Comparing exponential and exponentiated models of drug demand in cocaine users

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31 Scopus citations


Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r ± .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability.

Original languageEnglish
Pages (from-to)447-455
Number of pages9
JournalExperimental and Clinical Psychopharmacology
Issue number6
StatePublished - Dec 1 2016

Bibliographical note

Funding Information:
This work was supported by grant R01DA025032, R01DA032254, R01DA033394, R21DA035481 (Principal Investigator: Craig R. Rush); R01DA033364 (Principal Investigator: Joshua A. Lile); and R01DA036553, R21DA034095, and R21DA035376 (Principal Investigator: William W. Stoops) from the National Institute on Drug Abuse and 1247392 from the National Science Foundation. These funding sources had no role in study design, data collection or analysis, or preparation and submission of the manuscript. The authors thank the staff at the University of Kentucky Laboratory of Human Behavioral Pharmacology for their expert medical and technical assistance. Justin C. Strickland and William W. Stoops developed the study concept and data collection measures. Data were collected by Justin C. Strickland. Justin C. Strickland performed the data analysis and interpretation under the guidance of William W. Stoops. Justin C. Strickland drafted the initial manuscript, and all authors provided critical reviews. All authors read and approved the final version of the manuscript for submission.

Publisher Copyright:
© 2016 American Psychological Association.


  • Alcohol
  • Behavioral economics
  • Cigarettes
  • Demand curve
  • Purchase task

ASJC Scopus subject areas

  • Pharmacology
  • Psychiatry and Mental health
  • Pharmacology (medical)


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