Characterizing the dynamics, reactivity and controllability of moods in depression with a Kalman filter

Background: Mood disorders involve a complex interplay between multifaceted internal emotional states, and complex external inputs. Dynamical systems theory suggests that this interplay between aspects of moods and environmental stimuli may hence determine key psychopathological features of mood disorders, including the stability of mood states, the response to external inputs, how controllable mood states are, and what interventions are most likely to be effective. However, a comprehensive computational approach to all these aspects has not yet been undertaken. Methods: Here, we argue that the combination of ecological momentary assessments (EMA) with a well-established dynamical systems framework—the humble Kalman filter—enables a comprehensive account of all these aspects. We first introduce the key features of the Kalman filter and optimal control theory and their relationship to aspects of psychopathology. We then examine the psychometric and inferential properties of combining EMA data with Kalman filtering across realistic scenarios. Finally, we apply the Kalman filter to a series of EMA datasets comprising over 700 participants with and without symptoms of depression. Results: The results show a naive Kalman filter approach performs favourably compared to the standard vector autoregressive approach frequently employed, capturing key aspects of the data better. Furthermore, it suggests that the depressed state involves alterations to interactions between moods; alterations to how moods responds to external inputs; and as a result an alteration in how controllable mood states are. We replicate these findings qualitatively across datasets and explore an extension to optimal control theory to guide therapeutic interventions. Conclusions: Mood dynamics are richly and profoundly altered in depressed states. The humble Kalman filter is a well-established, rich framework to characterise mood dynamics. Its application to EMA data is valid; straightforward; and likely to result in substantial novel insights both into mechanisms and treatments. Author summary: In this study, we aimed to understand the dynamics of mood in the context of depression, utilizing experience sampling data and well-established mathematical techniques. Our approach sought to overcome limitations of traditional methods and accurately capture the dynamics of moods in real-life situations. Through the application of a Kalman filter to examine mood trajectories in experience sampling data from various datasets, including both patients with depression and healthy controls, we were able to capture the evolution of mood, interaction among different mood items, and responsiveness to environmental inputs. The study revealed distinct dynamical features characteristic of depression, highlighted the potential of using external factors to influence mood and potentially shift between stable emotional states. The findings offer valuable insights into the impact of depression on mood dynamics and potential intervention strategies, contributing to a better understanding of depression mechanisms. The study also acknowledges the challenges of employing complex models to depict sparse and noisy data, emphasizing the need for further research to address these complexities.