Alternative Resource Allocation Strategies for a Daytime Scenario

Regarding the daytime scenario, the investigation of the coordination between emergency and elective medical service delivery is of particular interest. The study considered the possibility to develop alternatives to the strategy stated in the PEMAF (also referred as the “As-is” strategy), ie, activating and deactivating the reconfiguration of resources in 1 single step. The logic guiding such an approach is that of guaranteeing the maximum service delivery capacity to the ED for a matter of prudence. It is in fact considered unacceptable to put the conditions of urgent patients at risk to guarantee ordinary nonemergencies procedures. On the other hand, the disservice induced to ordinary patients is the drawback of this strategy. When considering ordinary patients, in particular those scheduled for a surgery, the heterogeneity of the procedures and of treatments cannot be neglected. There are cases in which a delay represents a very significant issue, beyond the revenue loss for the hospital. Figure 2 shows the current strategy suggested by the PEMAF.

Figure 2.

Time profile of resource reallocation in case of MCI: PEMAF strategy (baseline) (a), “Steps On-off” strategy (b), “Steps Off” strategy.

Two alternative resource allocation strategies were explored and compared against the current one: they are named “Steps On-Off” and “Steps Off.” The logic applied by researchers in designing these alternatives is grounded on the resilience principle of dynamic adaptation to changing demand or operating conditions. In particular, the aim was to determine whether a more gradual release of additional resources to the ED and restoration of normal operating conditions may limit the disruption of ordinary activities without worsening the capacity of the ED to promptly and fully respond to the MCI. A belt-shaped arrival rate of MCI patients is the underlying assumption (Figure 2).

According to the “Steps On-Off” strategy, ordinary activities (in particular ORs activity and admissions to wards) are gradually interrupted, in more than 1 step. Consequently, resources, in particular medical staff, are switched from ordinary to MCI activities in a gradual manner. In the recovery phase, as long as the amount of patients arriving in the ED decreases over time, ordinary activities are resumed gradually as well.

According to the “Steps Off” strategy, ordinary activities (in particular ORs activity and admissions to wards) are suddenly interrupted, similarly to the current PEMAF strategy. In the recovery phase, ordinary activities are resumed gradually, similarly to the “Steps On-Off” strategy. The underlining logic is that the maximum amount of available resources is allocated to the ED as soon as possible to respond to the sudden inflow of patients.

Alternative Resource Allocation Strategies for the Night/Holiday Scenario

The night/holiday scenario is the most critical one because of the limited available resources to sustain the hospital trauma capacity, either already on shift or that can be mobilized in a few minutes; the OSR’s PEMAF is mainly built considering this worst-case scenario.

In the present study, a detailed analysis was carried out on the maximum capacity for high-priority disaster patients (red and yellow codes) the ED is able to accept without reducing the level of care to nondisaster patients, with the available resources once the plan is activated. The aim is identifying the most critical resources and the best option for increasing the ED capacity. ^{Reference Hick, Einav and Hanfling50} More specifically, taking the current PEMAF as a reference, alternative combinations of resources were analyzed and compared by the researchers. In particular, an increase of 1 or 2 units of the following critical resources was considered: shock rooms, anesthesiologists, general surgeons, entire trauma team, nurse and porter.

Modeling Approach and Method

Model boundaries were set around the core processes related to the treatment of critical patients (red code), because they absorb the highest amount of resources. Starting from activities, procedures, and resources involved in the ED, the focus was expanded modularly to those hospital areas that interact with the ED and generate synergies or trade-offs. The ED, the ORs, as well as the critical wards were all set within the scope of the analysis. Table 1 accounts for the main process parameters and the resources allocated to the ED and ORs, respectively, under normal operating conditions.

Table 1.

Main operational parameters and resources allocated to the ED and ORs

The operating block, includes 28 ORs, where general and specialized surgeries are performed. Elective surgical interventions begin at 8:00 am and ends at 8:00 pm, without any interruption. Among the 28 ORs, there is also 1 OR specifically dedicated to emergencies (24/7 logic). Each OR was modeled including the induction room (presurgery) and the recovery room (postsurgery), because it was considered as the appropriate level of detail for the aim of the study.

Other medical wards were modeled as a unique “black box,” where hospitalized patients, outpatients in day hospital, or those who entered the hospital through the ED spend a certain period of time and then are discharged. Incoming patients are: patients from ORs, patients from the intensive care unit (ICU), red code patients from the shock room, yellow and green code patients from the MCI, and ordinary patients. The overall balance between the hourly inflow and outflow determines the level of saturation of wards beds that are subdivided into nonsurgical and surgical.

Information regarding OSR activities was collected through a series of in-field visits and meetings with the medical officer responsible for the PEMAF. A flowchart representing the main processes of each unit was the main output in this phase. Other sources of information were exploited as well, such as the database of patients treated in ED in the past 2 y (2017-2018) as generated by the ED information system. The availability of resources under different scenarios were estimated by taking into consideration the predefined shifts of the personnel and the information contained in the hospital PEMAF.

The discrete event simulation (DES) ^{Reference Zhang51} technique was selected to model the ED and the ORs, to secure the full time tracking of each single patient. Other wards were modeled by means of system dynamics (SD) ^{Reference Samuel, Gonapa and Chaudhar52} to represent the required balance between admitted patients and resources (beds and personnel). The 2 models were implemented into a unique integrated simulation model within AnyLogic^® suite. The data presented in this study are completely anonymous. OSR Ethical Committee authorized the publication of the study’s data on October 6, 2020.

Performance Measurement of Different Resource Allocation Strategies

When it comes to quantitative studies on emergency medical service management, quality of care and time-related performance metrics are typically used. Chow et al. (2012) proposes 2 different indicators for measuring quality of care in the ED: adverse non-admit events and adverse hospital events; the first one is the number of patients who will suffer an adverse impact due to the inability to access hospital treatments in time, while the second refers to the number of patients who will suffer an adverse event while inside the hospital. Several studies refer to the “backlog” of patients, such as in Hirsh (2004) ^{Reference Hirsch53} , Manley and Hardy (2005) ^{Reference Manley, Homer and Hoard30} , Yu Wang et al. (2012) ^{Reference Wang, Luangkesorn and Shuman54} . Measuring the proportion of patients who voluntarily leave the ED because of the delay in receiving a medical evaluation (the so-called “walkouts”) is proposed by the General Accounting Office (GAO), in a report published in 2003. Time-based performance metrics reported in the literature are mainly of 2 types: the number of patients treated per time unit (eg, Alsubaie et al., 2015 ^{Reference Alsubaie, Alutaibi and Marti55} ; Lubyansky, 2005 ^{Reference Lubyansky56} ), and the patient’s waiting time. Bayram and Zuabi (2012) ^{Reference Bayram and Zuabi57} proposed the injury to hospital interval (IHI) indicator, which is the time interval from the occurrence of the injury event to the completion of care to critical patients.

Patient waiting time is largely used in resilience studies to measure ED ability to provide emergency care to all the injured during an MCI (eg, Cimellaro et al., 2016 ^{Reference Cimellaro and Piqué58} ; Cimellaro et al., 2010)^{Reference Cimellaro, Reinhorn and Bruneau59.} Coherently, in the present study the patient waiting time parameter was selected as the key performance indicator. To account for different patients’ critical conditions, importance weights of waiting times in different phases of the care path were assigned by means of experts’ judgement elicitation using the AHP method, ^{Reference Saaty60} a robust and widely used multi-criteria assessment method based on pairwise comparisons. In this way, priorities for waiting time minimization were set, as reported in Table 2.

Table 2.

Relative importance of waiting times for different patient categories during an MCI

The importance of red code patients’ waiting time before being admitted to shock room was considered incomparable to any other waiting condition. As will be illustrated in the next paragraph, those patients who are not admitted in shock room in a sufficiently short time have been considered as “patient-at-risk” and counted through a specific performance parameter (PAR). Normalized weights of the remaining 6 categories were used to create the “Weighted Waiting Time Index” (WTI) indicator. WTI is computed as the weighted average of the waiting time of the last patient in queue for each patient class, that is:

(1) $$WTI = {(\sum\limits_{i = 1}^n {({w_i}*W{T_i})} )_t}\forall t$$

where: i = patient class, ie, green, yellow, and red code.

t = minute of the simulation run;

WT _i = waiting time of the last patient in queue of class i-th;

w _i = relative importance (priority) of patient i-th (see Table 4).

Consequently, the WTI is expected to give a representation of the overall hospital performance dynamics along the simulation timespan: the lower the WTI, the better the ED performance. Grounding on WTI, 2 resilience indicators were developed:

• HR_k = Hospital resilience under different resource allocation strategies (k) or the baseline

(2) $$H{R_k} = {\rm{ }}\int_{First\,MCI\,patient}^{Return\,to\,normal\,operations} {WTI\left( t \right)dt} $$

which provides a quantification of the hospital’s overall performance: the lower the value of HR_k, the better the performance, provided the lower the peak of waiting time or the shorter the time to normal operations, or both.

• HRI_k = Hospital Resilience Improvement under different resource allocation strategies (k) against the baseline

(3) $$HR{I_k} = {{H{R_{Baseline}}} \over {H{R_k}}}$$

The higher HRI_k the better the considered response strategy in comparison to the baseline (ie, the current PEMAF resource allocation strategy in the present study).

Moreover, the number of red code PAR was assumed as an additional indicator to assess the performance of different alternative strategies. This parameter refers to the situations in which critical patients have to wait before accessing the shock room; it represents a very significant risk for a red patient leading to a catastrophic adverse event. In the simulation, these types of events are represented by red code patients (agents) leaving the queue before entering the shock room (through a cut-off exit time) after the time threshold of 15 min set by the medical officer responsible for the PEMAF. PAR is a variable counting the number of cut-off events that occur in the simulation run. This index was evaluated against the expected number of PAR under normal operating conditions, assessed by a specific simulation campaign.

Considering the peculiar hospital’s operational setting under the night scenario, performance was evaluated by means of 3 indexes:

• Red code PAR;

• Patients assigned to an incomplete team, so resulting in a lower level of care (LLoC); it refers to the possibility of reducing the standard quality of care, in terms of staff assigned to a single patient, to face a sudden increase of incoming patients at the ED, which is above the available resources;

• Maximum waiting time of red code patients to be admitted in the shock room (MaxWT).

Characteristics of the Simulated MCI

The MCI assumed for all the simulation campaigns was conceived as a sudden onset external to OSR MCI, characterized by peak demand soon after the alarm but limited in time.

To consider a severe MCI, a sequence of patients was generated stochastically departing from the dynamics of a real event, a rail derailment incident that directly involved OSR on January 25, 2008. ^{Reference Faccincani, Stucchi and Carlucci61} On that date, a 5-car train, with approximately 300 passengers aboard, derailed in the eastern suburbs of Milan resulting in a total of 133 patients managed by the EMS. In accordance with START triage (the triage routinely used by EMS in Lombardy in the case of an MCI), 3 patients (2%) were dead at the time of access to scene by medics (black code), 5 (4%) were red (highest priority for evacuation), 9 (7%) yellow (intermediate priority for evacuation), and 116 (87%) were green (low priority). Of 133 patients, 78 (59%) were hospitalized. OSR represented the trauma center nearest to the scene of the incident and received the most severe patients.

It was further assumed that no green code patients, more than the ordinary ones, arrive to the hospital from the scene of the event (either through EMS or self-presented). This hypothesis corresponds to an MCI that is properly managed by EMS as incident Type 2 according to Lennquist’s definition. ^{Reference Lennquist45}

The generated sequence was recorded and replicated deterministically in every simulation, so as to simulate always the same event, which comprised 18 red code patients and 27 yellow code patients entering the ED in approximately 6 h. Triggering times of the event were set when simulating the daytime (Tuesday, September 17 at 11:00 am) and at night (Wednesday, September 18, at 02:00 am) scenarios.

Calibration and Validation

Two different methods were applied to validate the simulation model against the available data and the experience of the medical officer responsible for the PEMAF.

For what concerns the green and yellow code ordinary patients’ waiting times in the ED, a comparison of simulated data with real historical data under normal operating conditions was performed, using data recorded in the ED database in the period June 2017 to June 2018 (total number of records: 70,012). In Table 3, the simulated demand profile is reported and compared with the real profile extracted from the OSR ED database. According to historical data, the simulated demand falls in the 0.75 percentile of registered peak demand and according to the OSR PEMAF medical officer’s experience; it represents almost the upper bound of the total number of patients acceptable in the ED per week based on its current normal capacity. Table 3 also reports the comparison between simulated and real waiting time distributions of green and yellow code patients. Again, the OSR PEMAF medical officer considered the simulated data satisfactory and adequate to capture and assess the real behavior of the ED.

Table 3.

Simulated vs real case demand parameters for the OSR ED: average number of patients by type, average waiting times of green and yellow code patients

Abbreviation: MPE, Mean Percentage Error; WT, waiting time.

A focus group of experienced doctors and nurses from different OSR departments (ED, OR, wards) was involved in the validation of the simulation data generated by the remaining part of the hospital model, ie, OR procedures and hospitalization in wards, under the guidance of the OSR medical officer responsible for the PEMAF. Finally, the same focus group decided on the most effective way of implementing the alternative resource allocation strategies in the context of the simulated MCI, under the daytime scenario, provided that the available resources are those reported in the PEMAF for all the cases.