We developed a DES model based on a regional inpatient healthcare system to formulate hospital demand projections for one Polish administrative region. We decided to use the DES method because it enables the modelling of individual treatment histories and patients' stays in hospital wards. By using the DES method, we were able to define patient characteristics such as age, gender, home address, and clinical-specific attributes such as diagnosis, hospital ward, length of stay, basic medical consultations, and interventions. Another extremely important feature of DES is that it allows observing, over time, changes in the status of patients’ health conditions and comparing the existing capacity of the healthcare system with the forecasted level of demand.
According to recently published surveys on the application of DES in the healthcare sector [25] the majority of published papers are unit-specific and focus on individual providers. This is primarily due to the need to track carefully the operational level processes of a healthcare facility. However, there are also reports [14] of the use of DES on a more aggregate level, especially when researchers intend to link global trends (e.g. demography) to treatment processes that relate to small, clearly distinguished patient groups. We designed the DES model using the Arena ® software to examine the impact of demographic changes observed at the regional level on the intensity of admissions to hospital wards. Each simulation experiment consisted of 10 independent runs, each of which covered a full calendar year.
Simulation model
The simulation model focuses on the inflow of patients to 17 hospitals located in the Wrocław region (WR). The WR, which, together with three other regions, is a part of Lower Silesia—a big administrative province in southwest part of Poland—serves as Lower Silesia’s main economic, scientific, and administrative centre. All hospitals are accessed by elective and emergency patients who mostly live in the region’s capital or in any of the eight communes around it. Additionally, hospitals also admit patients from communes adjacent to the region and patients from other regions of Poland. The inhabitants of nine main communes (the capital plus eight adjacent municipalities) belong to 36 age–gender cohorts, which in turn generate 36 independent patient flows (Fig. 1). Affiliation to a particular cohort determines, based on the fitted random distribution, the commune of a patient’s residence and the main diagnosis, which is then indicated on the hospital admission sheet (Fig. 2). The main diagnosis, in turn, is the premise for choosing the hospital to which the patient is referred. The hospital choice is thus strongly correlated with the age–gender cohort.
The next modelling phase describes patients’ pathways within hospitals and allows mapping out the treatment and care received. However, this phase goes beyond the scope of this paper and will not be discussed here in detail.
Data collection and model parameters
The model is populated with data from two main sources. The medical and administrative details of all patients admitted in 2010 to WR hospitals were extracted from the branch registry of the Lower Silesian National Health Fund (NHF). In particular, two medical data sets were analysed. The first one describes 183,517 patients living in the WR who were registered in any hospital in Lower Silesia during 2010. The second data set encompasses 201,636 patients who were registered in one of the 17 hospitals located in the WR in 2010. The analysis of NHF datasets provided information regarding the spatial distribution of patients, arrival rates by calendar month, and patients’ pathways during hospital treatment. The next set of source data included demographic projections formulated separately for 36 cohorts of the WR population through 2030. For this purpose we used the results of our earlier work [23,24] during which we simulated, among others, three main demographic scenarios (Table 1): the baseline scenario assumes a slight increase in life expectancy and a high increase in fertility; the high scenario assumes a high increase in life expectancy and a high increase in fertility; and the medium scenario assumes a small increase in life expectancy and a very high increase in fertility.
For model validation, we used a data set that contains information on patients admitted to WR hospitals in 2011.
Fig. 1 Patients’ arrival at Wrocław region (WR) hospitals. Legend: Each age–gender cohort of WR residents corresponds to patients who arrive at WR hospitals. Additionally, patients from Lower Silesia (LS) and other regions of Poland (PL) may also register at the WR hospitals.
Fig. 2 Relationships between patients’ attributes in the discrete event simulation model
Table 1 The main scenarios for forecasting possible demographic changes in the Wrocław region population
Scenario
|
Description
|
Scenario 1. Baseline scenario
|
High fertility rate values, medium mortality rate values, and migration unchanged
|
Scenario 2. High scenario
|
High fertility rate values, low mortality rate values, and migration unchanged
|
Scenario 3. Medium scenario
|
Very high fertility rate values, high mortality rate values, and migration unchanged
|
Model assumptions and output measures
Our study focuses on the number of patients who will be admitted to hospitals in the region over the next few years, broken down by age–gender cohorts and diagnosis groups. We look for the extent to which demographic changes (assuming stability of other factors) influence the incidence rates and affect the number of hospitalised patients.
The key assumption is based on the determination of age–gender specific demand rates. These values, interpreted as coefficients of use of hospital services, have been determined as the quotient of the number of hospitalisations performed on patients from a given age–gender subgroup and the population of the relevant cohort (Fig. 3). During the first phase of the study, it was assumed that the coefficients would remain stable for the entire forecast horizon. However, in the next experiment, this assumption was lifted, and the number of hospitalisations was examined taking into account increased values of demand rates for the oldest age groups.
Fig. 3 Age–gender specific demand rates for the Wrocław region population
The demand rates presented in Fig. 3 confirm differences in the number of hospitalisations, both in relation to gender and age. Higher rates can be observed among the male population in practically every age group, except for the two oldest cohorts: 7579 and 85+, for which higher rates are reported for the female population. For example, in the oldest female cohort (85+), for every 1,000 women there are 368 hospital visits per year, while in the male cohort (85+), this rate is 347 visits per 1,000 inhabitants per year. Another distinct correlation characteristic of both genders are the lower values of the indicators for the population aged 20 to 50 years, slightly higher for the youngest age groups, and very high for the oldest cohorts.
In the DES model, the arrival of patients is based on the heterogeneous Poisson process. As demographic data are considered with a time step of one year, the simulation of the number of hospital visits is also determined at the end of each year. However, the data obtained from the NHF allow observing patient admissions on individual days, months, and quarters. Therefore, after a comprehensive analysis of the NHF data set we identified the month-of-the-year arrival patterns across every age–gender group and calculated the demand distribution parameters as the number of admissions per hour that is constant for the given month. This means that patients who arrive at the WR hospitals one at a time are independent of each other, and the number of arriving patients during a given calendar month is described by a Poisson random variable. The DES model works with data differentiated for each age–gender group. A characteristic feature of the arrival process is that more arrivals are observed in the summer, whereas fewer patients register in the winter.
Verification and validation of the model
We examined the validity of the model in several ways. Specifically, the model was validated using face validation, hypothesis testing, and historical validation [26]. The latter technique allows verifying the reliability of the model in relation to the correctness of the forecasts. For this purpose, we compared the results of the simulation for 2011 and the historical data obtained from the NHF regional branch. Table 2 shows mean absolute percentage error (MAPE) values when comparing the number of patients arriving at WR hospitals, grouped based on gender and by different ages. There is generally good agreement between the age–gender specific demand from the DES model and that from the NHF. The results of the simulation are consistent with historical data, although the model overestimates the oldest female cohorts slightly more strongly.
We also compared the annual distribution of patients arriving at the WR hospitals. The temporal distribution of patient arrivals exhibits, in some months, certain discrepancies, as compared with historical demand (Fig. 4). Larger differences can be observed in winter months; this is related to the significantly increased incidence of influenza. However, the averages calculated for each month for the validated year (2011) are highly convergent, indicating that the simulation model provides, on average, good results for the estimation of the WR demand.
Table 2 Validation of the simulation model: Annual number of patients registered in different age–gender groups
|
Historical
|
Simulation
|
MAPE
|
|
Historical
|
Simulation
|
MAPE
|
Female
|
92284
|
91911.9
|
0.4%
|
Male
|
92094
|
88850.2
|
3.5%
|
F20+
|
71984
|
72991.8
|
1.4%
|
M20+
|
66655
|
65062.5
|
2.4%
|
F30+
|
59500
|
62286.9
|
4.7%
|
M30+
|
52394
|
52722.5
|
0.6%
|
F40+
|
48298
|
50934.1
|
5.5%
|
M40+
|
39672
|
39977.2
|
0.8%
|
F50+
|
40774
|
43119.3
|
5.8%
|
M50+
|
30999
|
31372.0
|
1.2%
|
F60+
|
28612
|
31974.9
|
11.8%
|
M60+
|
19172
|
20453.4
|
6.7%
|
F70+
|
18796
|
21289.0
|
13.3%
|
M70+
|
10249
|
10953.1
|
6.9%
|
F+M
|
184378
|
180762.1
|
2.0%
|
|
|
|
|
Fig. 4 Monthly trends of arrivals by gender. Legend: A comparison of historical (2011) and simulation data (average values from 10 replications) for (a) female and (b) male population
We carried out a large number of tests to check the model's response to a sudden and rapid increase or decrease in demand. We also validated the model through visual demonstrations to NHF decision makers and healthcare professionals. After testing the model, we conclude that the model has a high degree of face validity.