Modeling the Determinants of Time-to-age at First Marriage in Ethiopian Women: A Comparison of Various Parametric Shared Frailty Models

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.