Evaluation of multiple linear regression function and generalized linear model types in estimating natural menopausal age: A crosssectional study
Background: Since women spend about one-third of their lifespan in menopause, accurate prediction of the age of natural menopause and its effective parameters are crucial to increase women’s life expectancy.
Objective: This study aimed to compare the performance of generalized linear models (GLM) and the ordinary least squares (OLS) method in predicting the age of natural menopause in a large population of Iranian women.
Materials and Methods: This cross-sectional study was conducted using data from the recruitment phase of the Shahedieh Cohort Study, Yazd, Iran. In total, 1251 women who had the experience of natural menopause were included. For modeling natural menopause, the multiple linear regression model was employed using the ordinary least squares method and GLMs. With the help of the Akaike information criterion, rootmean- square error (RMSE), and mean absolute error, the performance of regression models was measured.
Results: The mean age of menopausal women was 49.1 ± 4.7 yr (95% CI: 48.8-49.3) with a median of 50 yr. The analysis showed similar Akaike criterion values for the multiple linear models with the OLS technique and the GLM with the Gaussian family. However, the RMSE and mean absolute error values were much lower in GLM. In all the models, education, history of salpingectomy, diabetes, cardiac ischemic, and depression were significantly associated with menopausal age.
Conclusion: To predict the age of natural menopause in this study, the GLM with the Gaussian family and the log link function with reduced RMSE and mean absolute error can be a good alternative for modeling menopausal age.
Key words: Menopause, Etiology, Statistics, Numerical data.
 Muka T, Asllanaj E, Avazverdi N, Jaspers L, Stringa N, Milic J, et al. Age at natural menopause and risk of type 2 diabetes: A prospective cohort study. Diabetologia 2017; 60: 1951–1960.
 Koukouliata A, Nena E, Koutlaki N, Liberis V, Constantinidis TC. Correlation of age at natural menopause with occupational status and other epidemiologic factors in women from Prefecture of Kavala, Greece. Hippokratia 2017; 21: 32–37.
 Golshiri P, Akbari M, Abdollahzadeh MR. Age at natural menopause and related factors in Isfahan, Iran. J Menopausal Med 2016; 22: 87–93.
 Costanian Ch, McCague H, Tamim H. Age at natural menopause and its associated factors in Canada: Crosssectional analyses from the Canadian longitudinal study on aging. Menopause 2018; 25: 265–272.
 Gordon JL, Eisenlohr-Moul TA, Rubinow DR, Schrubbe L, Girdler SS. Naturally occurring changes in estradiol concentrations in the menopause transition predict morning cortisol and negative mood in perimenopausal depression. Clin Psychol Sci 2016; 4: 919–935.
 Ali AM, Ahmed AH, Smail L. Psychological climacteric symptoms and attitudes toward menopause among Emirati women. Int J Environ Res Public Health 2020; 17: 5028.
 Kozakowski J, Gietka-Czernel M, Leszczyńska D, Majos A. Obesity in menopause: Our negligence or an unfortunate inevitability? Prz Menopauzalny 2017; 16: 61– 65.
 Muka T, Oliver-Williams C, Kunutsor S, Laven JSE, Fauser BCJ, Chowdhury R, et al. Association of age at onset of menopause and time since onset of menopause with cardiovascular outcomes, intermediate vascular traits, and all-cause mortality: A systematic review and metaanalysis. JAMA Cardiol 2016; 1: 767–776.
 Rahman I, Åkesson A, Wolk A. Relationship between age at natural menopause and risk of heart failure. Menopause 2015; 22: 12–16.
 de Sá MFS. Premature ovarian insufficiency and bone health care: A concern of the gynecologist. Rev Bras Ginecol Obstet 2018; 40: 305–308.
 Dunneram Y, Greenwood DC, Cade JE. Diet, menopause and the risk of ovarian, endometrial and breast cancer. Proc Nutr Soc 2019; 78: 438–448.
 La Vecchia C. Ovarian cancer: Epidemiology and risk factors. Eur J Cancer Prev 2017; 26: 55–62.
 Roett MA. Genital cancers in women: Uterine cancer. FP Essent 2015; 438: 11–17.
 Hansen J. Environmental noise and breast cancer risk? Scand J Work Environ Health 2017; 43: 505–508.
 Dall GV, Britt KL. Estrogen effects on the mammary gland in early and late life and breast cancer risk. Front Oncol 2017; 7: 110.
 Anderson CJ, Verkuilen J, Johnson T. Applied generalized linear mixed models: Continuous and discrete data. New York: Springer; 2012.
 McCullagh P, Nelder JA. Generalized linear models. 2nd Ed. New York: Routledge; 2019.
 Moran JL, Solomon PJ, Peisach AR, Martin J. New models for old questions: Generalized linear models for cost prediction. J Eval Clin Pract 2007; 13: 381–389.
 Agresti A. Foundations of linear and generalized linear models. New York: John Wiley & Sons; 2015.
 Eghtesad S, Mohammadi Z, Shayanrad A, Faramarzi E, Joukar F, Hamzeh B, et al. The Persian cohort: Providing the evidence needed for healthcare reform. Arch Iran Med 2017; 20: 691–695.
 Salmerón R, García CB, García J. Variance inflation factor and condition number in multiple linear regression. J Stat Comput Simulat 2018; 88: 2365–2384.
 Delignette-Muller ML, Dutang Ch. Fitdistrplus: An R package for fitting distributions. J Statist Software 2015; 64: 1–34.
 Chai T, Draxler RR. Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature. Geosci Model Dev 2014; 7: 1247– 1250.
 Willmott CJ, Matsuura K. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Res 2005; 30: 79–82.
 Fallahzadeh H. Age at natural menopause in Yazd, Islamic Republic of Iran. Menopause 2007; 14: 900–904.
 Saei Ghare Naz M, Sayehmiri F, Kiani F, Ozgoli G. A systematic review and meta-analysis on the average age of menopause among iranian women. Evidence Based Care J 2019; 8: 26–34.
 Wang M, Gong WW, Hu RY, Wang H, Guo Y, Bian Z, et al. age at natural menopause and associated factors in adult women: Findings from the China Kadoorie Biobank study in Zhejiang rural area. PloS One 2018; 13: e0195658.
 Zhu D, Chung HF, Pandeya N, Dobson AJ, Kuh D, Crawford SL, et al. Body mass index and age at natural menopause: An international pooled analysis of 11 prospective studies. Eur J Epidemiol 2018; 33: 699– 710.
 Tao X, Jiang A, Yin L, Li Y, Tao F, Hu H. Body mass index and age at natural menopause: A meta-analysis. Menopause 2015; 22: 469–474.
 Whitcomb BW, Purdue-Smithe AC, Szegda KL, Boutot ME, Hankinson SE, Manson JE, et al. Cigarette smoking and risk of early natural menopause. Am J Epidemiol 2018; 187: 696–704.
 Yang HJ, Suh PS, Kim SJ, Lee SY. Effects of smoking on menopausal age: Results from the Korea national health and nutrition examination survey, 2007 to 2012. J Prev Med Public Health 2015; 48: 216–224.
 Morris DH, Jones ME, Schoemaker MJ, McFadden E, Ashworth A, Swerdlow AJ. Body mass index, exercise, and other lifestyle factors in relation to age at natural menopause: Analyses from the breakthrough generations study. Am J Epidemiol 2012; 175: 998–1005.
 Omidi A, Bakht R, Moghimbeigi A, Balali Z. A study of age at menopause and related factors. Life Sci J 2013; 10: 1295–1299.
 Santoro N. Perimenopause: From research to practice. J Womens Health 2016; 25: 332–339.
 Sasi Sekhar TVD, Medarametla S, Rahman A, Adapa SS. Early menopause in type 2 diabetes: A study from a south Indian tertiary care centre. J Clin Diagn Res 2015; 9: OC08–10.
 Monterrosa-Castro A, Blümel J, Portela-Buelvas K, Mezones-Holguín E, Barón G, Bencosme A, et al. Type II diabetes mellitus and menopause: A multinational study. Climacteric 2013; 16: 663–672.