Multitask Boosting for Survival Analysis with Competing Risks
The co-occurrence of multiple diseases among the general population is an important problem as those patients have more risk of complications and represent a large share of health care expenditure. Learning to predict time-to-event probabilities for these patients is a challenging problem because the risks of events are correlated (there are competing risks) with often only few patients experiencing individual events of interest, and of those only a fraction are actually observed in the data. We introduce in this paper a survival model with the flexibility to leverage a common representation of related events that is designed to correct for the strong imbalance in observed outcomes. The procedure is sequential: outcome-specific survival distributions form the components of nonparametric multivariate estimators which we combine into an ensemble in such a way as to ensure accurate predictions on all outcome types simultaneously. Our algorithm is general and represents the first boosting-like method for time-to-event data with multiple outcomes. We demonstrate the performance of our algorithm on synthetic and real data.
This paper has the aim to estimate cause-specific as well as overall survival distributions in a competing risk setting, and employs boosting algorithms in a multitask learning framework to obtain estimators. The paper is well-written and clear in its presentation, and applies established methods and algorithms to the setting. While there exist applications of all employed methods (tree-based, boosting, multitask learning) to estimation in competing-risks, which is very well described in the related work section, the paper presents novelty in the details of their approach and their goal to estimate full cause-specific and all-cause hazards. Further, evaluations on both synthetic as well as real-data show an improvement of prediction compared to existing approaches.  Strengths of the paper: - Aim of the paper is clearly stated and mathematical notation is well defined. - The related work section is well-written, and their proposed approach is compared with different existing approaches. - Synthetic and real-data applications are described in a reproducible manner and show that the proposed approach can yield an improvement in prediction in multiple scenarios.  - Nice idea of visualizations in Figures 1-2, which help to get an illustration of boosting and intuition on the partitions (but which could be improved, see below), further the description throughout the paper is easily accessible with very few typos.  Some comments: - Description of the toy example in Figure 1 and lines 52-67 could be improved: when reading the text and looking at the figure, it was not clear to me if the goal in the example was to improve the estimation of cause-specific hazards (i.e. for death due to CVD and death due to BC separately) or of all-cause hazard by using boosting. The presentation here seems to focus on all-cause hazards while the later synthetic and real-data examples seem to focus on cause-specific hazards, which was a bit confusing to me and might be improved, e.g. in line 61 (“… best partition of the data …”):  best partition with respect to what, high/low overall survival? - Line 2: “… have a higher risk …” instead of “… have more risk …”? - Line 75: add “given covariates“ in “represents the probability of a specific event of type k happening before time t given covariates”? - Line 77: What can \mathcal{X} and \mathcal{T} be, e.g. \mathbb{R}^k and \mathbb{R}^+ ? - Line 98: results in flexible estimates of task-specific time-to-event distributions? - Lines 227ff: it could help the reader to explicitly state that \bold{X} encompasses X_1 … X_100 - Lines 109-115: Here, it could be helpful to remind the reader what exactly is tested using Gray’s test statistic, i.e. if the equality of all subhazards is tested vs. that at least two subhazards differ.  - Figure 2: I looked at the example in the figure to get an intuitive understanding how the partition is obtained, i.e. which partition maximizes Gray’s test statistic. As the authors describe in the figure legend, the partition is supposed to maximize “a composite measure of the difference between the CIFs in each subset”. Now by looking at the figure, I was wondering if other partitions might not yield a great difference between the CIFs, and I was confused that the green dot with third-lowest feature value is different in the left and right plot. Is this point upweighted in the right plot, or is this a typo? - In the introduction (line 25-26), the authors describe that existing approaches can do well in prediction of all-cause survival but not well for cause-specific survival. As far as I could tell, their proposed approach was only compared in its estimation of cause-specific survival to existing approaches. How does it compare in prediction of overall survival? - What is shown in Table 1 in the supplements? Mean and SD? - The description and algorithm focuses on competing risks, and it seems to me that there is potential to include recurrent events (e.g. not only focus on death due to CVD/BC but also re-occurrence of BC) in the model as future work.  AFTER AUTHOR RESPONSE: I have read the author response, and think that the paper will be further strengthened by the corrections and additional results described in the rebuttal letter.