Identifying treatment response subgroups in observational time-to-event data

• There was one famous work called "Deepsurv"[1] in this field which was published in 2018. Although it does not consider subgroup identification, but I think you should compare your work with theirs in terms of IAE.
• For identifying the subgroup analysis, the work states that it utilizes a vector $l_k$ (please consider change the notation to $v$ as in your previous sections $l$ is used for log-liklihood), however, there is no description how you got the $l_k$. Is $l_k$ a trainable parameters for your model to learn or some features extracted directly from the baseline table? I would give you a borderline score for now as I didn't get your point at this time but will consider increasing the score if you can explain it clearly in the rebuttal.
• As illustrated in this paper[2], another key information when estimating the treatment effects over time-to-event data is the confidence interval to quantify the how much difference do you observe in the identified subgroup. I think it does matter in the medical science.
• Lastly, I would say the contribution of this work is limited in both methods and application scenario. The methods uses a neural network to model the survival distrbution and estimate the treatment effects is not something new as the work [1] has proposed simiar idea in 2018. The work's framework for addressing the potential bias in observational data is also a classic stragegy used in this field as earliest proposed in "DragonNet"[3]. And in terms of the application scenario, I didn't see any advantage of your method over other external interpretation method as you illustrated in your real-world case study. In your appendix Figure 8, my understanding is that it is very similar to Shapley value like Figure 5 in [2], and it seems that it does not consider the interaction effects based on your interpretation.

[1] Katzman, J. L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., & Kluger, Y. (2018). DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network. BMC medical research methodology, 18, 1-12.

[2] Jiang, L., Xu, C., Bai, Y., Liu, A., Gong, Y., Wang, Y. P., & Deng, H. W. (2024). Autosurv: interpretable deep learning framework for cancer survival analysis incorporating clinical and multi-omics data. NPJ precision oncology, 8(1), 4.

[3] Narendra, K. S., & Mukhopadhyay, S. (1997). Adaptive control using neural networks and approximate models. IEEE Transactions on neural networks, 8(3), 475-485.

1. The main limitation lies in the interpretability of subgroups, especially regarding how these identified subgroups can be understood and applied by clinical practitioners. For example, in Appendix C, it would be helpful to know the characteristics of the two subgroups. If a patient presents with specific features, how would doctors classify them into a subgroup? Additionally, how statistically stable are these subgroups?
2. The presentation of the paper is somewhat tedious. The problem setup section (lines 89 to 289) contains an excess of basic concepts that are likely familiar to scholars in the field, making it less engaging. I recommend condensing the key assumptions and focusing on the unique aspects of the proposed approach.
3. In the synthetic experiment, the number of clusters is known to be three, and the authors use the negative log-likelihood to identify the optimal number of clusters. This heuristic indeed suggests three clusters, aligning with the generative process of the synthetic data. However, in the appendix for the real-world experiment, the cluster number is set to two, which seems questionable, with no verification provided for its accuracy. In summary, the proposed method assumes a pre-determined cluster number, which itself is a complex issue. I am concerned that the performance of the new method may heavily rely on the correctness of this cluster number, and the paper does not provide a robust solution to address this dependency.

My main criticism toward the work is that it is too assumption heavy. Authors assume observational study is perfect for causal analysis (e.g., no unmeasured confounding) and that the censoring time is conditionally independent of the time-to-event variable. On top of those, the assumption that the number of subgroups is known a priori makes the setting too simple/unrealistic.

While this may not necessarily be a reason for criticism, the results derived in this work follow rather straighforwardly via an amalgamation of the existing work in the literature, bringing the amount of non-incremental contribution made by this work under question, which for me the key takeaway being using nonlinear models for the nuisance functions.

Given this restrictive assumptions, I think it is valuable to evaluate how well the models perform under different violations of the assumptions. The authors could run ablation studies, isolating the violations of different assumptions one at a time to analyze the sensitivity to those assumptions (e.g., no unmeasured confounding and independent censoring and time-to-event).

Authors seem to do this for choosing the number of clusters in Appendix B.3., and to me, there seems to be a non-trivial degrade in performance (larger confidence intervals). This should be more clearly acknowledged in the main text and supported with more discussions in the Appendix for the underlying reasons. In the current form, it seems to be brushed off by saying the model is robust to this, but I do not totally agree.

• The structure of the paper could be clearly improved to clarify the exact research gap, comparison to existent works, and contribution:
  • In the introduction (line 44-52), method section (l. 201-255), and related work (l.472-479), this paper references mostly CATE methods in the static setting and thus neglecting to explain the connection to CATE methods on survival data (e.g., SurvITE, etc.) or subgroup identification for CATE which makes it hard to judge the novelty of the work.
  • The potential outcome framework could be introduced more formally and earlier to properly describe the causal nature of the problem
  • Instead of normal survival forests with clustering, the causal survival forest could be used as a baseline, e.g. also with the R-learner / DoubleML to adjust of selection bias.
  • The motivation for the subgrouping could be improved, e.g., usually the objective is to get interpretable subgroups
  • In Eq. (5) and (6), the authors should clearly explain how and why inverse propensity weighting benefits their method, e.g., by properly showing the theoretical benefits under selection bias.
• The Equations and theoretical motivations seem to be inaccurate and could be improved and extended:
  • Eq. (4): what exactly is $l_F^*$, what exactly does the “log-likelihood consisting of both factual and counterfactual[...]” represent? Especially wrt to the motivation of IPW later, this is an important part.
  • What are the consequences and motivation of propensity clipping in Eq.(5) “avoid unstable weights”? (introducing bias but lowering variance, still unbiased but faster convergence?)
  • Eq. (6) should present an equation or objective and could be better motivated
  • $u$ should be introduced in Eq. (2) & (6)
• The contribution seems to be mainly incremental, combining existing ideas from subgroup analysis, clustering for survival analysis, and inverse propensity weighting