Virtual Evaluation of a Hospital Congestion Prevention Method

9 Background: Hospital congestion is a common problem for the healthcare sector. Numerous 10 studies explored reasons for crowding within some parts of the hospital. However, to deal with 11 more general, hospital-wide problems, examining the hospital as a connected whole is 12 necessary. The purpose of this study was to evaluate de-congestion interventions through a 13 whole hospital simulation model and offer objective reasoning to support hospital management 14 decisions. 15 Method: This study tested a congestion prevention method that estimates the current day’s 16 hospital congestion risk level R at a set time every morning, and activates minimum 17 intervention when R is above certain threshold R(C), using a virtual hospital created by 18 simulation modelling. The color-coding system was adopted to demonstrate the impact and the 19 extent of effectiveness of this method in preventing hospital congestions. 20 Results: The results indicated that adding 8 flex beds to the medical department resulted in 21 more reductions (70.93%) of red-days comparing with the surgical ward (37.15%). Red days 22 reduction per affected patient when discharging two medical patients was 0.1 which was higher 23 than when discharging two surgical (0.04) or two long-stay patients (0.07). Also, the efficiency of red days reduction per affected patient is always greater if removing 2 patients than if 25 discharging more patients. 26 Conclusions: The expected outcome based on theoretical prediction of this method was 27 confirmed, that is, applying a less disruptive intervention is often enough, and more cost 28 effective, to reduce the risk level of hospital congestion. Making a small number of extra beds 29 available was a superior solution compared to discharging approaches to reduce crowding in 30 hospitals. In addition, the virtual implementation approach enabled testing of the method at a 31 more detailed level, thereby revealed some interesting findings difficult to achieve theoretically, 32 such as discharging extra two medical inpatients, rather than surgical inpatients, a day earlier 33 on days when R>R(C), would bring more benefits in terms of congestion reduction for the 34 hospital.


( ) ≈ ( > )
(1) 113 In order apply this approach to control the risk of hospital congestion, this formulation has been 114 refined to become more implementable and controllable for decision-makers. The following 115 equation was considered at the beginning: 116 Where Nt indicates the new arrivals at the hospital ED on the day. Et is defined as the elective 118 patients scheduled to stay in the hospital at least one night. Mt-1 is the midnight occupancy of 119 the previous day.
∈ (0, 1], ∈ (0, 1], ∈ (0,1] denotes the admission rate of the new 120 arrivals, cancelled elective patients and inpatients discharged, respectively. 121 The following task is to investigate the dependence of the congestion risk R(C) on 122 , and which are treated as control parameters. Due to the fact that Nt is the only random 123 variable on the right-hand side of equation 2, the equation 1 was refined as follows: As a result, R(C) became the simplified notation R(C, , , ) which is composed of the 127 control parameters. Since Nt is random, the negative binomial distribution and the normal 128 distribution were employed to fit the histogram exhibited in Figure 1 The bright spot of this method is that it allows decision-makers to change the control parameters 138 to prevent hospital congestion when the congestion risk R(C) is high. That is to say, if we adjust 139 the threshold C or the rate of admitted or discharged patients , R(C) will be changed 140 accordingly. 141 Figure 2 illustrates the R(C) change of an example with different admission and discharge rates 142 (Mt-1 = 595, Et = 28, C = 600). The horizontal and vertical axes represent admission rates ∈ 143 (0, 1] and discharge rates ∈ (0,1] respectively. The solid green indicates low risk values and the thinner the wedge, the more sensitive is the risk R(C) changing from red to green. 147 Theoretically, smaller changes in the numbers of admitted or discharged patients exhibit more 148 effective and sensitive impacts on R(C) which indicates the probability of hospital congestion 149 occurrences because of the relative thinness of the wedge. 150 151 Figure 2 The change of R(C) with different admission and discharge rates 152 of congestion occurrence might also be high during the day. Therefore, managers will plan to 155 make an adjustment to the number of admissions or to discharge a few patients to weaken this 156 discordant possibility. Relying on the above method using historical patient flow data allows us 157 to understand the change of congestion probability R(C) when interventions are adopted. 158 However, it is impossible to demonstrate the expected, but more intuitive and quantitative, 159 impacts on congestion episodes by the method. Moreover, when managers attempt to 160 manipulate different numbers of patients for congestion prevention, other issues might emerge 9 including the type of patients or department that should be the focus for the intervention(s). In 162 other words, from a managerial perspective, the type of patients affected by an intervention can 163 impact on de-congestion effectiveness. Smaller adjustments affecting several different types of 164 patients may be more effective and sensitive in reducing congestion risk. To address these 165 issues, simulation modelling carries an advantage due to the fact that it provides a risk-free 166 platform to help stakeholders access changes in operations, managerial policies and examine 167 different alternatives. Through implementing the method and designing more specific 168 indicators for hospital congestion based on the HESMAD simulation model, the impacts of 169 interventions on congestion prevention were investigated explicitly and in depth. 170

171
This study was based upon work-flows through a large Australian metropolitan hospital 172 previously re-designed to improve efficiency and the quality of patient care by using Lean 173 Thinking [3,15,16]. Aiming to provide a safer and more accessible service is not a simple task 174 for the healthcare system because hospitals are complex and dynamic. To achieve hospital 175 service improvement, a comprehensive modeling of this complex system was undertaken in 176 order to imitate the dynamic behaviours necessary for, and consequent to, each theoretical 177 intervention.  In order to clarify the decongestion effects of different strategies more thoroughly, the 206 intervention ideas from the method were transcribed into scenarios for investigating in the 207 simulation model. Furthermore, a color-coding system was also adopted for each scenario 208 evaluation before, during and after hospital overcrowding. 209 The process of this simulation-based evaluation is illustrated in Figure 4. We assumed that 210 hospital managers check the congestion risk using the method in the morning and start to plan 211 for the day. When R(C) exceeded 0.85, managers could add beds or cancel operations on a few 212 patients for that particular day. In the simulation platform, the same process was realized. The 213 model calculates R(C) in 8:00 am every day. If R(C)>0.85, the intervention is executed for that 214 day. All parameters used for R(C) calculation are generated by the simulation model on a daily 215 basis. 216

Threshold scenarios 217
The threshold was defined as the hospital capacity in the risk prevention method in this study.
In this large tertiary hospital, there are 330 base beds including 170 medical beds, 130 surgical 219 beds and 30 AMU beds in separate inpatient departments. 8 flex beds can be arranged when the 220 hospital is nearing exhaustion of its finite capacity. Using the congestion risk prediction method, 221 the impacts on congestion prevention of using flex beds to change the threshold number 222 (Scenario 1-4) were estimated by the HESMAD model. Furthermore, the department to which 223 the flex beds are added (scenario 5, 6) can influence decongestion efficiency (Table 2). 224

Discharge scenarios 225
Discharging patients was considered as a way to reduce the risk of hospital crowding. In the 226 simulation platform, this intervention was transcribed into different scenarios to test its effects 227 on hospital congestion. However, the type of patients more likely to impact on congestion could 228 be an issue and smaller adjustments for different types of patients may be more effective and 229 sensitive in congestion prevention. To address these issues, an intervention that only 230 implements discharge operations through the tool is not sufficient. Therefore, interventions on 231 different types of patients were executed by the simulation model on a daily basis but only when 232 the congestion risk rate reaches or exceeds 0.85 (Scenario 10-21) at 8 am each day (Table 3). 233 From an ethical aspect, those patients who have recently started treatment are not considered 234 for discharge. The model only discharged patients who have 1 day left of their hospital stay. 235 The simulation model generates patients who were assigned all information including Length 236 of stay and personal information related to the whole treatment process, therefore, discharging 237 patients 1 day earlier is easily realized. Since this study concentrates on the congestion 238 prevention of differing inpatient departments, the model was adjusted for inpatients including 239 medical, surgical and long stay patients (Table 4)  A color-coding system, similar to traffic signals used by SA Health to trace hospital 242 overcrowding status, was adopted into the HESMAD on a daily basis [16]. 243  Green day means that the hospital has at least 10% of total inpatient beds available. 244  Amber day means that the hospital has between 3% and 10% of total inpatient beds 245 available. 246  Red day means that the hospital has less than 3% of total inpatient beds available. 247 The accumulated numbers of green, amber and red days were collected finally to indicate the 248 congestion situation. Also, the midnight hospital occupancy, R(C), and the number of patients 249 affected by each intervention were recorded every day for each simulation-based evaluation.  Table 5. 258

259
The base case scenario in Table 5  and 31.52% of red-days reduction respectively in scenario 9 and 10. Differing from threshold 279 scenarios, the amber days increased from 250.6 to 260.8 when 2-8 inpatients were discharged 280 (scenario 7-scenario 10). These scenarios also offered increases of 31%, 35%, 41% and 45% 281 in green days respectively. 282 The midnight occupancy decreased from 311.8 to 304.45 while executing scenarios 11-14. 283 Discharging medical patients produced greater levels of red-days reduction compared to other 284 discharging scenarios. Removing 2 medical patients when R(C) exceeds 0.85 led to a 34.7% 285 reduction in red days (scenario 1). Particularly discharging 8 medical patients generated a 48.66% 286 reduction in red days. Amber days increased 6.46%, 9.18%, 9.72% and 8.54% respectively 287 when 2-8 medical patients were discharged. Discharging medical patients also achieved a green 288 days increase from 33.45 to 97. 289 For surgical patients, these discharging interventions maximally reduced red days by 21.01% Red days reduction per affected patient was also calculated to evaluate the efficiency of each 300 scenario in Table 4. Red days reduction per affected patient when discharging two medical 301 patients was 0.1 which was higher than when discharging two surgical (0.04) or two long-stay 302 patients (0.07). This suggests that a discharge strategy is more effective and less disruptive if 303 medical patients are discharged. The other discovery was that for all discharging scenarios, the 304 efficiency of red days reduction per affected patient is always greater if removing 2 patients 305 than if discharging more patients. 306

Discussion 307
This study embedded the congestion prevention method in the simulation model to investigate 308 the potential impacts of different approaches on hospital overcrowding. It also demonstrates 309 that piloting interventions in a virtual environment allows us to further understand major 310 influences on hospital congestion. It is a fact that the congestion risk calculation method is able 311 to predict the probability of congestion occurrence. However, using the simulation model 312 allows us to test the impacts of a variety of interventions in depth and to safely compare the 313 cumulated effects of different approaches. 314 This study adopted a colour-coding system which is similar to traffic signals to describe the 315 status of hospital overcrowding and used it for results comparison of different scenarios. It is 316 demonstrated that the number of red-days declined significantly when flex beds were added to 317 inpatient departments. Also, threshold scenarios were more effective for red day reductions than 318 discharging scenarios. For instance, compared to 54.75 red days occurring per annum after 319 discharging 8 patients in response to every day of high congestion risk, the number of red days 320 occurring per annum was much lower (37.2) if the intervention was adding 4 beds to each of 321 the medical and surgical inpatient departments. In a nutshell, adding beds is preferable to 322 discharging patients. We considered that an additional bed facilitates patient flow. In other 323 words, adding a bed might benefit a considerable number of patients during a period of hospital 324 congestion. However, discharging patients seems to have fewer effects because it only involves 325 a small number of discharged patients and hence might only slightly influence hospital 326 overcrowding. Another interesting discovery is that adding 4 beds and 6 beds have very similar 327 effects on red-days reductions. One possibility is that some patients waiting in the queue are 328 admitted to these additional beds which sustains the occupancy, consequently, the red-days gap 329 between adding 4 beds (scenario 2) and 6 beds (scenario 3) is not obvious. Further increasing 330 flex beds above six leads to more reductions of red-days compare to scenario 2 and 3. 331 Adding beds especially in the medical department brings more expected benefits in respect of 332 congestion reduction for the hospital. Also, discharging medical patients rather than surgical 333 patients brings benefits in respect of congestion prevention and leads to impressive red-days 334 reduction and elevations in the numbers of green-days. To seek to understand this phenomenon, 335 by tracing the historical data in Table 6, it has been found that there were 21773 medical patients surgical patients whose LOS are less than 21 days. The proportion of medical patients whose 343 LOS exceeds 21 days is higher than that of surgical patients. The total period of time where 344 hospital beds are occupied by medical patients for one year is longer than surgical patients. 345 Consequently, we believe that medical patients contribute to hospital congestion more 346 significantly than other types of patients. When interventions are implemented for medical 347 patients and medical departments, the effect on red days reduction is more obvious. In this study, the cumulated numbers of red days, amber days and green days for each one-year 351 simulation period were recorded based on the colour-coding system. A reduction in the number 352 of red days is the common goal of all interventions. However, for the change of amber days and 353 green days, we still need to discuss further. In the face of a reduction in red days, there are three 354 patterns of change possible for the number of amber and green days (Table 7). If, when red days 355 decrease, an intervention can lead to amber days decreasing and green days increasing, this 356 suggests decongestion is occurring. But this might be construed as inefficient in terms of a 357 resourcing perspective. From the utilization efficiency point of view, the preferable operating 358 pattern of the hospital is that resources are utilized as much as possible while patients can still 359 flow smoothly. That is to say, a more desired consequence of decongestion or red day reduction 360 is an increase in the numbers of both amber days and green days, such as pattern 2 in Table 7. 361 It has been seen that amber days increase, but green days decrease in pattern 3 in Table 7. In 362 this case, decision-makers should consider some parameters such as queue length of patients 363 waiting for the treatment and midnight occupancy to confirm patients still flow smoothly. 364 Otherwise, this latter pattern of intervention has a limited effect on hospital overcrowding. Discharging inpatients (scenario 7-10) especially discharging 2 surgical patients (scenario 15) 366 and long-stay patients (scenario 19-20) will slightly increase amber days which belongs to 367 pattern 2 in Table 7. From the utilization efficiency perspective, those interventions are 368 preferred to an intervention such as scenario 16. 369 We also calculated the ratio of the reduction in red days expressed relative to the number of 370 patients affected by each intervention and we called this the efficiency of each scenario. We 371 discovered that for different types of patients, red days reduction per affected patient when 372 removing fewer patients is always more favourable than when discharging more patients. This 373 finding confirmed "the hospital instability wedge" phenomenon which demonstrates that a less 374 disruptive intervention applied may be a more cost-effective way to address congestion risk. 375 At the beginning, random discharging interventions were designed to validate the simulation 376 model [13,16]. Therefore, discharging patients occurred throughout the whole simulation 377 period. Also, patients might unrealistically be discharged when they had only recently been 378 admitted. Thus, the midnight occupancy would drop significantly in those other studies unlike 379 the present study. In the present study, the congestion prevention method was adopted to 380 calculate R(C) which provides the condition to execute a range of interventions. The value of 381 0.85 was selected as the threshold for scenarios execution. However, scenarios were also tested 382 for different R(C) values. For example, Table 8 exhibits the results of executing scenario 11 383 when R(C)>0.75, 0.85 and 0.95. The total number of days that R(C)>0.75, 0.85 and 0.95 also 384 influences the total numbers of patients discharged during the simulation period. Red day 385 reduction per discharge was calculated as red days reduction compared to base case scenario 386 divided by total numbers of patients discharged. According to the result in Table 8, red day reduction per discharge of scenario 11 is 0.2 which is higher than scenario 11-1 and 11-2. That 388 is to say, selecting R(C) > 0.85 for the condition maximises occupancy benefits for the least 389 disruption to patient care. 390 It must be recognized that a large amount of effort was made in HESMAD validation [13]. Also, 391 while some approaches can be easily achieved by the simulation model, similar approaches 392 would be challenging in the real world. For example, we can discharge patients early because 393 we know each patient's LOS in the simulation model, but we do not know their LOS in the real 394 world. However, it is important to keep in mind that the simulation study does not attempt to 395 propose exact mechanisms for hospitals. Rather, the simulation results demonstrate where 396 greater attention should be paid when addressing patient flow congestions within a hospital if 397 improvements are desired. In addition, due to the fact that the risk-free platform of simulation 398 model allows us to "repeat history" easily in the virtual environment or estimate what-if 399 assumptions, hence, it is an outstanding tool to support healthcare management decision making. 400

Conclusion 401
In conclusion, compared to analytical methods, this simulation model exhibits unsurmountable 402 advantages for understanding the possible effects of system change. The risk-free platform of 403 simulation model allows us to do pre-implementation evaluations, hence, it is an outstanding 404