Venue: ICLR 2022 Conference

Reviews:

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: In this work, the authors propose a model for clustering survival data which accounts for both survival time as well as covariates, such as patient demographics. The model is similar to previous approaches, though it incorporates a neural network encoder to handle unstructured data types as input. A modest set of experiments suggest that the proposed approach identifies more meaningful clusters than similar approaches. Also, while not the focus of the proposed approach, empirical evaluation shows that the proposed method performs similarly to existing approaches on time-to-event predictions.
main_review: The novelty of the proposed work is modest. As the authors point out, similar clustering-based approaches for survival analysis have already been proposed. Likewise, encoding data types such as images into a latent representation using neural networks is common. To the best of my knowledge, though, combining these approaches is novel.

In terms of technical soundness, the proposed approach is reasonable. I didn’t verify it in detail, but the ELBO approximation appears to follow typical conventions. The experiments are well designed with good baselines and evaluation methodology. The results seem to be presented fairly, and the authors discuss both the strengths and limitation of their approach.

The paper is generally well written and easy to follow.

In terms of reproducibility and contribution to the community, the authors provide technical details in the appendix. They also make their code available. While I did not run the code, it does adhere to a clear style, so I believe that would be a helpful contribution to the community.
summary_of_the_review: Overall, the proposed work is an incremental step forward for survival analysis. While the impact may not be huge, I believe the proposed approach is a reasonable, novel view on the problem. The experimental results are not overwhelming, but they show that the proposed approach does succeed at clustering patients. This is key for precision medicine, so other researchers could also build on this formulation and approach.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper proposes a new latent variable model for clustering survival data. Experiments with simulated and real data demonstrate that the proposed method can identify accurate/meaningful cluster assignments while simultaneously providing survival predictions that are on par with the existing methods.
main_review: his paper proposes a new latent variable model for clustering survival data. The new method aims to identify clusters that have characteristic generative survival mechanisms or associations between the auxiliary covariates and the survival times, contrary to methods that identify clusters solely based on the survival times or solely based on covariates. The model is formulated as a latent variable model that combines a general latent variable model with neural network parameterized decoder likelihood for covariates as well as Weibull distribution model for the survival function. Model inference is developed suing the auto-encoding variational Bayes. Amortised variational inference combines a neural network parameterized encoder for the covariates as well as a separate encoder block for the cluster assignments that is defined directly by the generative model, which also naturally handles data points where the survival time is missing/censored. Overall, the model specification seems well-motivated, and the description of the model/results admirably clear.

The proposed method is compared against a large collection of previous methods on both synthetic and real data sets. Performance metrics include clustering assigngment accuracy and survival time prediction accuracy. Overall, experiments with simulated and real data demonstrate that the proposed method can provide more accurate/meaningful cluster assignments than previous methods, while at the same time providing survival predictions that are on par with the existing methods. 

This manuscript proposes an interesting latent mixture survival model that makes a useful contribution to the field. Technical details appear correct.  I do not have any major concerns with the manuscript. 

Concerning the experiments with simulated data, the differences in cluster-specific Kaplan-Meyer curves appear perhaps unreasonably large compared to what is typically expected in real applications.  Can you provide additional experiments with modified versions of the data set where differences between the KM curves would be smaller?  Results for such simulations would also reveal how the performance of different methods behave when you make your dataset more difficult. 

summary_of_the_review: This manuscript proposes an interesting latent mixture survival model that makes a useful contribution to the field.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The paper proposed a novel variational deep survival clustering (VadeSC) method to discover underlying distribution of both the explanatory variables and censored survival times. Its main contributions are jointly modeling variables and censored survival outcomes and comprehensive comparison of proposed methods on state-of-art existing models on both synthetic and real-world datasets.
main_review: Strengths:
- The literature review on related clinical survival analysis research is thoroughly summarized with clear statement on the relevance and differences with comparison to the proposed method.
- Experiment design is comprehensive and rigorous with various important evaluation metrics of clustering analysis and survival predictions, on different types of datasets (synthetic, semi-synthetic and real-world benchmark data)
- Detailed experiment assumptions, parameters, implementations, as well as results (enough Appendix references and supplementary material to reproduce the proposed work as well as baseline models)
- Meaningful discussion of method limitations and future work

Weaknesses:
- My major complaint originated from the potential fair practical utility of the proposed method in clinical applications indicated by Figure 5, the comparison of Kaplan-Meier curves between DSM and VaDeSC among identified clusters. One major purpose of the survival analysis is to guide bedside clinicians and nurses for timely intervention for better survival outcome and the clustering analysis could offer meaningful grouping of risk-stratified patients with intervention priorities. Thus a clear separation of different shapes of KL curves might be more helpful in real-time bedside practice and guidance, than the visual separation of images and allocation of tumors. In this case, DSM seems to perform better for this purpose in indicate "When to intervene" on the NSCLC dataset. However, VaDeSC, by its nature to differentiate variants, might be better utilized in diagnosis process for image data. I also wonder whether it's the same case for tabular data.
- Color visualization of Figure 4: KM curves of assigned clusters are very hard to see and compare. Yellow and blue might be better replaced with e.g. red and green for better contrast. 
- Is there any justification for why FLChain results are in Appendix instead of main text? section 5.2 on page 7. Methods and datasets are not uniform across the paper e.g. table 2, 3 and 4 are of different subsets. If space is limited, is it possible to provide complete table of results comparison of all metrics, all methods and all datasets in the Appendix. 
- The content of the paper is very dense to read due to the great efforts the author(s) have put. Sometimes the results lack immediate clear interpretation in the main text and referring to Appendix seems to be too frequent. It will be better if the main content could be more targeted and focused.   

Additional question:
- Would you pls comment how the performance of different models vary by the %censored of the datasets? 

summary_of_the_review: The paper which proposed a novel survival clustering algorithm is well-written with thorough literature review, clear analysis assumptions, comprehensive experiment design and results comparison with state-of-art baselines models and closely related benchmark datasets, which is a good example for dedicated research work.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This work tackles the problem of clustering in the context of survival data using a generative model. A variational autoencoder is used for modelling the data, while the latent representation is leveraged to model the survival outcome conditionned on the assigned cluster following a Weibull distribution. This approach allows to leverage both the survival outcome and the covariates for clustering. Moreover, the latent state associated to each cluster is then used for interpretability of the observed cluster.
Synthetic and real world datasets demonstrate the competitiveness of the method on both discriminative and clustering performances.
main_review: The paper is well written and easy to follow. 

Nonetheless, Figure 4 is hard to read and interpret, it would be interesting to do this analysis on a dataset with a smaller number of clusters. Further description of the clustering evaluation would also be valuable: in figure 4, is the latent representation obtained on the test split only? It seems the authors use a Monte Carlo cross-validation, it would be beneficial to add this point in the experiment section.
Finally, in Figure 5, were the number of clusters and their shapes consistent over multiple iterations? An experiments measuring this stability would be a good addition.

Finally, it would be necessary to further articulate the technical contributions of the paper, as the proposed model is similar to [1] in which they also propose a variational approach to obtain a better embedding that influences the baseline distributions. The main difference resides in the baseline distributions which are parametric in [1]. The proposed appraoch merges [1] and [2] and extends it to a fully generative model. This should be clearly stated and a comparison with the distribution obtained in [1] would be a valuable addition.

[1] Nagpal, C., Yadlowsky, S., Rostamzadeh, N. and Heller, K., 2021. Deep Cox mixtures for survival regression. 
[2] Nagpal, C., Li, X.R. and Dubrawski, A., 2021. Deep survival machines: Fully parametric survival regression and representation learning for censored data with competing risks. 
summary_of_the_review: An interesting work, well-described and with in-depth experiments. However, the technical contribution has to be described in greater details.
review_title: null

Meta-review: Four knowledgeable referees recommend Accept. I also think the paper provides a unique contribution to the field of deep survival models and I, therefore, recommend Accept
Decision: Accept (Poster)