Markov chain analysis for the neonatal inpatient flow in a hospital
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Markov chain analysis for the neonatal inpatient flow in a hospital Yuta Kanai1 · Hideaki Takagi2 Received: 3 September 2019 / Accepted: 16 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Discrete-time Markov chain and queueing-theoretic models are used to quantitatively formulate the flow of neonatal inpatients over several wards in a hospital. Parameters of the models are determined from the operational analysis of the record of the numbers of admission/departure for each ward every day and the order log of patient movement from ward to ward for two years provided by the Medical Information Department of the University of Tsukuba Hospital in Japan. Our formulation is based on the analysis of the precise routes (the route of an inpatient is defined as a sequence of the wards in which he/she stays from admission to discharge) and their length-of-stay (LoS) in days in each ward on their routes for all neonatal inpatients. Our theoretical model calculates the probability distribution for the number of patients staying in each ward per day which agrees well with the corresponding histogram observed for each ward as well as for the whole hospital. The proposed method can be used for the long-term capacity planning of hospital wards with respect to the probabilistic bed utilization. Keywords Hospital capacity planning · Bed utilization · Neonatal patient flow · Patient-days · Operations research · Markov chain · Queueing theory · Poisson process Mathematics Subject Classification (2010) 60J20 · 62P10 · 92C50 Highlights •
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Operations research-based theoretical formulation for the neonatal patient flow over an ordinary ward, a growing care unit, and a neonatal intensive care unit in a hospital. Descriptive statistical analysis of operational data from the order log by doctors and the daily counting of hospitalized patients in each ward.
This work was partially supported by the Grant-in-Aid for Scientific Research (A) No. 23241047 from the Japan Society for the Promotion of Science (JSPS) during the fiscal years 2011– 2013 for data acquisition as well as by (C) No. 17K00435 in 2017–2019 for the theoretical analysis. Hideaki Takagi
[email protected] Yuta Kanai [email protected] 1
Tsukuba Institute of Research, 1-7 Takezono, Tsukuba-shi, Ibaraki-ken, 305-0032, Japan
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University of Tsukuba (Professor Emeritus), 747-3 Serizawa, Chigasaki-shi, Kanagawa-ken, 253-0008, Japan
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Data integration with respect to the load on a hospital in terms of patient-days from the patient-wise tracking of length-of-stay along a route of wards and from the ward-based patient number counting over the same observation period. A method of constructing a simple theoretical probability distribution for the number of patients staying in each ward that agrees fairly well with the observed histogram.
1 Introduction This paper is concerned with the bed occupancy management in hospitals. Basic performance measures include the bed utilization and the patient-days. Bed utilization is the ratio
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