We suggest a pragmatic extension of the non-parametric copula-graphic estimator to a depending competing risks model with covariates. Our model is an attractive empirical approach for practitioners in many disciplines as it does not require knowledge of the marginal distributions. Although non-observable and only set-identifiable in most applications, classical duration models typically impose ad-hoc assumptions on their functional forms. Instead of directly estimating these distributions, we suggest a plug-in regression framework which utilises an estimator for the observable cumulative incidence curves which specification can be visually inspected. We perform simulations and estimate an unemployment duration model to demonstrate the advantages of our model compared to classical duration models such as the Cox proportional hazard model.