Mathematical model for the distribution of major depressive episode durations

BACKGROUND: The duration of major depressive episodes varies widely, ranging from one month to more than several years. Despite the accumulation of knowledge regarding the course of major depressive episodes, no mathematical model has been developed to describe the durations of major depressive episodes. We evaluated which mathematical model is fitted to describe the distribution of the durations of major depressive episodes using data from the Group for Longitudinal Affective Disorder Study (GLADS), a prospective study conducted in Japan. RESULTS: The distribution of the cumulative probability of major depressive disorder duration plotted on a double-logarithmic scale exhibited an approximately linear form. A log-normal distribution fit the distribution of major depressive episodes better than an exponential distribution or a Weibull distribution. CONCLUSIONS: In this study, we evaluated which mathematical model fit the distribution of major depressive episode durations using data from GLADS. The results showed that a log-normal model and a power law model may fit the distribution of major depressive episode durations.