The predictive problem analyzed in this paper concerns survival analysis. A d-dimensional r.v. X is observed, modelling some information a priori useful to predict a partially observed random duration \(T\ge 0\) . Motivated by various applications ranging from public health resource management to predictive maintenance in industry, the goal is to build a ranking function \(f:\mathbb {R}^d\rightarrow \mathbb {R}_+\) for operational prioritization purposes, so that f(X) and T tend to increase or decrease together with (hopefully) largest probability. While Harrell’s concordance index (C-index) is a natural performance criterion for this problem, the statistical learning framework often encountered in practice stipulates that only right-censored realizations of the duration T are present in the training database. Since discarding censored observations and analyzing only complete ones leads to considerable bias and error, we explain how to calculate an empirical version of the C-index in a censored context, which is amenable to optimization. We then establish learning rate bounds for empirical C-index maximizers and present numerical results empirically confirming the relevance of this approach.