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Survival analysis is a crucial statistical technique used to estimate the anticipated duration until a specific event occurs. However, current methods often involve discretizing the time scale and struggle with managing absent features within the data. This becomes especially pertinent since events can transpire at any given point, rendering event analysis a continuous concern. Additionally, the presence of missing attributes within tabular data is widespread. By leveraging recent developments of Transformer and Self-Supervised Learning (SSL), we introduce SSL-SurvFormer. This entails a continuously monotonic Transformer network, empowered by SSL pre-training, that is designed to address the challenges presented by continuous events and absent features in survival prediction. Our proposed continuously monotonic Transformer model facilitates accurate estimation of survival probabilities, thereby bypassing the need for temporal discretization. Additionally, our SSL pre-training strategy incorporates data transformation to adeptly manage missing information. The SSL pre-training encompasses two tasks: mask prediction, which identifies positions of absent features, and reconstruction, which endeavors to recover absent elements based on observed ones. Our empirical evaluations conducted across a variety of datasets, including FLCHAIN, METABRIC, and SUPPORT, consistently highlight the superior performance of SSL-SurvFormer in comparison to existing methods. Additionally, SSL-SurvFormer demonstrates effectiveness in handling missing values, a critical aspect often encountered in real-world datasets.