We introduce two approaches to topic modeling supervised by survival analysis. Both approaches predict time-to-event outcomes while simultaneously learning topics over features that help prediction. The high-level idea is to represent each data point as a distribution over topics using some underlying topic model. Then each data point's distribution over topics is fed as input to a survival model. The topic and survival models are jointly learned. The two approaches we propose differ in the generality of topic models they can learn. The first approach finds topics via archetypal analysis, a nonnegative matrix factorization method that optimizes over a wide class of topic models encompassing latent Dirichlet allocation (LDA), correlated topic models, and topic models based on the "anchor word" assumption; the resulting survival-supervised variant solves an alternating minimization problem. Our second approach builds on recent work that approximates LDA in a neural net framework. We add a survival loss layer to this neural net to form an approximation to survival-supervised LDA. Both of our approaches can be combined with a variety of survival models. We demonstrate our approach on two survival datasets, showing that survival-supervised topic models can achieve competitive time-to-event prediction accuracy while outputting clinically interpretable topics.
The paper addresses the problem of survival analysis (predicting time until, e.g., death) using topic modeling. The point of introducing topic modeling here is to gain better insight into what helps predict survival times of unseen test subjects. This contrasts with much of the earlier work in survival analysis, which is mainly or only concerned with getting the best prediction without concern with the “thematic structure” of features. Such a thematic structure could be useful to clinicians, but analysis of the learned topic structure by clinical experts is apparently left for future work. Empirical results on pancreatitis and metabric datasets show that the methods of the paper are comparable to several established baselines.
I think the goals of the paper are well motivated, as time-to-death is not the only measure of interest and clinicians and other domain experts may want to get better insight into why a given model makes certain predictions. The two approaches presented in the paper are mostly on par with (but do not outperform) the best baselines considered in the paper, which would be fine in the approaches were particularly novel and/or the learned “thematic structures” would have demonstrated uses. Unfortunately, I feel the latter conditions are not met, as I have the following concerns:
(1) I find the paper to be relatively incremental in terms of ML methods, and I consider it to be more of an applied ML paper. The paper builds largely upon survLDA (Dawson and Kendziorsky, 2012), using Car et al. (2018)’s way of approximating LDA in a neural framework. Much of the exposition of Survival-Scholar (i.e., section 4) is based on Scholar (Card et al.). The paper presents another method based on archetypal analysis, which adds a supervised term to the loss. The archetypal approach of the paper merely consists of an “algorithmic modification” and otherwise borrows extensively from Javadi and Montanari (2019) and Bolte et al. (2014). In both cases (survLDA extension and archetypal analysis), most of the equations/algorithms can be traced back to these previous papers.
(2) The main point of the paper is to go beyond simply predicting time-to-event outcomes, and instead gaining some insight into the features helping predict time of death. The authors rightly “note that for both datasets, the vast majority of words we used require clinical expertise to interpret”, but it doesn’t seem they have given the learned topics to clinicians to judge whether they make sense or are helpful in any ways. Instead, appendix F provides lots of tables that are difficult to interpret for non-domain experts with little medical background. 
(3) I have some more minor concerns (or questions) about the experimental results. See detailed comments.
Overall, I found the paper to be clear and well written, but algorithmic and empirical contributions are I think rather small (small or no empirical gains, incremental ideas).
Detailed comments/questions:
- Table 1: I don’t think it makes sense to label a system as either first or second. With differences of less than 1% and the small size the test set, most of the top systems are probably within the same confidence intervals, which I think the authors should compute and add to the tables. Many of the earlier works cited in the paper (e.g., DeepSurv, DeepHit) provide such confidence intervals, which are crucial in the case of the submission as its dataset is relatively small compared to e.g. SEER used with DeepHit.
- “For all methods, if the method does not already have a hyperparameter selection procedure, we use 5-fold cross-validation on the training data to select hyperparameters prior [..]”. Shouldn’t cross-validation for hyperparameter selection be used with all the methods of the paper, as the paper doesn’t define a validation set? I’m a bit concerned results may not be fully comparable if the selection procedure is not consistent across algorithms (e.g., 5-fold vs other methods). I presume “already have a hyperparameter selection procedure” refers to a procedure applied to the MIMIC dataset (as original hyperparameters borrowed from previous work might not work well). If so, I think the paper should say this explicitly.
- Experimental results consist of single table that leaves much to be desired in terms of understanding why a method works well or not. For example, what about indicating the number of model parameters (for the parametric methods) and learned hyperparameters. With such a small dataset, cross-validation could still be noisy and prone to selecting a bad set of hyperparameters (e.g., significant differences in terms of number of parameters). An indication of how sensitive to hyperparameters the methods are would be useful too.