{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T02:55:07Z","timestamp":1783392907772,"version":"3.54.6"},"reference-count":19,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2016,10,20]],"date-time":"2016-10-20T00:00:00Z","timestamp":1476921600000},"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":[[2018,7]]},"abstract":"<jats:p>Drug self-administration experiments are a frequently used approach to assessing the abuse liability and reinforcing property of a compound. It has been used to assess the abuse liabilities of various substances such as psychomotor stimulants and hallucinogens, food, nicotine, and alcohol. The demand curve generated from a self-administration study describes how demand of a drug or non-drug reinforcer varies as a function of price. With the approval of the 2009 Family Smoking Prevention and Tobacco Control Act, demand curve analysis provides crucial evidence to inform the US Food and Drug Administration\u2019s policy on tobacco regulation, because it produces several important quantitative measurements to assess the reinforcing strength of nicotine. The conventional approach popularly used to analyze the demand curve data is individual-specific non-linear least square regression. The non-linear least square approach sets out to minimize the residual sum of squares for each subject in the dataset; however, this one-subject-at-a-time approach does not allow for the estimation of between- and within-subject variability in a unified model framework. In this paper, we review the existing approaches to analyze the demand curve data, non-linear least square regression, and the mixed effects regression and propose a new Bayesian hierarchical model. We conduct simulation analyses to compare the performance of these three approaches and illustrate the proposed approaches in a case study of nicotine self-administration in rats. We present simulation results and discuss the benefits of using the proposed approaches.<\/jats:p>","DOI":"10.1177\/0962280216673675","type":"journal-article","created":{"date-parts":[[2016,10,21]],"date-time":"2016-10-21T20:20:13Z","timestamp":1477081213000},"page":"2038-2049","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["A Bayesian hierarchical model for demand curve analysis"],"prefix":"10.1177","volume":"27","author":[{"given":"Yen-Yi","family":"Ho","sequence":"first","affiliation":[{"name":"Department of Statistics, College of Arts and Sciences, University of South Carolina, South Carolina, SC, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tien","family":"Nhu Vo","sequence":"additional","affiliation":[{"name":"Division of Epidemiology, School of Public Health, University of Minnesota, Minnesota, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haitao","family":"Chu","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, School of Public Health, University of Minnesota, Minnesota, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xianghua","family":"Luo","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, School of Public Health, University of Minnesota, Minnesota, MN, USA"},{"name":"Masonic Cancer Center, University of Minnesota, Minnesota, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chap T","family":"Le","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, School of Public Health, University of Minnesota, Minnesota, MN, USA"},{"name":"Masonic Cancer Center, University of Minnesota, Minnesota, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2016,10,20]]},"reference":[{"key":"bibr1-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-004702-4.50010-2"},{"key":"bibr2-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1097\/00008877-199000140-00003"},{"key":"bibr3-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1406324111"},{"key":"bibr4-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1901\/jeab.1988.50-419"},{"key":"bibr5-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1016\/j.pbb.2013.10.020"},{"key":"bibr6-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1093\/ntr\/nts162"},{"key":"bibr7-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1037\/a0017684"},{"key":"bibr8-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1002\/jeab.7"},{"key":"bibr9-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1037\/0033-295X.115.1.186"},{"key":"bibr10-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2013.862491"},{"key":"bibr11-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1007\/s00213-012-2899-2"},{"key":"bibr12-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1037\/a0031610"},{"key":"bibr13-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1032280214"},{"key":"bibr14-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10476213"},{"key":"bibr15-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2672"},{"key":"bibr16-0962280216673675","doi-asserted-by":"publisher","DOI":"10.1901\/jeab.1991.56-377"},{"key":"bibr17-0962280216673675","unstructured":"Plummer M. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In:\n                      Proceedings of the 3rd international workshop on distributed statistical computing\n                      , Vienna, Austria, 20\u201322 March 2003. 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