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This paper introduces a novel non-parametric deep model for estimating time-to-event (survival analysis) in presence of censored data and competing risks. The model is designed based on the sequence-to-sequence (Seq2Seq) architecture, therefore we name it Survival Seq2Seq. The first recurrent neural network (RNN) layer of the encoder of our model is made up of Gated Recurrent Unit with Decay (GRU-D) cells. These cells have the ability to effectively impute not-missing-at-random values of longitudinal datasets with very high missing rates, such as electronic health records (EHRs). The decoder of Survival Seq2Seq generates a probability distribution function (PDF) for each competing risk without assuming any prior distribution for the risks. Taking advantage of RNN cells, the decoder is able to generate smooth and virtually spike-free PDFs. This is beyond the capability of existing non-parametric deep models for survival analysis. Training results on synthetic and medical datasets prove that Survival Seq2Seq surpasses other existing deep survival models in terms of the accuracy of predictions and the quality of generated PDFs.