When constructing new biomarker or gene signature scores for time-to-event outcomes, the underlying aims are to develop a discrimination model that helps to predict whether patients have a poor or good prognosis and to identify the most influential variables for this task. In practice, this is often done fitting Cox models. Those are, however, not necessarily optimal with respect to the resulting discriminatory power and are based on restrictive assumptions. We present a combined approach to automatically select and fit sparse discrimination models for potentially high-dimensional survival data based on boosting a smooth version of the concordance index (C-index). Due to this objective function, the resulting prediction models are optimal with respect to their ability to discriminate between patients with longer and shorter survival times. The gradient boosting algorithm is combined with the stability selection approach to enhance and control its variable selection properties.