Bivariate Copula Model on Fitting Correlated Time-to-Event Outcomes: Age at First Sex and Age at First Marriage Among Youth in Tanzania

Traditionally, age at first sex (AFS) and age at first marriage (AFM) have been analysed independently. While useful for summarising risk factors for each outcome individually, these approaches offer limited insight into the interdependence between these events. This study used an Archimedean copula model for bivariate right-censored data to jointly model AFS and AFM reported by 9726 young people aged 15–24 years in Kisesa, Tanzania. The dependence structure was identified, the degree of association between these events and their associated factors assessed, and the trends of predicted medians examined. Various Archimedean copulas (Ali–Mikhail–Haq, Clayton, Frank, Gumbel, Copula2, and Joe) were evaluated. Copula function selection was based on the Akaike information criterion (AIC), Bayesian information criterion (BIC), and log-likelihood values, with the Frank copula and a log-logistic marginal distribution performing best. The Frank copula’s dependency parameter (θ) was highly significant, with an estimated θ of 39.49, translating to a Kendall’s τ of 0.903 in the unadjusted model, which included only sex as a covariate, indicating a strong positive correlation between AFS and AFM. Similar results were observed in the adjusted model (Kendall’s τ = 0.89), which incorporated additional variables such as education and residence area. Trends show a better estimation of AFS and AFM for both females and males over the period 1994–2016 when analysed jointly rather than separately. The strong positive correlation suggests these events are highly correlated; hence, using joint models captures interdependence and provides more accurate estimates. This approach can inform targeted interventions to improve youth health outcomes.