Modeling the Determinants of Time-to-age at First Marriage in Ethiopian Women: A Comparison of Various Parametric Shared Frailty Models
Science Journal of Public Health
Volume 3, Issue 5, September 2015, Pages: 707-718
Received: Jun. 1, 2015; Accepted: Jun. 11, 2015; Published: Aug. 1, 2015
Views 5166      Downloads 236
Bedasa Tessema, Department of Statistics, College of Natural & Computational Sciences, Drie-dawa University, Drie-dawa, Ethiopia
Salie Ayalew, Department of Statistics, College of Natural & Computational Sciences, University of Gondar, Gondar, Ethiopia
Kasim Mohammed, Department of Statistics, College of Natural & Computational Sciences, University of Gondar, Gondar, Ethiopia
Article Tools
Follow on us
Marriage is an important part of human life and age at first marriage is the age at which individuals get married. This varies across communities and individuals in different country. Ethiopia is one of the Sub-Saharan Africa in which highest at early marriage and a small number of delayed marriages are occurred. Survival analysis is a statistical method for data analysis where the outcome variable of interest is the time to the occurrence of an event. Frailty model is an extension of Cox's proportional hazard model in which the hazard function depends upon an unobservable random quantity, the so-called frailty. Regional states of the women were used as a clustering effect in all frailty models. The study aimed to model the determinants of time-to-age at first marriage in Ethiopia. The data source for the analysis was the 2011 EDHS data collected during September 2010 through January 2011 from which the survival information of 12208 woman on age at first marriage. The gamma and inverse Gaussian shared frailty with exponential, Weibull and log-logistic baseline models was employed to analyze risk factors associated with age at first marriage using socio-economic and demographic factors. All the fitted models were compared by using AIC. Out of the total, about 69.3% of women were married and 30.7% were not married at different age of marriage. The median of age at first marriage was 17 years. The log-logistic with inverse Gaussian shared frailty model had minimum value of AIC when compared with other models for age at first marriage dataset. The clustering effect was significant for modeling the determinants of time-to-age at first marriage dataset. Based on the result of log-logistic-inverse Gaussian shared frailty model, women educational level, head/parents occupation, place of residence, educational level of head/parents, access to media and respondent work status were found to be the most significant determinants of age at first marriage. The estimated acceleration factor for the group of women's who had secondary and higher educational level were highly prolonged age at first marriage by the factor of ϕ=1.0796 and ϕ=1.1497 respectively. The log-logistic with inverse Gaussian shared frailty model described age at first marriage dataset better than other models and there was heterogeneity between the regions on age at first marriage. Improving girls and young women access to education was an important avenue for rising women's age at first marriage and for empowering women.
Time-to-age at First Marriage, Risk Factors, Comparison of Models
To cite this article
Bedasa Tessema, Salie Ayalew, Kasim Mohammed, Modeling the Determinants of Time-to-age at First Marriage in Ethiopian Women: A Comparison of Various Parametric Shared Frailty Models, Science Journal of Public Health. Vol. 3, No. 5, 2015, pp. 707-718. doi: 10.11648/j.sjph.20150305.27
Adebowel A., Fagbamigbe A., Okareh O. and Lawal O. (2012). Survival Analysis of Timing of First Marriage among Women of Reproductive age in Nigeria: African Journal of Reproductive Health.
Akaike H. (1974). A new look at the statistical model identification. IEEE Trans Automatic Control.
Bayisenge J. (2010). Early Marriage as a Barrier to Girl’s Education Rwanda: National University of Rwanda.
Bennett S. (1983). Analysis of survival data by the proportional odds model. Statistics in Medicine, 2, 273.
Bedassa B. (2015). Risky Sexual Behavior and PredisposingFactors to HIV/STI Among Students in Mizan-Tepi University(Acase of Tepi Campus). Science Journal of Public Health, Vol.3,No.5,Pp.605-611.
Cox D. (1972). Regression models and life tables (with discussions). Journal of the Royal Statistical Society. 34: 187-220.
Cox D. R. and Oakes D. (1984). Analysis of Survival Data. Chapman and Hall, London.
Cox D. R. and Snell E. J. (1968). A general definition of residuals with discussion. Journal of the Royal Statistical Society. Series B 30 (1968), 248-275.
Duchateau L. and Janssen P. (2008). The Frailty Model. Springer-Verlag, New York.
Erulkar A. (2013). Early Marriage, Marital Relations and Intimate partner violence in Ethiopia.
Goncalves L., Duarte H. and Cabral M. (2015). Prevalence of Hemoglobin S in Blood Donors in the Hospital Dr. Agostinho Neto, Praia City-Cape Verde. Science Journal of Public Health,3:5, 600-604.
Hougaard P. (1984). Life table methods for heterogeneous populations. Biometrika 71,75-83.
Hougaard P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387 - 396
Hougaard P. (1995). Frailty Models for Survival Data. Lifetime Data Analysis. 1: 255-273.
Hougaard P. (2000). Analysis of Multivariate Survival Data, Springer-Verlag, Newyork.
Ibrahim J.G., Chen M. and Sinha D. (2001). Bayesian survival analysis. Springer Verlag, New York.
IPPF and UNFPA. (2006). Ending Child Marriage: A Guide for Global Policy Action, International Planned Parenthood Federation (IPPF), London
Joseph N., M.Fajar R. and Mayang R. (2012). Prevalence of Child Marriage and Its Determinants among Young women in Indonesia, Child poverty and social protection Conference. Journal of Statistics 14, 19 - 25.
Kadane J. and Lazar N. (2001). Methods and Criteria for Model Selection. Technical Report, 759, Carnegie Mellon University.
Kamal S.M.Mostafa (2011). Socio-Economic Determinants of Age at First Marriage of the Ethnic Tribal Women in Bangladesh, Asian Population studies.
Klein J. (1992). Survival analysis: techniques for censored and truncated data. Medical College of Wisconsin.
Klein P. and Moeschberger L. (2003). Survival Analysis Techniques for Censored and Truncated Data - Google Books.htm
Mosammat Zamilun Nahar, Mohammad Salim Zahangir and S.M. Shafiqul Islam (2013). Age at first marriage and its relation to fertility in Bangladesh, Chinese Journal of Population Resources and Environment, 11:3, 227-235, DOI:10.1080/10042857.2013.835539
Munda M., Rotolo F. and Legrand C. (2012). Parametric Frailty Models in R. Journal of American Statistical Association: 55:1-21.
Nour N. M. (2006). Health Consequences of Child Marriage in Africa. Emergence Infection Disease 12(11):1644-9.
Peninah A., Leonard K. Atuhaire. and Gideon Rutaremwa (2011). Determinants of age at first marriage among women in western Uganda. Presented in European Population Conference 2010, Vienna 1-4 September 2010
Population Council (2004). Supporting Married Girls: Calling Attention to a Neglected Group.
Rao C. and Wu Y. (2001). On Model Selection (with discussion). In P. Lahiri (Ed.), Model Selection, Volume 38 of IMS Lecture Notes - Monograph Series. Institute of Mathematical Statistics.
Shapiro, D. (1996). Fertility Decline in Kinshasa, Population Studies Vol50, No.1, pp 89- 103.
Tezera A. (2013). Determinants of Early Marriage among Women in Ethiopia.
Thomas E. (2010-2011). Multilevel Survival Analysis of the Determinants of Age at First marriage Among Women living in Nigeria. Thesis for Master of Statistical Data Analysis, Gent University.
UN . (2000). World Urbanisation Prospects. New York, United Nations.
UN. (1990).Patterns of First Marriage: Timing and Prevalence, New yorkeVol.4. No. 3 (April), pp: 221-235.
UN. (2007). The Millennium Development Goals, Report 2007, United Nations, New York. Retrieved 12, August, 2013
UNFPA. (2003). State of World Population 2003: Making 1 Billion Count: Investing in Adolescents’ Health and Rights. New York
UNFPA. (2006). In ending child marriage, a guide for global policy action International Planned Parenthood Federation and the Forum on Marriage and the Rights of Women and Girls. U.K.
UNICEF. (2005). Early Marriage: A Harmful Traditional Practice: A Statistical Exploration. UNICEF: New York, NY.
UNICEF. (2011). Child Protection from Violence, Exploitation and Abuse.
Vaupel J., Manton K. and Stallard E. (1979). The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality. Demography. 16: 439-454.
Westoff C. F. (2003). Trends in Marriage and Early Childbearing in Developing Countries. DHS Comparative Reports No.5. Macro International Inc.: Calverton, Maryland.
Wienke A., Lichtenstein P. and Yashin A.I. (2003). A bivariate frailty model with a cure fraction for modeling familial correlations in diseases. Biometrics, 59, 1178-83.
Wienke A., Ripatti S., Palmgren J., Yashin A.I. (2010). A bivariate survival model with compound Poisson frailty. Statistics in Medicine 29, 275–83.
Yu B. (2006). Estimation of shared gamma frailty models by a modified EM algorithm. Computational Statistics and Data Analysis 50, 463-474.
Zahangir M. S., M. A. Karim, M. R. Zaman, M. I. Hussain and M. S. Hossain, 2008. Determinants of age at first marriage of rural women in Bangladesh: A cohort analysis Trends Applied Science. Res. 4(3):335-343, Academic journal, Department of Statistics.
Zahangir M.S. and Kamal M.M. (2011). Several Attributes Linked with Child Marriage of Females' in Bangladesh, International Journal of Statistics and Systems, volume 6.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186