Implementation and validation of a new method to model voluntary departures from emergency departments

Carlo Ricciardi; Alfonso Maria Ponsiglione; Giuseppe Converso; Ida Santalucia; Maria Triassi; Giovanni Improta; Carlo Ricciardi; Alfonso Maria Ponsiglione; Giuseppe Converso; Ida Santalucia; Maria Triassi; Giovanni Improta

doi:10.3934/mbe.2021013

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 253-273. doi: 10.3934/mbe.2021013

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Implementation and validation of a new method to model voluntary departures from emergency departments

Running Title: Modeling Voluntary departures from emergency departments

1.
Department of Advanced Biomedical Sciences, School of Medicine and Surgery, University of Naples "Federico II", Naples, Italy
2.
Department of Electrical Engineering and Information Technology, University of Naples "Federico II", Naples, Italy
3.
Department of Chemical, Materials and Production Engineering, University of Naples "Federico II", Naples, Italy
4.
Department of Public Health, School of Medicine and Surgery, University of Naples "Federico II", Naples, Italy
5.
Centro Interdipartimentale Di Ricerca In Management Sanitario E Innovazione In Sanità (CIRMIS), University of Naples "Federico II", Naples, Italy
^† These authors equally contributed to the work

Received: 06 July 2020 Accepted: 15 November 2020 Published: 27 November 2020

In the literature, several organizational solutions have been proposed for determining the probability of voluntary patient discharge from the emergency department. Here, the issue of self-discharge is analyzed by Markov theory-based modeling, an innovative approach diffusely applied in the healthcare field in recent years. The aim of this work is to propose a new method for calculating the rate of voluntary discharge by defining a generic model to describe the process of first aid using a "behavioral" Markov chain model, a new approach that takes into account the satisfaction of the patient. The proposed model is then implemented in MATLAB and validated with a real case study from the hospital "A. Cardarelli" of Naples. It is found that most of the risk of self-discharge occurs during the wait time before the patient is seen and during the wait time for the final report; usually, once the analysis is requested, the patient, although not very satisfied, is willing to wait longer for the results. The model allows the description of the first aid process from the perspective of the patient. The presented model is generic and can be adapted to each hospital facility by changing only the transition probabilities between states.
- Markov Chain,
- emergency department,
- simulation,
- voluntary departure
Citation: Carlo Ricciardi, Alfonso Maria Ponsiglione, Giuseppe Converso, Ida Santalucia, Maria Triassi, Giovanni Improta. Implementation and validation of a new method to model voluntary departures from emergency departments[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 253-273. doi: 10.3934/mbe.2021013

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Abstract

In the literature, several organizational solutions have been proposed for determining the probability of voluntary patient discharge from the emergency department. Here, the issue of self-discharge is analyzed by Markov theory-based modeling, an innovative approach diffusely applied in the healthcare field in recent years. The aim of this work is to propose a new method for calculating the rate of voluntary discharge by defining a generic model to describe the process of first aid using a "behavioral" Markov chain model, a new approach that takes into account the satisfaction of the patient. The proposed model is then implemented in MATLAB and validated with a real case study from the hospital "A. Cardarelli" of Naples. It is found that most of the risk of self-discharge occurs during the wait time before the patient is seen and during the wait time for the final report; usually, once the analysis is requested, the patient, although not very satisfied, is willing to wait longer for the results. The model allows the description of the first aid process from the perspective of the patient. The presented model is generic and can be adapted to each hospital facility by changing only the transition probabilities between states.

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