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Markov chain analysis for the neonatal inpatient flow in a hospital

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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.

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Acknowledgements

The order log of patient transfers used in this paper was provided to us by the University of Tsukuba Hospital (UTH) through the approval of its Research Ethics Committee. The authors are grateful to the following staff of the UTH during 2011–2013 for their support of this work: Dr. Tetsuya Igarashi, the then Director of UTH, Dr. Hiromi Hamada and Dr. Tsuyoshi Ogura of the Obstetrics and Gynecology Section, Dr. Hiroyuki Hoshimoto of the Medical Information and Medical Records, and Mr. Masaki Suzuki of the Head Division of Accounting and Management. The authors thank Editor-in-Chief of the journal and two reviewers of the original manuscript for their valuable and constructive comments as well as a list of additional references, which were very useful in revising the manuscript.

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  1. Tsukuba Institute of Research, 1-7 Takezono, Tsukuba-shi, Ibaraki-ken, 305-0032, Japan

    Yuta Kanai

  2. University of Tsukuba (Professor Emeritus), 747-3 Serizawa, Chigasaki-shi, Kanagawa-ken, 253-0008, Japan

    Hideaki Takagi

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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.

Appendices

Appendix 1: Routes of neonatal patients in two groups

Numerical characteristics for the two groups of routes taken by neonatal patients are given in Table 4. A set of 12 routes of neonatal patients in Group 1 which do not pass Ward 430 are displayed in Fig. 6. The symbol λr stands for route r given in Table 4 (a), 1 ≤ r ≤ 12. A set of 10 routes of neonatal patients in Group 2 which pass Ward 430 and do not pass Ward 300 are displayed in Fig. 7. The symbol \( \lambda ^{*}_{r} \) stands for route r∗ given in Table 4 (b), 1 ≤ r∗≤ 10. Due to the complexity of these routes, Ward 500 is shown in several separate places in these figures.

Fig. 6
figure 6

Twelve routes of the neonatal patients which do not pass Ward 430 (Group 1)

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The complexity of the routes may contribute to the observed independence assumption for the arrival process of patients from mixed routes in each ward mentioned in Section 6.4.

Fig. 7
figure 7

Ten routes of the neonatal patients which pass Ward 430 and do not pass Ward 300 (Group 2)

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Appendix 2: Patient arrival process observed during the two years

The counted numbers of neonatal patients who are admitted to the hospital (a) in each month, (b) in each quarter, (c) on each day-of-the-week, and (d) on each lunar-calendar day during two fiscal years 2010 and 2011 are shown in Table 10. It is not appropriate to try to draw any definite conclusion about the seasonal variability from the data observed only for these two particular years. We observe that more neonatal patients are admitted in the 4th Q than in any other quarters in the fiscal year 2010, but that the least patients are admitted in the 4th Q in the fiscal year 2011. There was the Great East Japan Earthquake in the 4th Q of the fiscal year 2010 (March 11, 2011). We also observe that twice as many neonatal patients are admitted on Monday as on Sunday. There seems to be no particular dependence on the lunar calendar.

Table 10 Number of neonatal patients admitted to the hospital during two fiscal years 2010 and 2011
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Kanai, Y., Takagi, H. Markov chain analysis for the neonatal inpatient flow in a hospital. Health Care Manag Sci 24, 92–116 (2021). https://doi.org/10.1007/s10729-020-09515-3

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