Although 30-day hospital readmission is far from the

Although data analytics and machine learning offered a plethora of opportunities for every stakeholder in the health care industry and a lot of efforts are invested in machine learning in medicine citep{kruse2016challenges, raghupathi2014big} the effectiveness and sustainability of predictive modeling focusing on a 30-day hospital readmission is far from the acceptable cite{stiglic2014readmission}.

Using machine learning algorithms to predict readmission risk is a common way to predict patient readmission to the hospital. It is considered as one of the most challenging problems in machine learning community in medical applications. In a paper cite{zhou2014micro} assessed risk for certain diagnosis using electronic medical records (EMR). They tackled the problem using Individual Basis Approach, which assumes the phenotypes (list of diseases) are different for every patient and Shared Basis Approach, which assumes the patient population shares a common set of phenotypes. By both approaches, temporal aspect of patient admission is considered. This is achieved by matrix densification and similar to singular value decomposition, where latent medical concepts are mapped. This type of research induced new features which are considered to be more interpretable by domain experts, and also can provide more general models. This paper also highlights that more general features or higher level concepts are more understandable for medical research and clinical studies. Also, using these higher concepts as features provides a more stable (general) model. Since feature construction and feature selection are distinct machine learning tasks and using them separately can lead to suboptimal solutions they created a method that utilizes both tasks at the same time, where feature generalization is done based on the temporal graph. Performance obtained using this method are promising and also the more stable solution is obtained by projecting high-dimensional space to low-dimensional space. As one of the findings of former paper was that induces features are more general and interpretable and since diagnoses are naturally organized in the form of hierarchy we evaluated the performance of induced aggregated features both using expert-driven hierarchy, in the form of CCS hierarchy, and data-driven hierarchy, obtained by using hierarchical clustering.

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Usage of multi-label classification in medicine is presented in cite{cotha2015multi}. Their goal was to predict patients’ quasi-identifiers such as race and gender. In order to achieve this, they applied ensembles of several multi-label classification algorithms. They concluded that best-performing multi-label algorithm includes decision trees. This conclusion might be interpreted that medical domain applications are non-linear and that decision trees are suitable for medical applications. This gives us a motivation to apply Predictive Clustering Trees since it utilizes decision trees in process of model creation.

Combining domain knowledge in forms of hierarchies (taxonomies) and machine learning is done for hospital readmission problem cite{radovanovic2015domain}. Feature construction and selection method is obtained through the ICD-9-CM hierarchy of diagnoses, where more general features are extracted and used in learning algorithm. However, newly created (augmented) input space is large which provides less interpretable and less usable models. A new method for hierarchical feature selection is proposed. This method uses the hierarchical information to extract and select features. Proposed method obtained comparable performance compared to learning algorithm using original feature set and a great reduction in feature space. However, it was trying to answer the traditional problem where hospital readmission is one label problem.

The impact of ICD-9-CM hierarchy which is used in this paper has been tested in cite{jovanovic2016building}. They compared two logistic regression algorithm, one which ignores hierarchy (Lasso regression) and one which include information about the hierarchical grouping of diagnoses (Tree-Lasso) which is represented as a domain-knowledge hierarchy. It is shown that usage of domain-knowledge hierarchies improves model interpretability while overall accuracy is similar. They concluded that information loss is higher for Lasso regression, which means that hierarchy influence model interpretability. This gives us a motivation to include hierarchy since we can expect our model to have similar or better performance while improving model interpretability.

Above-mentioned approach although using domain knowledge predicts only the readmission risk and does not account readmit diagnosis. This makes the problem more challenging because the predictive models should predict a set of diagnoses/symptoms with which a patient is likely to be re-admitted (instead of just predict the readmission risk). This kind of problems, called multi-label classification, in medical applications is addressed by using recommender systems. To the best of our knowledge collaborative filtering is mostly used cite{hussein2012efficient, liu2014pathway}. One paper worth mentioning is citep{saha2017framework} where multiple outputs are being predicted simultaneously with guaranty of optimality. However, they are of mixed type, namely categorical, numerical or count data. Framework is tested for medical application and it showed good predictive performance. However, as most of the papers it tried to predict readmission as a single label.