Mathematical model for the distribution of major depressive episode durations

BMC Research Notes

Toshiaki A Furukawa¹  Shinichiro Tomitaka² 

[1] Department of Health Promotion and Human Behavior, Kyoto University Graduate School of Medicine/School of Public Health, Yoshida Konoe-cho, Sakyo-ku, Kyoto 606-8501, Japan;Department of Mental Health, Panasonic Health Center, Landic building 3F, Nishishinbashi 3-8-3, Minato-ku, Tokyo 105-0003, Japan

关键词: Mathematical model;    Power law distribution;    Log-normal distribution;    Depression;   

Others  :  1129554
DOI  :  10.1186/1756-0500-7-636

 received in 2013-11-25, accepted in 2014-09-09,  发布年份 2014

【 摘 要 】

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.

【 授权许可】

   
2014 Tomitaka and Furukawa; licensee BioMed Central Ltd.

【 图 表 】

Figure 1.

Figure 2.

【 参考文献 】

• [1]Angst J: Prediction of course and outcome. In Depressive illness. Edited by Helgason T, Daly RJ. Berlin: Springer-Verlag; 1988:10-11.
• [2]Coryell W, Akiskal HS, Leon AC, Winokur G, Maser JD, Mueller TI, Keller TI: The time course of nonchronic major depressive disorder. Uniformity across episodes and samples. Arch Gen Psychiatry 1994, 51:405-410.
• [3]Furukawa TA, Kitamura T, Takahashi K: Time to recovery of an inception cohort with hitherto untreated unipolar major depressive episodes. Br J Psychiatry 2000, 177:331-335.
• [4]Spijker J, de Graaf R, Bijl RV, Beekman AT, Ormel J, Nolen WA: Duration of major depressive episodes in the general population: results from The Netherlands Mental Health Survey and Incidence Study (NEMESIS). Br J Psychiatry 2002, 181:208-213.
• [5]Keller MB, Lavori PW, Mueller TI, Endicott J, Coryell W, Hirschfeld RMA, Shea T: Time to recovery, chronicity, and levels of psychopathology in major depression: a 5-year prospective follow-up of 431 subjects. Arch Gen Psychiatry 1992, 49:809-816.
• [6]Klein JP, Zhang MJ: Survival Analysis, Software. Encyclopedia of Biostatistics. 111 River Street Hoboken, NJ USA: Wiley Online Library; 2005.
• [7]Lee ET, Wang J: Statistical methods for survival data analysis. 3rd edition. Hoboken: Wiley; 2003.
• [8]Sartwell PE: The distribution of incubation periods of infectious disease. Am J Hygiene 1950, 51:310-318.
• [9]Sartwell PE: The incubation period of poliomyelitis. Am J Public Health Nation’s Health 1952, 42:1403-1408.
• [10]Royston P: The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors. Statistica Neerlandica 2001, 55:89-104.
• [11]Tai P, Tonita J, Yu E, Skarsgard D: Twenty-year follow-up study of long-term survival of limited-stage small-cell lung cancer and overview of prognostic and treatment factors. Int J Radiat Oncol Biol Phys 2003, 56:626-633.
• [12]Moriyama O, Itoh H, Matsushita S, Matsushita M: Long-tailed duration distributions for disability in aged people. J Phys Soc Jpn 2003, 72:2409-2412.
• [13]Gibrat R: Une loi des r’eparations ’economiques: l’effet proportionnel. Bull Statist g’en Fr 1930, 19:469.
• [14]Montroll EW, Shlesinger MF: Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: a tale of tails. J Stat Phys 1983, 32:209-230.
• [15]Mitzenmacher M: A Brief History of Generative Models for Power Law and Lognormal Distributions. Internet Math 2004, 1:226-251.
• [16]Champernowne D: A Model of Income Distribution. Economic J 1953, 63:318-351.
• [17]Mandelbrot B: Fractals and Scaling in Finance. New York: Springer- Verlag; 1997.
• [18]Jain R, Ramakumar S: Stochastic dynamics modeling of the protein sequence length distribution in genomes: Implications for microbial evolution. Physica A 1999, 273:476-485.
• [19]Nakajima T, Higurashi A: A Use of two-channel radiances for an aerosol characterization from space. Geophysical Res Lett 1998, 25:3815-3818.
• [20]Allen AP, Li B, Charnov EL: Population: Fluctuations, power Laws and mixtures of lognormal distributions. Ecol Lett 2001, 4:1-3.
• [21]Li W: Random texts exhibit Zipf’s-law-like word frequency distribution. IEEE Trans Inf Theory 1992, 38:1842-1845.