":{},"ISSN":["0323-3847","1521-4036"],"issn-type":[{"value":"0323-3847","type":"print"},{"value":"1521-4036","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,15]]}}}