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The authors have declared that no competing interests exist.

Conceived and designed the experiments: ST. Performed the experiments: ST. Analyzed the data: ST. Wrote the paper: ST YK TF.

Previous research has reported that the mean of depressive symptoms is stable in the general population through middle adulthood. To understand the stability of depressive symptoms during middle adulthood, we investigated the nature of the distribution of depressive symptoms.

We analyzed 24,890 subjects aged 15 to 84 years who participated in the Active Survey of Health and Welfare, Japan. Depressive symptoms were assessed using the Japanese version of the Center for Epidemiologic Studies Depression Scale (CES-D). The descriptive statistics and frequency curves of the distributions were then compared according to age group.

The distribution of depressive symptoms was stable through middle adulthood. The right tail which covers clinical depression was more stable than the left tail or peak of the distributions. The right tail of the distribution during middle adulthood exhibited a linear pattern with a log-normal scale.

The right tail of the distribution of depressive symptoms is stable and exhibits an exponential pattern during middle adulthood.

Depression is a common mental disorder that is among the leading causes of disability worldwide [

Although there are a few exceptions, cross-sectional surveys and longitudinal studies have found that the trajectory of depressive symptoms across the adult lifespan follows a U-shaped pattern, with symptoms being high during young adulthood, decreasing during middle adulthood, and then increasing again during older age [

While depressive symptoms follow a U-shaped pattern across adulthood, age-related changes in depressive symptoms seem relatively mild. The estimated average change per decade in the Center for Epidemiological Studies Depression Scales (CES-D) score is less than 1 point between the ages of 20 and 70 years, whereas the standard deviation of CES-D scores in community surveys is between 5 to 10 points [

While a lot of attention has been paid to the increase in depressive symptoms during young adulthood and older age, little attention has been given to the stability of depressive symptoms during middle adulthood. However, an investigation of the stability of depressive symptoms is similarly important to understand the course of depression. The stability of the mean of depressive symptoms indicates that depressive symptoms recover on average. Furthermore, the stability of depressive symptoms suggests that depressive symptoms are steadily regulated in some way. A certain rule may exist in the distribution of depressive symptoms during middle adulthood. To understand the stability of depressive symptoms, the nature of the distribution of depressive symptoms must be characterized.

The present study used the depressive symptoms assessment of the Active Survey of Health and Welfare, which has been conducted annually to evaluate the health status of a representative sample of the Japanese general population [

We used data from the Active Survey of Health and Welfare (ASHW) conducted by the Japanese Ministry of Health, Labor and Welfare in 2000 [

The questionnaire was returned by 32,729 respondents. The response rate was not publicized by the Ministry of Health, Labor and Welfare and Health. However, the response rates for similar surveys conducted 3 and 4 years earlier were 87.1% and 89.6% [

Depressive symptoms were assessed using the Japanese version of the Center for Epidemiologic Studies Depression Scale (CES-D). This 20-item scale assesses the frequency of a variety of depressive symptoms within the previous week (0 = rarely or none of the time, 1 = some of the time, 2 = much of the time, and 3 = most or all of the time) [

The respondents were grouped into the following age groups: 15–19 years, 20–29 years, 30–39 years, 40–49 years, 50–59 years, 60–69 years, 70–79 years, and 80–84 years. Descriptive statistics, such as the mean, standard deviation, skewness, kurtosis, and frequency curve, were calculated for each age group. To estimate the proportion of high CES-D scores, we calculated the 90th percentile of the CES-D score for each group.

The first step in this analysis was to ascertain the U-shaped effect by comparing the mean CES-D of each age group. After confirming the U-shaped-effect, we compared the frequency curve among a young adult group (15–19 years, 20–29 years, 30–39 years), a middle adulthood group (30–39 years, 40–49 years, 50–59 years, 60–69 years), and an older age group (60–69 years, 70–79 years, and 80–84 years). After confirming that the middle adulthood group to be the most stable among the three groups and the right tails of the distributions which cover clinical depression were more stable than the left tails or peaks of the distributions, the right tails of the distributions for middle adulthood were analyzed using a log-normal scale to examine the similarities over a wide range of CES-D scores. Finally, to illustrate the patterns of the frequency of depressive symptoms during middle adulthood, the tail of the distribution, including the ages between 30–69 years, was evaluated using a log-normal scale. We used JMP version 11 for Windows to calculate the descriptive statistics and the frequency distribution curve.

The descriptive statistics of the distributions of CES-D in the Japanese general population according to age groups are shown in

^{th} percentile |
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15–19 | 1854 | 48 | 14.8 ± 8.4 | 0.76 | 0.69 | 13 | 27 |

20–29 | 4275 | 53 | 13.6 ± 8.6 | 1.04 | 1.46 | 12 | 25 |

30–39 | 4334 | 53 | 12.6 ± 8.1 | 1.10 | 1.91 | 11 | 23 |

40–49 | 4408 | 52 | 13.3 ± 8.3 | 1.19 | 2.46 | 12 | 24 |

50–59 | 4785 | 52 | 13.3 ± 7.9 | 1.09 | 2.10 | 12 | 23 |

60–69 | 3198 | 51 | 13.2 ± 8.1 | 1.18 | 2.63 | 12 | 23 |

70–79 | 1663 | 56 | 14.7 ± 9.3 | 0.97 | 1.05 | 13 | 28 |

80–84 | 373 | 75 | 17.0 ±10.4 | 0.88 | 0.80 | 15 | 31 |

As shown in

To demonstrate the patterns of the distribution of depressive symptoms during middle adulthood, the right tail of the distribution, including all ages from 30 to 69 years (N = 16,725), was evaluated using a log-normal scale (

The aim of the present study was to investigate the stability of depressive symptoms during middle adulthood by analyzing the distributions of CES-D scores in the general population according to different age groups. Our findings showed that the distribution of depressive symptoms, especially the right tail of the distribution, was stable among middle adulthood group. A number of studies have found that the mean of depressive symptoms stabilizes during middle adulthood [

Interestingly, during middle adulthood, when the distribution of depressive symptoms is most stable, the right tail of the distribution of the CES-D scores exhibits a linear pattern with a log-normal scale, suggesting that the right tail of the distribution of depressive symptoms follows an exponential curve. In accordance with our results, Meltzer et al. (2002) reported that an exponential curve provided the best fit for total neurotic symptoms and depressive scores from British National Survey of Psychiatric Morbidity, but floor effects produced deviations at symptom counts of 0–3 [

The reason why the right tail of the distribution of depressive symptoms follows an exponential curve is unknown, but the conditions that enable such a distribution can be speculated upon. Exponential distribution is observed where individual variability and total stability are organized together, such as the barometric formula and the Boltzmann-Gibbs law [

To form the exponential distribution of atmosphere pressure with altitude, three factors are needed: the random movement of gas molecules, the force of gravity, and a boundary (the surface of the ground). In other words, an exponential distribution is formed when these three conditions are satisfied. In the case of depressive symptoms, if individual depressive symptoms corresponding to the random movements that comprise the individual variability could be demonstrated and both a boundary and the force to a boundary that constitute the stability of the distribution could be identified, the reason why depressive symptoms follow an exponential curve could possibly be explained. Further consideration regarding this speculation is needed.

This study had some limitations. First, people with depression might have been less likely than others to participate in the survey. Evidence suggests that a bias toward a reluctance to participate exists for psychiatric epidemiological surveys, although our findings are consistent with cross-sectional studies of age-related associations in depressive symptoms [

Despite these limitations, the present study provides important information regarding the nature of the distribution of depressive symptoms. The degree to which these results can be generalized to other populations or other scales for depressive symptoms is unclear but warrants examination.