{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T09:49:32Z","timestamp":1790070572348,"version":"4.0.1"},"reference-count":46,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T00:00:00Z","timestamp":1333324800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p>Summary<\/jats:p>\n                  <jats:p>\n                    Two-part random effects models (Olsen and Schafer,\n                    <jats:sup>1<\/jats:sup>\n                    Tooze et al.\n                    <jats:sup>2<\/jats:sup>\n                    ) have been applied to repeated measures of semi-continuous data, characterized by a mixture of a substantial proportion of zero values and a skewed distribution of positive values. In the original formulation of this model, the natural logarithm of the positive values is assumed to follow a normal distribution with a constant variance parameter. In this article, we review and consider three extensions of this model, allowing the positive values to follow (a) a generalized gamma distribution, (b) a log-skew-normal distribution, and (c) a normal distribution after the Box-Cox transformation. We allow for the possibility of heteroscedasticity. Maximum likelihood estimation is shown to be conveniently implemented in SAS Proc NLMIXED. The performance of the methods is compared through applications to daily drinking records in a secondary data analysis from a randomized controlled trial of topiramate for alcohol dependence treatment. We find that all three models provide a significantly better fit than the log-normal model, and there exists strong evidence for heteroscedasticity. We also compare the three models by the likelihood ratio tests for non-nested hypotheses (Vuong\n                    <jats:sup>3<\/jats:sup>\n                    ). The results suggest that the generalized gamma distribution provides the best fit, though no statistically significant differences are found in pairwise model comparisons.\n                  <\/jats:p>","DOI":"10.1177\/0962280212443324","type":"journal-article","created":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T21:56:13Z","timestamp":1333403773000},"page":"133-152","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":44,"title":["Analyzing repeated measures semi-continuous data, with application to an alcohol dependence study"],"prefix":"10.1177","volume":"25","author":[{"given":"Lei","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Preventive Medicine, Northwestern University, Chicago, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert L","family":"Strawderman","sequence":"additional","affiliation":[{"name":"Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bankole A","family":"Johnson","sequence":"additional","affiliation":[{"name":"Department of Psychiatry and Neurobehavioral Sciences, University of Virginia, Charlottesville, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John M","family":"O'Quigley","sequence":"additional","affiliation":[{"name":"Laboratoire de Statistique Th\u00e9orique et Appliqu\u00e9e Universit\u00e9 Pierre et Marie Curie, Paris VI, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2012,4,2]]},"reference":[{"key":"bibr1-0962280212443324","doi-asserted-by":"publisher","DOI":"10.1198\/016214501753168389"},{"key":"bibr2-0962280212443324","doi-asserted-by":"publisher","DOI":"10.1191\/0962280202sm291ra"},{"key":"bibr3-0962280212443324","doi-asserted-by":"publisher","DOI":"10.2307\/1912557"},{"key":"bibr4-0962280212443324","first-page":"103","volume-title":"Health, Economics, and Health Economics","author":"Manning 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