Bayesian Nonparametric Survival Analysis via Deep Dirichlet Process

$\bullet$ At first, experiments are somewhat limited in datasets. Besides the considered datasets, there are various datasets such as SEER, GBSG, METABRIC, etc. More datasets are required to validate the generalization.

$\bullet$ I don’t know the effect of the usage of a heavy-tailed kernel. This paper lacks of delicate analysis of the design of DP. To validate the effect of a heavy-tailed kernel, experiments with one kernel or controlling the ratio of kernels by $k_1$ and $k_2$ are required. It seems that the performance gain is not impressive, especially in the 90% quantile time horizon.

• The paper is not easy to understand, notations could be more clear, some statements are contradictory and there are many typos and errors, which should be fixed. Parts of the appendix are missing.
• I don't understand how the proof is relevant to the model in the paper. The authors assume the hazard rate is given by a neural network and use the survival loss in the proof, but the actual model is a mixture of distributions with an ELBO optimization. I might be missing something here, but it seems just based on established literature and irrelevant.
• If the proof is relevant, the implications of the proof could be explained better and it should be explained how this is distinguishing the model from other models.
• Dirichlet Process Mixture models for survival is not novel, nor is adding long tailed distributions (cure-models). Encoding the parameters with a NN and using VI, while seemingly working well, is in my opinion not novel enough for this venue.

In general, I feel the major weakness comes from the significance section, where I find it’s very hard to differentiate the key differences between the current method and related work.

1. I feel like this looks like a simple adaptation of well-known technology. Therefore I could not identify the actual novelty or significance of current submission. For example, using the dirichlet process, or non-parameter bayes are not new in the related work (e.g, [1-5]). This reviewer finds it very difficult to know the actual new contributions, compared with previous large amounts of related papers. For example, in [3], it is a book to systematically discuss dirichlet process and survival analysis. I would think authors should make more clear explanations on the key novelties.

2. The two key contributions, handling high-dimensional data and long tail survival approximation are seemingly not effectively justified. For example, the high-dimensional data is incorporated with a regular deep learning model, where it seems no very high-dimensional data (such as medical images) are tested. Besides, the mean-field approximation makes it a bit hard to believe how this can indeed tackle the long-tail.

References

1. Neural Survival Clustering: Non-parametric mixture of neural networks for survival clustering. 2022
2. Bayesian nonparametric Erlang mixture modeling for survival analysis. 2023
3. Dirichlet Process – with Applications on Survival Analysis. Zhaoheng Li and Yeheng Zong. 2021-12-15
4. Reliable survival analysis based on the Dirichlet process. 2015
5. Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model. 2021

The methodological components of the paper are very difficult to follow. Specifically:

• Figures 1 and 2, and Algorithm 1 are not mentioned or discussed in the text.
• Some quantities have not been defined, e.g., \tilde{X}, p(Z=k|x,beta), Z, \phi. Some can be guessed from the figures though.
• Equation (5) needs further explanation. Where is zeta, zeta are the parameters of (2) but (2) is not in (5), there are only K_1 \zeta values but they are indexed to K_1+K_2?
• Algorithm 1 describes a collection of networks that are not described.

The Theoretical results in Section 4 are welcome but are completely decontextualized of the rest of the paper.

The datasets need to be described in more detail, specially, the synthetic dataset and MIMIC. The former for being introduced in the paper and the latter from being a general dataset and survival tasks can be specified in a multitude of ways.

In the main experiment (Table 2) it is not clear why C-indices are not presented over the complete time horizon or at least done over time. Further, some of the gains by the proposed model are not statistically significant after accounting for variation.

Results in Table 3 are underwhelming because one will expect the proposed model which is specifically designed for long tails to more clearly outperform other models on long horizons, however, that does not seem the case. In fact the proposed model seems to perform better on lower quantiles (comparing Table 2 and 3).

Though it is good to see ablation studies for the number of mixture components, concentration rate and censoring rate, these are only selectively compared to a few other modeling approaches and largely disconnected from the tail behavior and performance of the model.