This paper introduces a prognostic method called FLASH that addresses the problem of joint modelling of longitudinal data and censored durations when a large number of both longitudinal and time-independent features are available. In the literature, standard joint models are either of the shared random effect or joint latent class type. Combining ideas from both worlds and using appropriate regularisation techniques, we define a new model with the ability to automatically identify significant prognostic longitudinal features in a high-dimensional context, which is of increasing importance in many areas such as personalised medicine or churn prediction. We develop an estimation methodology based on the EM algorithm and provide an efficient implementation. The statistical performance of the method is demonstrated both in extensive Monte Carlo simulation studies and on publicly available real-world datasets. Our method significantly outperforms the state-of-the-art joint models in predicting the latent class membership probability in terms of the C-index in a so-called ``real-time'' prediction setting, with a computational speed that is orders of magnitude faster than competing methods. In addition, our model automatically identifies significant features that are relevant from a practical perspective, making it interpretable.

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