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Original Article |

Major Depressive Episodes and Random Mood FREE

[+] Author Affiliations

Author Affiliations: Kernfysisch Versneller Instituut of the University of Groningen (Dr van der Werf); Discipline Group Psychiatry, University Hospital of Groningen (Drs Kaptein, de Jonge, and Korf); Netherlands Institute of Mental Health and Addiction, Utrecht (Drs Spijker and de Graaf), the Netherlands.

Arch Gen Psychiatry. 2006;63(5):509-518. doi:10.1001/archpsyc.63.5.509.
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Context  Mathematical models describing changes in mood in affective disorders may assist in the identification of underlying pathologic and neurobiologic mechanisms and in differentiating between alternative interpretations of psychiatric data.

Objective  Using time-to-event data from a large epidemiologic survey on recovery from major depression, to model the survival probability, in terms of an underlying process, with parameters which might be recognized and influenced in clinical practice.

Design  We present a sequential-phase model for survival analysis, which describes depression as a state with or without an additional incubation phase. Recovery is seen as the transition to a nondepressive state. We show that this sequential-phase model finds a microscopic realization in a dynamic description, the random-mood model, which depicts mood as governed by an Ornstein-Uhlenbeck type of stochastic process, driven by intermittent gaussian noise.

Results  For reversible depression (80%), the fractional probability of recovery is remarkably independent of the history of the depression. Analysis with the sequential-phase model suggests single exponential decay in this group, possibly with a short incubation phase. Within the random-mood model, the data for this reversibly depressed cohort are compatible with an intermittent noise pattern of stimuli with average spacing of 4 months and incompatible with nonintermittent noise.

Conclusions  Time-to-event data from psychiatric epidemiologic studies can be conceptualized through modeling as intrasubject processes. The proposed random-mood model reproduces the time-to-event data and explains the incubation phase as an artifact due to the inclusion criterion of 14 days in most current psychiatric diagnostic systems. Depression is found to result more often from pileup of negative stimuli than from single life events. Time sequences, generated using the random-mood model, produce power plots, phase-space trajectories, and pair-correlation sums, similar to recent results for individual patients. This suggests possible clinical relevance along with the model's use as a tool in survival analysis.

Figures in this Article

Mathematical models describing changes in mood in affective disorders may assist in the identification of underlying pathologic and neurobiologic mechanisms and in distinguishing between alternative interpretations of psychiatric data. Current mood models are based on data collected in long-term observational studies. Mood in individual persons is subject to change, which may occur within a relatively short time, and a recorded time sequence of mood may look haphazard to an outside observer. Stochastic behavior and, on the other hand, chaotic and deterministic mechanisms have been suggested.17 Mood models, based on nonlinear differential equations, have been proposed, and the addition of a noise component has been studied.1,810

The models presented herein are derived from and applied to epidemiologic data. We modeled time-to-event data from the Netherlands Mental Health Survey and Incidence Study (NEMESIS),11,12 a prospective psychiatric epidemiologic survey of nonhospitalized subjects in the Dutch population. We investigate whether the underlying hazard rate can be understood in terms of sequential phases or states. Such an approach has also been proposed by Aalen and Gjessing,13,14 who describe a model based on diffusion-type transitions between states. Economizing on the complexity of such a model, we specifically address the question whether a 2-state description, depressed vs nondepressed, is a sufficient basis (1-step model) or whether the data provide evidence for 2 distinct states of depression, the first of which would act as an incubation phase preceding the second phase, from which recovery occurs (2-step model).

The analysis with this sequential-phase model gives values for the fraction of subjects who remain depressed and the fraction of those who do eventually recover. For the latter group, the decay times (mean durations) of the phases are determined. These are the global parameters that characterize the average time course of depression. One would like to get an understanding of the mechanisms that drive the time sequences of mood in individual subjects or, one step less ambitious, the average time course of depression in a group (ensemble) of subjects. We propose here that this purpose is served by a random-mood model, which is based on a linear, noise-driven, equation describing an Ornstein-Uhlenbeck process.1517 To simulate an ensemble of subjects, a very long time sequence of mood is generated and characteristic parameters, such as average time between noise stimuli and the relaxation time by which mood is restored to normal, are regularly randomized. The time-to-event pseudodata derived from this simulation are then compared with the NEMESIS data and the sequential-phase analysis of these data.

We further investigated whether this random-mood model holds any promise for application in individual subjects. Power plots and phase-space trajectories are presented and compared with available data, such as those of Gottschalk et al2,3 and Heiby et al.5 As these data have been interpreted as possible evidence for low-dimensional chaotic and deterministic behavior, we investigated whether simulation data of the (largely nondeterministic) random-mood model, when analyzed with the method of Grassberger and Procaccia,18,19 suggest a higher dimensionality than the 1-dimensional space on which it has been defined.


Data used are from NEMESIS.11,12 This prospective psychiatric epidemiologic survey of the Dutch population aged 18 to 64 years was conducted in 3 waves, in 1996, 1997, and 1999. From each selected household, 1 respondent was randomly chosen. In the first wave, data were collected for 7076 subjects; 1458 of these were lost to attrition in the second wave, and 822 were lost in the third wave. The remaining 4796 subjects were interviewed during all 3 waves. The respondents were interviewed using the Composite International Diagnostic Interview version 1.1.20 Using the DSM-III-R,21 a variety of diagnoses was identified, including bipolar disorder, major depression, and dysthymia. Further details are described elsewhere.11,12

The focus of the present study is on major depression. To include only new (first or recurrent) cases, respondents with a diagnosis of major depression in the period between T1 (1997) and T2 (1999) but no diagnosis of major depression during the month before T1 (1997), were identified. Subjects with bipolar disorder and primary psychotic disorder were excluded. The state of the major depressive episodes was assessed at 3-month intervals using the Life Chart Interview22 and was retrospectively discretized into 6-week intervals from recall.

Ten respondents were classified as having had a major depressive episode of 0.5-month duration. The duration of major depressive episodes in 250 respondents with depression was determined for the first depressive episode recorded on the Life Chart Interview. Data from NEMESIS are summarized in Table 1, which also gives the nonparametric estimates of the survival or Kaplan-Meier23 curve and the conditional recovery probability estimates per time interval. We analyzed all respondents as a single group. The role of risk factors such as severity of depression, comorbid anxiety, comorbid dysthymia, somatic disease, recurrence vs nonrecurrence, sex, and treatment status are discussed in a forthcoming article (S.Y.W., K.I.K., P.J., J.S., R.G., J.K., unpublished data).


Data are analyzed in terms of a sequential model, which depicts recovery from depression as a transition from one state, A (depressed), to another state, B (nondepressed). In the general population, the prevalence of depression is rather constant, giving rise to a quasi-equilibrium, and the rates at which subjects become depressed (BA) or recover from depression (AB) are constant.

The assumption of exponential decay as a starting point may be justified by the following simple argument: just as in a chemical reaction, the equilibrium condition is d[A]/dt = k[A]+k′[B] = 0, where k and k′ are the forward and backward rate constants and [A] and [B] are the numbers of subjects in states A and B. Considering only the process AB, that is, selectively following the time course of depression to recovery, without taking into account its starting point in time, the process is governed by d[A]/dt=k[A], which describes exponential decay.

For the model to represent the general population, compatible with NEMESIS, it needs a few refinements. Depression appears irreversible in about 20% of the cases, as is already evident from inspection of Table 1. We, therefore, dichotomize the subjects retrospectively into a nonrecoverable fraction, S(∞), and a recoverable fraction, [1 − S(∞)], where S(∞) is the value to which the survival curve converges for large times. Exponential decay is assumed for the recoverable cases. In this 1-step model, the time-to-event probability reads


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Figure 1

Survival curve (A-C) and conditional decay curve (D-F), normalized to 1.5-month intervals, shown with their statistical errors, compared with a maximum likelihood fit for a 1-step model (A and D) and a 2-step model (B and E). C and F, Same data with the first 2 intervals combined into 1; all intervals are 1.5 months. Dashed lines show the partial fits that apply to the reversible cases only, here 80% of the total. NEMESIS indicates Netherlands Mental Health Survey and Incidence Study.

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Figure 2

A and B, Mood curves generated with the random-mood model. Dashed line at −2 gives the level below which mood is defined as depressive. A, Typical mood pattern stretching over an average human lifetime. B, Same pattern followed to 1000 years. The parameter choice is D = 120 days,<T> = 365 days, Z = 1.

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Figure 3

A and C, Time to recovery and conditional decay data from the Netherlands Mental Health Survey and Incidence Study (NEMESIS), reversible cases only. Dashed lines indicate the 1-step fits obtained for this subgroup. B and D, Simulation data from the random-mood model, with the parameter choice as described in the text (ie, D = 120 days,<T> = 365 days, Z = 1). D, Note that some points are included for a shorter (1-day) inclusion criterion.

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Figure 4

Random-mood power plot simulation data and their means (solid lines). A, Parameterization, described in the text (ie, D = 120 days,<T> = 365 days, Z = 1). The dotted line indicates the continuous-time Fourier transform of the exponential that underlies the data. B, Simulation data for different single relaxation times.

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Figure 5

Phase-space trajectories for random-mood simulation data for different relaxation times. A, C, and E, Intermittent noise of variance 1 and an average spacing between stimuli of 120 days. B, D, and F, Nonintermittent noise of variance 1/120.

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Figure 6

A, Correlation sum for a 4000-day random-mood sequence with D = 16 days, T = 64 days, plus a nonintermittent component with variance 0.01 and T = 1, vs r, the distance between pairs. Embedding dimensions are 1, 2, 4, . . . , 16. B, Local slope in a log-log plot.

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