Paper:
Currently available survival analysis methods are limited in their ability to deal with complex, heterogeneous, and longitudinal data such as that available in primary care records, or in their ability to deal with multiple competing risks. This paper develops a novel deep learning architecture that flexibly incorporates the available longitudinal data comprising various repeated measurements (rather than only the last available measurements) in order to issue dynamically updated survival predictions for one or multiple competing risk(s). Unlike existing works in the survival analysis on the basis of longitudinal data, the proposed method learns the time-to-event distributions without specifying underlying stochastic assumptions of the longitudinal or the time-to-event processes. Thus, our method is able to learn associations between the longitudinal data and the various associated risks in a fully data-driven fashion. We demonstrate the power of our method by applying it to real-world longitudinal datasets and show a drastic improvement over state-of-the-art methods in discriminative performance. Furthermore, our analysis of the variable importance and dynamic survival predictions will yield a better understanding of the predicted risks which will result in more effective health care.

Review:
The paper proposes a deep architecture that conducts survival analysis from longitudinal data where multiple competing risks are present. Experimental results demonstrate the effectiveness of the proposed method.  Specific comments follow:
1. A primary concern in the reviewer's opinion is the scalability of the architecture. While the reviewer appreciates the discussion of the scalability issue in terms of the output layer in the paper, the architecture might also not scalable if the number of competing risks is large because of the increase of the cause-specific subnetworks in the architecture.  Overall, the reviewer finds the lack of a principled approach to deal with competing risks and long time horizon presented in the paper.  Since dealing with competing risks in survival analysis is the goal of the paper, the reviewer finds the method presented insufficient for acceptance. As a remedy, for example, for the output layer, can the author consider the use of a neural net to model o_k at a particular time using time and f_{c_k}() as input?
Other issues:
2. it will be nice to explain (1) and (2) a little after presenting the formula.
3. page 5, $\mathbf{y}_j$ should also be explained because the next place where $\mathbf{y}_j$ is present is (4), which is one page later.
4. the term "dynamic survival analysis" is also obscure. What exactly does "dynamic" mean? To the reviewer's understanding, compared to standard survival analysis, the architecture models directly from raw longitudinal data of repeated measurements, and hence is called "dynamic".
5. even the "dynamic" part of the dynamic survival analysis is not very novel, see, for example, 
Recurrent Marked Temporal Point Processes: Embedding Event History to Vector
and the follow-up works in the use of deep learning for point process modeling.
===============After Reading Authors' Response ================
The reviewer would like to thank the authors for their detailed response and careful revision of the paper to address the reviewer's concern. However, the reviewer is not persuaded by the authors' response. Specifically,
1. the reviewer is not satisfied with the explanation and modification to address the scalability issue stemming from both the cause-specific subnetworks and the output layer. Simplifying the structure and parameterization of cause-specific subnetworks when many are present seems like a comprise rather than a principled approach to address the issue. The same is true for the exponentially distributed parameterization of the output layer.
2. It is the reviewer's impression that for point process neural networks, it is possible to use the covariate information for prediction, as opposed to the claim given by the author.