Exact solutions for area-based delay discounting analyses

Novel methods are provided for calculating a model-based area under curve (MB-AUC) using exact solution. These model-specific calculations produce an AUC ratio that does not need numerical approximation nor access to the source discounting data to perform. This approach supports a calculation of MB-AUC that is useful in summarizing current and retrospective discounting analyses using fitted models (e.g., k and s) and corresponding study parameters (i.e., range of delays). Solutions were compared against numerical methods for various discounting models and results indicated that each approach provided identical results. This newer, simpler, and more efficient method is reviewed and demonstrated to show how comparisons can be drawn between the fitted discounting models and empirical methods, such as the empirical point-based area under curve. Reanalyses of published findings revealed that reconstituting published findings using a common scale (i.e., area) yielded similar AUC ratios, despite varying approaches, suggesting new avenues for research synthesis (e.g., reducing sources of measurement error). The MB-AUC measure is discussed as one means of addressing the challenges encountered when research synthesis includes metrics on varying scales and differing domains. (PsycInfo Database Record (c) 2023 APA, all rights reserved).