Longitudinal data analysis is essential in various fields, providing insights into associations between interpretable explanatory variables and temporal response variables. Recent progress in generative modelling has demonstrated models that can learn low-dimensional representations of complex longitudinal data and capture intricate interactions between high-dimensional features. Ideally, the trained generative model can be used for various downstream tasks, such as data generation, prediction and classification. In this work, we evaluate the performance of the longitudinal variational autoencoder model in predicting adverse events in clinical trials. We also propose a general training approach that can learn versatile generative models while simultaneously optimising performance on a specific downstream task. Our experiments on two simulated datasets and one clinical trial dataset demonstrate that the proposed training objective provides results that are either comparable or better than results obtained with the standard training methods. Our results also suggest that longitudinal information is useful for adverse event prediction in clinical trials.