Female genital mutilation (FGM), also known as female genital cutting or female circumcision, is one of the deeply rooted traditional practices, in which the external female genital organ is either partially or totally removed for non-medical reasons. In Ethiopia, FGM is widespread across the majority of regions and ethnic groups, having the highest national prevalence that leads them to various complications such as immediate urinary and genital tract infection, pain and hemorrhage, complications in childbirth and social, psychological and sexual complications. This study aimed to model and investigate the potential risk factors of time-to-circumcision of girls in Ethiopia using parametric shared frailty models where regional states of the girls were used as a clustering effect in the models. The data source for the analysis was the 2016 EDHS data collected from January 18, 2016 up to June 27, 2016 from which the survival information of 2930 girls on age at circumcision obtained. The gamma and inverse Gaussian shared frailty distributions with Exponential, Weibull and log-logistic baseline models was employed to analyze risk factors associated with age at circumcision using socio-economic and demographic factors. All the fitted models were compared by using AIC and BIC values from simulation study and actual dataset. The result revealed that about 22.4% of girls were circumcised and 77.6% were not circumcised. The median age at circumcision was 3 years. Based on AIC and BIC values from simulation experiment and graphical evidences, log-logistic model with inverse Gaussian shared frailty distribution preferred when compared with other models for age at circumcision dataset. The clustering effect was significant for modeling the determinants of time to circumcision of girls dataset. Based on the result of log-logistic inverse Gaussian shared frailty model, mothers and fathers educational level, place of residence and religion of parents were found to be the most significant determinants of age at circumcision of girls. The estimated acceleration factor for the group of mothers who had secondary and higher educational level were highly prolonged age at circumcision of girls by the factor of = 3.119 and = 3.933 respectively. The log-logistic model with inverse Gaussian shared frailty distribution described age at circumcision of girls better than other models and there was heterogeneity between the regions on age at circumcision. Improving parents access to education would be an important way approach for preventing girls' circumcision.
