Learning (predictive) risk scores in the presence of censoring due to interventions

Abstract

A large and diverse set of measurements are regularly collected during a patient's hospital stay to monitor their health status. Tools for integrating these measurements into severity scores, that accurately track changes in illness severity, can improve clinicians ability to provide timely interventions. Existing approaches for creating such scores either 1) rely on experts to fully specify the severity score, 2) infer a score using detailed models of disease progression, or 3) train a predictive score, using supervised learning, by regressing against a surrogate marker of severity such as the presence of downstream adverse events. The first approach does not extend to diseases where an accurate score cannot be elicited from experts. The second assumes that the progression of disease can be accurately modeled, limiting its application to populations with simple, well-understood disease dynamics. The third approach, also most commonly used, often produces scores that suffer from bias due to treatment-related censoring (Paxton et al, 2013). Specifically, since the downstream outcomes used for their training are observed only noisily and are influenced by treatment administration patterns, these scores do not generalize well when treatment administration patterns change. We propose a novel ranking based framework for disease severity score learning (DSSL). DSSL exploits the following key observation: while it is challenging for experts to quantify the disease severity at any given time, it is often easy to compare the disease severity at two different times. Extending existing ranking algorithms, DSSL learns a function that maps a vector of patient's measurements to a scalar severity score subject to two constraints. First, the resulting score should be consistent with the expert's ranking of the disease severity state. Second, changes in score between consecutive periods should be smooth. We apply DSSL to the problem of learning a sepsis severity score using a large, real-

Sparse Learning of the Disease Severity Score for High-Dimensional Data

“…A multitask DSSL was proposed in [11], which utilizes matrix norm regularization to couple multiple distinct tasks. Nonlinear version of DSSL framework, as well as its solution in form of gradient boosted regression trees, was also proposed in [6]. Nevertheless, mentioned DSSL approaches are dense in a sense that they operate on all variables (in case of a linear version, all coefficients are typically nonzero).…”

“…The approach in [11] is based on expensive proximal gradient optimization algorithm, which makes it unsuitable for highdimensional problems. The utility of the approaches in [6] was presented on an application with a moderately small number of different pieces of clinical information, vitals, and laboratory analysis variables and it is not clear how the approach would perform in situations with high-dimensional data common in high-throughput techniques like genetic, genomic, epigenetic, proteomic, and so on.…”

“…In our Sparse Learning of Disease Severity Score (SLDSS) formulation, we combine attractive properties (and terms) of previously mentioned approaches, ranking SVM (see (3)) [7], temporal smoothness constraint (see (4)) [6], and 1 norm from sparse methods (see (1) and (2)) [3,9]:…”

“…An additional issue is that it might be sensitive to censoring due to treatment, where the severity of state is not acknowledged because treatment prevented undesired outcomes from happening. Some of the mentioned drawbacks are addressed in a more recent approach [5,6] that is based on a clever observation that comparing two cases according to severity is easier to assess than to directly quantify the severity of a particular case. It was built upon the existing work on learning scoring functions for information retrieval tasks [7].…”

“…We build on top of existing efforts by simultaneously performing feature selections that are most relevant for severity score learning. In particular, we are introducing the 1 norm in the formulation of ranking SVM [7] along with the temporal smoothness constraint [6]. Attractive regularization properties of 1 norm are already well acknowledged and exploited in a number of statistical learning methods since its introduction [9].…”