Summary
The authors propose a neural architecture to estimate the survival function for observations of survival times and censored survival times. The authors describe a methodology to include heterogeneity among the population by including the frailty component. The authors then theoretically and empirically illustrate properties of their approach. The theoretical results are used to provide additional justification for why a neural network architecture is appropriate for this kind of problem. Empirical results are added to place into context the performance of the proposed methods with respect to existing methods.
Strengths
The paper provides a thorough analysis on using neural networks for survival estimation beyond the analyses present in previous works. The authors also consider frailty which they naturally include within their modelling framework, removing some of the homogeneity assumptions of previous works. The empirical results suggest that the method performs well in the considered scenarios. I did not check the details of the proofs, but the theoretical component seems useful and original for predicting convergence rates of the estimator and applicable to other similar estimators. Finally, the writing is clear and easy to follow.
Weaknesses
The main weakness involves the empirical evaluation of the paper. None of the empirical gains are major when considering the empirical experiments. This is expected with real world data since it's difficult to estimate the counterfactual (i.e. maybe the survival time could have been much longer/shorter). I would suggest to add an empirical result that compares the methods in idealized settings where the true survival distribution is known and that the metrics can be appropriately compared.
Another potential weakness involves the theoretical guarantees. If I'm understanding correctly, the theory applies in the case where the networks are well-learned, which is still subject to the issues associated with neural network optimization. It may be good to emphasize this in the text.
Questions
How does the empirical convergence compare with the theoretical?
The authors mention using Clenshaw-Curtis as the integrator, how does the parameters of the integrator (e.g. step size) affect the performance of the method? Is there some numerical bottleneck related to this integration?
In the theoretical results, the MLPs scale with the number of samples, is there a rigorous connection to the number of parameters in the network and the number of samples? Additionally, was this enforced in the experimental setup, I could not tell if this was the case in the hyper parameter section of the appendix?
Does the method extend to representing the joint distribution of multiple survival times? E.g. something like $P(T_1 > t_1, \ldots, T_d > t_d \mid Z)$?
Was a nonparametric model for the frailty component examined, i.e. could $f_\theta$ be represented by some generative model constrained to be positive?
Rating
7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Limitations
The authors did mention limitations in the appendix. Alongside their notes, it may be good to get a review of where the authors think that their method is appropriate and where other methods would be more appropriate. Additionally, it would be nice to see conditions where the method fails to get a better idea of the properties of the method. This could possibly come from some of the theoretical assumptions being violated (e.g. it’s unclear which ones are really necessary in practice versus for proving the theorems).