{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T12:22:51Z","timestamp":1788870171185,"version":"build-2803163510"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T00:00:00Z","timestamp":1375747200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"},{"start":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T00:00:00Z","timestamp":1375747200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T00:00:00Z","timestamp":1375747200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"UK MRC","award":["A731-5QL14"],"award-info":[{"award-number":["A731-5QL14"]}]},{"name":"UK MRC","award":["A735-5QP21"],"award-info":[{"award-number":["A735-5QP21"]}]},{"name":"UK MRC","award":["G0701619"],"award-info":[{"award-number":["G0701619"]}]},{"name":"UK MRC Unit Programme","award":["U105260558"],"award-info":[{"award-number":["U105260558"]}]},{"name":"UK MRC Unit Programme","award":["MC-US-A030-0015"],"award-info":[{"award-number":["MC-US-A030-0015"]}]}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2014,1,15]]},"abstract":"<jats:p>\n                    We are concerned with multiple imputation of the ratio of two variables, which is to be used as a covariate in a regression analysis. If the numerator and denominator are not missing simultaneously, it seems sensible to make use of the observed variable in the imputation model. One such strategy is to impute missing values for the numerator and denominator, or the log\u2010transformed numerator and denominator, and then calculate the ratio of interest; we call this \u2018passive\u2019 imputation. Alternatively, missing ratio values might be imputed directly, with or without the numerator and\/or the denominator in the imputation model; we call this \u2018active\u2019 imputation. In two motivating datasets, one involving body mass index as a covariate and the other involving the ratio of total to high\u2010density lipoprotein cholesterol, we assess the sensitivity of results to the choice of imputation model and, as an alternative, explore fully Bayesian joint models for the outcome and incomplete ratio. Fully Bayesian approaches using Win\n                    <jats:sc>bugs<\/jats:sc>\n                    were unusable in both datasets because of computational problems. In our first dataset, multiple imputation results are similar regardless of the imputation model; in the second, results are sensitive to the choice of imputation model. Sensitivity depends strongly on the coefficient of variation of the ratio's denominator. A simulation study demonstrates that passive imputation without transformation is risky because it can lead to downward bias when the coefficient of variation of the ratio's denominator is larger than about 0.1. Active imputation or passive imputation after log\u2010transformation is preferable. \u00a9 2013 The Authors. Statistics in Medicine published by John Wiley &amp; Sons, Ltd.\n                  <\/jats:p>","DOI":"10.1002\/sim.5935","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T12:17:35Z","timestamp":1375791455000},"page":"88-104","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Multiple imputation for an incomplete covariate that is a ratio"],"prefix":"10.1002","volume":"33","author":[{"given":"Tim P.","family":"Morris","sequence":"first","affiliation":[{"name":"Hub for Trials Methodology Research MRC Clinical Trials Unit  Aviation House, 125 Kingsway London WC2B 6NH U.K."},{"name":"MRC Biostatistics Unit Institute of Public Health  Robinson Way Cambridge CB2 0SR U.K."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ian R.","family":"White","sequence":"additional","affiliation":[{"name":"MRC Biostatistics Unit Institute of Public Health  Robinson Way Cambridge CB2 0SR 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