Power laws in covariability of anxiety and depression among newly diagnosed patients with major depressive episode, panic disorder and controls

Context Although symptoms of anxiety and depression correlate, they may covary in irregular and unpredictable ways. This non-linear covariation may be important to psychiatric diagnosis, treatment and relapse. This non-linear anxiety–depression interaction suggests that power laws may be observed. Power laws are statistical distributions found when systems vary in complex ways at the interface between chaotic dynamics and periodic dynamics, such that data points vary randomly but are still partially correlated with each other. Such non-linear dynamics and relationships should result in characteristic patterns of interaction among patients, stressors and treatment. This is important because non-linear dynamics could affect our understanding of mental disorders, the need for varied treatment approaches and patterns of early response to treatment. Objective To determine whether the relationships between anxiety and depression levels, changes and rates of change follow power law distributions among patients with newly diagnosed major depressive episode (MDE), panic disorder (PD) and neither disorder (controls). Design Time series of hourly mood variation. Setting Acute and continuity primary care clinics. Patients or other participants Five adult patients presenting each with MDE, PD and controls based on DSM-IV criteria. Four patients in each group completed 30 days of assessments. Main and secondary outcome measures Hourly self-assessments (while awake) of levels of anxiety and depression using visual analogue scales for a 30-day period. Covariation in level of symptoms, in the change of symptoms and in the rate of change were assessed. Anxiety–depression matrices were prepared for pooled subjects. Power laws were sought using log–log plots of frequency versus order of that frequency. Results Although visual inspection of plots for symptoms levels, change and rates of change all suggest power laws, statistical assessments provide stronger support for power laws in symptom change than for either symptom levels or rates of change. Adjusted R2 terms are larger for MDE and PD subjects compared with controls while the inverse slope is about 2.5 for controls and 1.7–1.9 for those with MDE or PD. This study found that power laws may be present in both the symptom change data for all three diagnostic groups. Evidence for power laws in symptom levels and rates of change was less compelling. The inverse slopes suggest that the anxiety–depression relationships among subjects with PD and major depression are similar but differ from those among controls. Conclusions First, power laws suggest a scale-free relationship; the differences seen in transition from symptom level to change level may reflect that complex events at the level of mood assessment affect change in mood. Second, this covariation may be due to external factors acting on the patient or multiple internal interrelated factors. Third, different factors and populations can yield different slopes. Future research is needed to confirm these preliminary findings and to understand the origin of these dynamics.