# University of Twente Student Theses

## Modeling patients flows through a hospital using ARIMA theory and Markov theory

Weggemans, S. (2012) Modeling patients flows through a hospital using ARIMA theory and Markov theory.

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 Abstract: In this paper we develop a holistic model which enables Ziekenhuis Groep Twente, ZGT, to predict patient volumes and occupancy rates of (sub)specialisms at outpatient clinics, operating theaters and nursing wards at least one month ahead. Moreover, ZGT is in- terested in how patients transfer from one (sub)specialisms to another in the outpatients clinics and the nursing wards. The estimation of patient volumes and occupancy rates is useful for allocating nursing beds and staff. Currently, ZGT uses common sense and experience of employees to predict the number of beds, operating time and staff. The model we propose, consists of three components: the arrival of patients at the three departments, outpatient clinics, operating theaters and nursing wards, the trans- fers between (sub)specialisms in the departments and the average service time. The first component is modeled by autoregressive integrated moving average (ARIMA) models. The second component is modeled by using Markov theory. The average service times are computed by statistical analysis. For the arrivals at outpatient clinics (first and repeated visit), operating theaters and nursing wards (one day-admission and more than one day admission), we propose ARIMA- models, which can predict weekly patient arrivals. We compute monthly transition prob- abilities for transfers between subspecialisms of surgery and the remaining part of the hospital for in- and outpatients. Also we compute weekly transition probabilities for transfers between 11 specialisms for inpatients. We demonstrate that for estimating pa- tient volumes, the subdivision in 11 specialisms is more useful than the subdivision in several small subspecialisms of surgery and one large part, which represents the remain- ing part of the hospital. Also we argue that weekly transfers yield a better computation of transition probabilities than monthly transfers. This is due to the fact that the aver- age nursing time of a single patient is much closer to one week than one month. We see this confirmed, as we compute the average service times. For 299 of 980 treatments, the nursing time is three days or more, for 181 treatments 5 days or more, for 60 treatments 10 days or more and for 0 treatments of 30 days or more. The input model for the arrivals and the transition probability matrix can be used for computing patient volumes at a combination of department and (sub)specialism. If we use the average service times, we can also compute the occupancy rates. In Chapter 8 ii we pay special attention to the applicability and the possibility of the implementation of the model with respect to ZGT. Also we briefly explain the ins and outs of the model in this chapter. The transition probabilities matrix demonstrates that more than 70% of the inpatients arriving at a specific specialism are also discharged within this specialism within one week. Thus less than 30% of the patients transfer from one specialism to another in the nursing ward, or stay in the hospital for a period longer than one week. We back-test our model for 20 weeks in 2011 by estimating the expected weekly patient volumes at the nursing wards for 11 specialisms and comparing them with the actual values. Approximately 40% of the weekly patient volume estimates, differ less than 10 patients in comparison with the actual data. About 25% of the estimations are in the range of a difference between 10 and 20 patients in comparison with the actual data. As said, ZGT uses common sense to allocate staff and nursing beds. Since these estimations are not entirely comparable, we also construct a simple measure and compare our model to this measure. This measure uses the 4 year average arrivals. In 53% of the cases, our model estimates the arrivals better than the 4 year average model. Moreover, our model predicts 14% more cases than the 4 year average model, in which the difference between the estimate and the actual data is only 10 patients or less. The 4 year average model estimates 8% more cases than our model, in which the difference is more than 25 patients compared to the actual data. To illustrate what these findings imply with respect to potential savings, we make a cost comparison of the two models. We calculate costs of wrongly planned nursing beds and staff per group of ten patients per week in case of an over- and underestimation by our model. We compare these costs to the cost estimates of the 4 year average model. For this purpose we use arbitrarily cost estimates of AC1; 200: Item Type: Essay (Master) Clients: ZGT Faculty: BMS: Behavioural, Management and Social Sciences Subject: 85 business administration, organizational science Programme: Industrial Engineering and Management MSc (60029) Link to this item: https://purl.utwente.nl/essays/62194 Export this item as: BibTeXEndNoteHTML CitationReference Manager

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