Paper:
Ability to quantify and predict progression of a disease is fundamental for selecting an appropriate treatment. Many clinical metrics cannot be acquired frequently either because of their cost (e.g. MRI, gait analysis) or because they are inconvenient or harmful to a patient (e.g. biopsy, x-ray). In such scenarios, in order to estimate individual trajectories of disease progression, it is advantageous to leverage similarities between patients, i.e. the covariance of trajectories, and find a latent representation of progression. However, to our knowledge, most of existing methods for estimating trajectories do not explicitly account for treatment events such as surgery in-between observations, which dramatically decreases their adequacy for clinical practice. In this study, we develop a first machine learning framework named Coordinatewise-Soft-Impute (CSI) for analyzing disease progression from sparse observations in the presence of confounding events. CSI is easy to implement and is guaranteed to converge to the global minimum of the corresponding optimization problem. Experimental results also demonstrate the effectiveness of CSI using both simulated and real datasets.

Review:
The paper introduces Coordinatewise-Soft-Impute (CSI) algorithm that attempts to estimate the progression of a disease while taking into account the effect of a single binary treatment intervention. The authors also provide prove that CSI converges to the global solution regardless of the initialization. The paper is concluded with experimental results on synthetic  and real-world data, comparing the proposed method with contender methods functional Principal Component Analysis (fPCA) and Soft-Longitudinal-Impute (SLI).
This paper should be rejected due to the following arguments:	
	- The authors claim that the “existing literature talks little about modeling treatment effect on disease progression.” However, this is not true. Here are a few works and the references within, for instance:
		Xu, Y., Xu, Y., & Saria, S. (2016, December). A Bayesian nonparametric approach for estimating individualized treatment-response curves. In Machine Learning for Healthcare Conference (pp. 282-300).
		Lim, B. (2018). Forecasting treatment responses over time using recurrent marginal structural networks. In Advances in Neural Information Processing Systems (pp. 7483-7493).
	- The proposed method is simple extension of that of (Kidzinski & Hastie, 2018), by adding a term that accounts for treatment and its timing. It does not present enough novelty.
	- CSI is empirically compared with fPCA and SLI, however, neither of these two methods take into account the effect of applying treatment. This comparison is unfair and therefore, cannot justify the superiority of CSI.
Things to improve the paper that did not impact the score:
	- Citations throughout the paper had wrong formatting. Often \citep should have been used instead of \citet.
	- Page 1, last par., last sentence: Thus, they need to “be” modeled differently.
	- Page 2, last par., line -2: Principle >> Principal
	- Page 3, par. 2, line 4: the observation matrix Y is N \times T (not N \times K).
	- Page 4, line 2 of Eq. (3.2): first argument misses Y.
	- Code was included but no description or readme file was provided for how to run the experiments.