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Predictive analytics in healthcare promise to significantly influence different processes of the stakeholders. In general, hospitals could benefit from more accurate predictive analysis by, among others, a more pronounced monitoring of quality indicators, or a more precise planning of accommodation capacities or an increase in optimization level of supplies etc. Insurance companies could increase their drive for sustainable growth and higher performance. The medical community could provide more individualized patient-centered care guided by clinical decision support, while patients could receive a higher quality of care and better price transparency cite{van2016randomized}. Health care governments should therefore organize health plans in such a way that particular attention is provided for these patient population characterized by augmented care at home preventing additional and costly hospital admissions. Inherent to the plan to cover care from the cradle to the grave, data gathering and exchange deserves as much attentions as the organization of the care itself.

Hospital readmission (admission to a hospital within 30 days of discharge) is disruptive to both patients and healthcare providers. Although it is sometimes inevitable, it is frequent and often associated with a higher cost. Modern care standards require effective discharge planning including the transfer of information to discharge, patient and parent education, and coordination of care after discharge. The analysis of hospital readmission continues to be challenging based on the multitude of influencing factors (e.g. seasonal variations) and is considered a critical metric of quality and cost of healthcare cite{stiglic2014readmission}. Based on cite{srivastava2013pediatric} report, readmission rate within 30 days is 19.6\%, 34.0\% within 90 days and 56.1\% within one year following discharge. According to the Institute for Healthcare Improvement, of the 5 million U.S. hospital readmissions, approximately 76\% can be prevented, generating the annual cost of about US$25 billion cite{srivastava2013pediatric}.

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Potential benefits of accurate models for readmission risk prediction led to many types of research based on patient data embedded in electronic health records (EHRs) cite{saunders2015impact, stiglic2015comprehensible}. However, all these approaches attempt to quantify the risk of readmission on patient’s discharge, but do not try to answer the very important question: which diagnoses are likely to be involved in readmission? Highly accurate models that could answer this question would provide not only indicator of readmission risk but also assessment of the risk of specific complications (diagnoses or symptoms) on next admission. These models could provide valuable decision support for doctors in time of discharge (they could decide if additional monitoring or testing is required for a specific patient) and push analytic models from predictive towards a prescriptive role in healthcare decision support.

In order to predict the set of diagnoses/symptoms with which a patient is likely to be re-admitted, in this work we utilize Predictive Clustering Trees cite{blockeel1998top, vens2008decision, kocev2013tree} framework. The predictive clustering trees generalize decision tree models. They seek for homogeneous clusters of observations for which a predictive model can be associated. The main difference between the algorithm for learning PCTs and a standard decision tree learner (for example, the C4.5 algorithm cite{quinlan1993combining}) is that the former considers the variance function and the prototype function, that computes a label for each leaf, as parameters that can be instantiated for multiple targets prediction cite{kocev2007ensembles, struyf2005constraint}(that includes multi-label classification) and hierarchical-multi label classification cite{vens2008decision}. Since Predictive Clustering Trees performs Decision Tree-like clustering of diagnoses with which patient is likely to be re-admitted, it is easy to interpret these models which is very important in medical health care. Having this in mind we applied this approach on data obtained from hospital discharge data from the California, State Inpatient Databases (SID), Healthcare Cost and Utilization Project cite{hcupnet2003utilization}, Agency for Healthcare Research and Quality. Obtained model is interpreted, analyzed and evaluated for compliance with current medical findings.

The following of the paper is structured as follows. In next section, we will provide the background needed for an understanding of the paper, the namely problem of hospital readmission, the research objectives and the definition of multi-label and hierarchical multi-label classification, domain hierarchy used for solving the problem and data-derived hierarchies. Next, we will briefly explain the Predictive Clustering Trees for the two classification tasks (multi-label and hierarchical multi-label classification) and present the experimental evaluation. Further, we provide results and discussion. Finally, we conclude paper and provide further directions of our study.

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