An alternative approach to calculating Area-Under-the-Curve (AUC) in delay discounting research

Applied to delay discounting data, Area-Under-the-Curve (AUC) provides an atheoretical index of the rate of delay discounting. The conventional method of calculating AUC, by summing the areas of the trapezoids formed by successive delay-indifference point pairings, does not account for the fact that most delay discounting tasks scale delay pseudoexponentially, that is, time intervals between delays typically get larger as delays get longer. This results in a disproportionate contribution of indifference points at long delays to the total AUC, with minimal contribution from indifference points at short delays. We propose two modifications that correct for this imbalance via a base-10 logarithmic transformation and an ordinal scaling transformation of delays. These newly proposed indices of discounting, AUC(log) (d) and AUC(or) (d,) address the limitation of AUC while preserving a primary strength (remaining atheoretical). Re-examination of previously published data provides empirical support for both AUC(log) (d) and AUC(or) (d) . Thus, we believe theoretical and empirical arguments favor these methods as the preferred atheoretical indices of delay discounting.