A Bayesian hierarchical model for demand curve analysis

Yen Yi Ho, Tien N Vo, Haitao Chu, Mark G. LeSage, Xianghua Luo, Chap T Le

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1 Scopus citations


Drug self-administration experiments are a frequently used approach to assess 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’s 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.

Original languageEnglish (US)
Pages (from-to)2401-2412
Number of pages12
JournalStatistical methods in medical research
Issue number8
StatePublished - Aug 1 2018

Bibliographical note

Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the funding support of NIH 1U54-DA031659-01 and U19-CA157345 for this work. Research reported in this publication was also supported by NIH grant P30 CA77598 utilizing the Biostatistics and Bioinformatics Core shared resource of the Masonic Cancer Center, University of Minnesota, and by the National Center for Advancing Translational Sciences of the National Institutes of Health Award Number UL1TR000114. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Publisher Copyright:
© 2016, The Author(s) 2016.


  • Bayesian hierarchical model
  • demand curve analysis
  • mixed effects regression
  • non-linear least square regression
  • prism


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