A Comparison of Mazur’s k and Area Under the Curve for Describing Steep Discounters

Abstract

Delay discounting describes how a reward loses value as a function of increasing delay to its receipt and has been reliably associated with a variety of vulnerable populations including those with substance use disorders (SUDs). Two commonly used models to assess delay discounting in the field of SUDs include log k derived from Mazur’s hyperbolic equation and area under the curve (AUC). In the current study, we compared log k with AUC on delay discounting data obtained from non-treatment seeking, cocaine- and methamphetamine-dependent volunteers. We specifically chose this population in order to obtain a distribution of relatively steep discounters. The results show that the relationship between AUC and log k is better described by a quadratic rather than a linear function. In other words, changes in discounting, as measured by AUC and log k, are reflected differently across a range of obtained responses. Additionally, the distribution of AUC values was skewed, which appears to be more likely among populations exhibiting greater discounting. Finally, closer examination of indifference points revealed that AUC was almost perfectly predicted by the area from the two longest delays, with relatively less input from shorter delays. Given these results, researchers should exercise additional caution when deciding which method to use to assess discounting data and how final results are to be interpreted, particularly when dealing with relatively high rates of discounting. High rates of discounting are likely in populations with impulsive disorders such as those with SUDs.