Modeling the Dynamics of Addiction Relapse via the Double-Well Potential System

Substance use relapse is difficult to define, and previous work has used one-size-fits-all ad hoc definitions. Researchers have called for a dynamic and personalized understanding of relapse as a concept and model, necessitating novel statistical tools.We aimed to develop and validate a novel statisticalmodel of latent relapse processes: the double-well potential model (DWPM). This model describes posttreatment substance use in terms of a dynamical system with stable equilibria of abstinence and relapse, person-specific dominant equilibria (tilt), the ease of changing between equilibria (steepness), and an overall relapse risk (RR).Using timeline follow-back data from N=139 adults with a substance use disorder transitioning back to the community after residential treatment, we examined individual differences and the criterion-related validity of DWPM parameters to determine the clinical utility of the double-well model. While nonuse was the predominant stable state across participants, we found significant between-subjects variability steepness and RR. These individual differences were predictable via demographics, baseline psychopathology, treatment history, and treatment condition. Steepness and RR also predicted long-termoutcomes, including life satisfaction and criminal behavior, above and beyond traditional metrics of relapse (proportion of days used and time to first use). Thus, the DWPM is a strong theoretical and statistical representation of the underlying relapse processes. Moreover, the parameters show criterion-related validity and may be useful in precision medicine.