Using Artificial Neural Networks and the Gutenberg-Richter Power Law to "Rightsize" a Behavioral Health Care System

Abstract

The authors propose a new paradigm for designing and managing behavioral health care systems by using artificial neural networks to measure quality of care (Q), using length-of-stay (LOS) prediction and the variation in LOS prediction, and subsequently using the variation of Q to obtain a measure of uncertainty in treatment. The paper proposes that mental illness is fractal in nature (self-similar at all scales) and conforms to power laws like the Gutenberg-Richter (G-R) law, whereby there is a log-log relationship between frequency of episodes (i.e., admissions) and the severity of those episodes. The paper also hypothesizes that 28% is the average uncertainty (residual or excess entropy) in the treatment of mental illness. The authors use the G-R paradigm to calculate the severity of admission and, subsequently, the minimum number of beds for different behavioral health care facilities and propose the optimal partition of beds between community and state services, thereby "balancing" the delivery system. The data presented support the notion that mental illness manifests complexity and "self-organized criticality." The authors hypothesize that correcting deviations from the theoretical G-R curve for each level of care will allow optimum resource distribution, improve quality of care, and reduce costs.