Simulating neonatal intensive care capacity in British Columbia

Simulating neonatal intensive care capacity in British Columbia

Socio-Economic Planning Sciences 47 (2013) 131e141 Contents lists available at SciVerse ScienceDirect Socio-Economic Planning Sciences journal homep...

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Socio-Economic Planning Sciences 47 (2013) 131e141

Contents lists available at SciVerse ScienceDirect

Socio-Economic Planning Sciences journal homepage: www.elsevier.com/locate/seps

Invited paper

Simulating neonatal intensive care capacity in British Columbia Derrick L. Fournier, Gregory S. Zaric* The Richard Ivey School of Business, The University of Western Ontario, 1151 Richmond St., London, Ontario, Canada N6A 3K7

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 10 February 2013

Each year, a small number of expectant mothers with high-risk pregnancies in British Columbia (BC) are sent to the United States (US) because of a lack of neonatal intensive care unit (NICU) beds. We developed a discrete-event simulation model to determine the impact of changing the number of NICU beds in BC on the probability of transfer to the US and on overall system costs. The model includes births in 25 different zones at five different levels of care; transitions between levels of care over time; and transfers of patients between zones and to the US when there is insufficient capacity. We parameterized the model using data from the BC Health System, the Canadian Institute for Health Information, published reports, internal hospital data and expert opinion. Our analysis suggests that the province should consider a modest increase in NICU capacity. In particular, the use of a bottleneck approach to identify the type and location of 4 new beds at select hospitals throughout the system resulted in a reduction in the probability of transfer to the US and an increase in annual system costs. A model like the one described in this paper may be useful to evaluate the tradeoffs associated with capacity expansion for a number of different services where Canadians seek care in the US. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Simulation Neonatal intensive care Health-care system

1. Introduction Every year, a number of Canadians receive medical care in the United States (US). A particularly high-profile example occurred in the 2007e2008 fiscal year when 98 newborns from British Columbia (BC) were sent to neonatal intensive care units (NICUs) in the US because of insufficient capacity within the province [1]. The policy of sending high-risk newborns to the US was seen as highly controversial and received local media coverage [2], as well as coverage in one of Canada’s national newspapers [1]. Although the number of BC newborns receiving care in the US decreased from 2008 to 2010, the issue remains a concern because the cost of treatment in the US is substantially higher than in Canada and because the demand for NICU services is likely to increase [2]. Several other cases of Canadians receiving care in the US have drawn academic and media attention (e.g., Refs. [3e6]). For example, in 2008, approximately 1660 Ontarians received bariatric surgery in the US, while the province had capacity to perform approximately only 244 of these procedures per year [7]. Katz et al. [8] examined records from the Ontario Health Insurance Plan (OHIP) to estimate the number of Canadians seeking care in the US. They found that in 1991, OHIP spent approximately $278 million (3% of the total OHIP budget) on services in the US, and in 1992, * Corresponding author. Tel.: þ1 519 661 3415; fax: þ1 519 661 3485. E-mail address: [email protected] (G.S. Zaric). 0038-0121/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.seps.2013.01.001

roughly half of all spending in the US was on emergency care. In a separate study, Katz et al. [9] proposed a set of reasons why Canadians might seek care in the US. The five reasons identified included: 1. To avoid excessive wait times; 2. To gain access to leading-edge technology that is not available in Canada; 3. Greater convenience, perhaps because there is less travel involved to receive care in the US; 4. Routine services provided to Canadian “snowbirds” who live in the US for several months each year; and 5. Services are perceived to be of higher quality in the US. Both articles by Katz and colleagues [8,9] concluded that the number of Canadians seeking care in the US was relatively small; however, highprofile incidents continue to receive attention, with some media sources seeing this situation as evidence of a crisis [10]. In this paper, we develop a discrete-event simulation (DES) model that would allow policy makers to investigate the impact of healthcare capacity expansion decisions. We tailor the model specifically to the case of NICU capacity in BC. The model simulates births at five different levels of acuity in each of 16 administrative areas in BC. We use a Markov chain to model changes in the level of care required over time. Transfers occur between hospitals within BC and from BC to the US, depending on available capacity at an appropriate level of care. The model is parameterized using a number of Canadian data sources. The model tracks the need to transfer patients to the US, bed utilization rates and total NICU system costs. The remainder of this paper includes a brief review of the literature, a description of our model, a discussion of our results and concluding comments.

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2. Literature review 2.1. DES models to analyze health-care system capacity There have been several applications of DES in health care (see Refs. [11e14] for reviews). Much of the work examines interventions to improve process flows in a particular unit or ward of a hospital. For example, DES has been applied to the study of

operating-room flows [15,16]; intensive care units [17e20]; obstetrics wards [21,22]; pharmacy automation and design [23,24]; diagnostic imaging workflows [25,26]; reduction of hospitalacquired infections [27]; and interventions to increase the efficiency of emergency departments [28e32]. One study used a DES model to investigate the impact of system-level changes in supply and demand for hip and knee replacements in Ontario, Canada [33,34]. The authors developed

Table 1 Base-case parameter values. Parameter Rates Infant mortality rate by gestational age (per thousand births) 37e41 Weeks 34, 35 & 36 Weeks 32 & 33 Weeks <32 Weeks Number of neonates transferred to the United States 2007e2008 2008e2009 2009e2010

Base case

[52]

[2] 98 20 4

2.1 3.55 7.26 17.83 22.37

Distributions Initial level of care required by neonate (%) Normal LVL I LVL IIA LVL IIB LVL III

84.06 6.88 4.37 3.28 1.41

Average daily fixed cost per bed by level of care (Canadian dollars) LVL I LVL II LVL III Average daily variable cost per bed by level of care (Canadian dollars) LVL I LVL II LVL III Average per case cost of treating a neonate in the United States (Canadian dollars)

a

2.39 7.32 16.06 182.45

Neonate average length of stay (days) in hospital Normal Level I Level IIA Level IIB Level III

Costs Average daily fee for treatment of a neonate inBritish Columbia by a doctor (Canadian dollars) LVL I LVL II LVL III

Source

[47,53,54]

b

Calculatedc

Calculated based on costing data from Ref. [50] and length of stay information from Ref. [47] 192.00 238.71 308.71 Costing data from an Ontario Hospital 97.00 314.00 423.86 Costing data from an Ontario Hospital 444.16 1165.36 1624.90 170,000

[1]

a Mortality rates by LOC were calculated by utilizing the Provincial Specialized Prenatal Services Classification [49] to categorize the rates described in Ref. [52] by gestational period. b Length of stay (LOS) for normal neonates was obtained from Ref. [53]. We calculated the length of stay for Level I hospitals in Ontario by taking the average length of stay for all neonates in Level I hospitals. Level I data was obtained from Ref. [54]. We calculated Level IIA LOS by averaging out the LOS data for all neonates having spent time only in a Level II nursery in BC from 2007 to 2009. We calculated Level III LOS by averaging out the LOS data for all neonates having spent time in both a Level III and Level II nursery in BC from 2007 to 2009. Data for Level IIA and Level III neonates was sourced from a data request from the Canadian Institute for Health Information Discharge Abstract Database [47]. Data for Level IIB LOS was not readily available and was estimated as part of the Markov Chain using a least squares procedure. c We derived this data through testing and experimentation with the model. The distribution was adjusted to reflect historical data from 2007 to 2009 [47].

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a model of demand for surgery in each of 19 administrative regions in the province (14 regions and 5 academic medical centers that handle the most complex cases) based on random arrivals and intra-regional transfers [33]. They used their model to evaluate the potential effectiveness of several strategies that had been proposed to reduce waiting times for this type of surgery [34]. We are aware of only three studies in which DES was used to analyze an NICU or NICU system [35e37]. In one study, the authors modeled the impact of various deployment strategies for a specific neonatal head-cooling technology and treatment [35]. This analysis included modeling of neonates through the perinatal system of the State of Massachusetts, variation of cost and the associated effect on patient outcomes. The authors concluded that, if deployed optimally, the head-cooling devices could lead to reduced costs and improved health outcomes. The other two papers described a DES model of NICU care in the Veneto region of Italy [36,37]. In both models, babies were born requiring one of three levels of care. Babies were sent to the closest hospital providing the required level of care, and if a spot could not be found for a baby requiring the highest level of care, then the baby was transferred out of the region. The authors allowed for the status of the baby to change at birth and at discharge. In one paper, the authors estimated the number of babies born outside of their home region [37], and in the other study, they concluded that the existing network was “absolutely insufficient” and in need of reorganization [36].

We are not aware of any theoretical analyses of a model with all of the properties just described. In addition, the most recent BC NICU bed allocation methodologies outlined in the Report on Tertiary Neonatal Care in British Columbia [45] and the Plan for Specialized Prenatal Services in BC [46] used past and projected demographicneed information but did not consider the daily cost of operating NICU beds. This approach fails to capture the tradeoff between cost and service quality, which is important in a resource-constrained environment like the publicly funded health-care system in Canada. The models by Da Fre et al. [36] and Facchin et al. [37] capture many of the technical properties of the queuing network just described, but they do not model continuous changes in an infant’s health status, and they do not include costs in their analysis. Thus, our work makes two contributions. First, we investigate a queuing network structure that, to our knowledge, has not been previously studied. Models of this type may be useful for other health-policy analyses involving capacity shortages. Second, we use the model to investigate the NICU network in BC, giving explicit consideration to cost, which was not done in previous policy analyses. Although the model described in the remainder of this paper is designed for NICU capacity in BC, it could easily be adapted for other situations.

2.2. Queuing models

We built a discrete-event simulation model using Simul8 software, and we estimated parameter values with data specific to NICU capacity in BC (Table 1). The model determines when neonates are born, what level of care they require at birth and at each point in time afterward, which hospital should care for them, how long the neonate requires care at each level of care and when the neonate is discharged (Fig. 1). Model steps will be described in more detail in the next section. Model parameters were estimated from four main sources:

Motivated by a health-care application, Wang [38] developed a two-class priority queuing model in which patients could die while waiting for service. He et al. [39] discussed a pre-emptive priority queue with identical servers, in which customers could upgrade while waiting for service, and Xie et al. [40] discussed a pre-emptive multi-class priority queuing network in which customers could upgrade to a higher class while waiting for service. Roy et al. [41] discussed a multi-class open queuing network with class switching in the context of autonomous vehicle-based storage and retrieval. There has been much theoretical work on priority queues and priority queuing networks with class switching, often in the context of telecommunications networks. Baskett et al. derived the joint equilibrium distribution of queue sizes for certain open and closed multi-class queuing networks [42]. Greiner et al. analyzed a multi-class priority queuing network with pre-emption and class switching [43]. They developed a method to transform open and closed variations of the network to allow them to be solved using product form techniques and illustrated their process with an example of multimedia services over a cellular network. Essafi and Bolch developed a method to estimate variance in the two-queue model with partial class switching [44]. 2.3. Contribution of this paper The model described at the end of Section 1 can be described as an open queuing network with the following properties: 1. Multiple classes of jobs and servers; 2. Job classes are indexed according to priority; 3. Jobs can change class over time, up or down; 4. Servers can handle jobs of a certain level or lower; 5. Service is non-preemptive; 6. Jobs cannot wait for service and will immediately reroute to another node if all servers at the current node are busy; and 7. One node has infinite capacity. In the context of a network of NICU facilities, the third property represents changes in the health status of newborns over time; the fourth property represents the need for highly specialized services to handle the highest acuity cases; and the seventh property allows for unlimited transfers out of the country.

3. Materials and methods 3.1. Model overview

1. The Discharge Abstract Database from the Canadian Institute for Health Information (CIHI) [47]. CIHI is a Canadian not-forprofit agency that collects and provides information about Canada’s health systems and the health of Canadians. The Discharge Abstract Database contains information on all hospital discharges in Canada, including patient demographics, admission and discharge dates, discharge disposition (including transfers), diagnoses, services provided, and other information. 2. Perinatal Services BC. Perinatal Services has province-wide oversight responsibility for Level III neonatal intensive care (NICU) and specialized acute maternity beds, and for Level I and II neonatal and high-risk maternity beds, as well as other perinatal services. 3. Relevant fee schedules from BC and detailed costing data from an Ontario hospital. 4. Secondary sources and expert opinion were used when direct sources were not available.

3.2. Patient flow through the system In this section, we discuss in detail the five steps illustrated in Fig. 1. 3.2.1. Steps 1 and 2: arrival of neonates Neonates arrive in the system at one of 16 Health Service Delivery Areas (HSDAs; an administrative unit used by the BC Ministry of Health Services). The province classifies six levels of care (LOCs)

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Fig. 1. Model process diagram.

for neonates: Normal, Level I, Level IIA, Level IIB, Level III and Level IIIþ [48]. To simplify the model, we grouped neonates requiring Level IIIþ and Level III care together, resulting in five LOCs. We did not observe seasonality in the number of births in the CIHI data and thus did not include any in the arrival pattern of neonates. We modeled the inter-arrival time of neonates in each of the HSDAs using an exponential distribution based on the average number of births per day in 2007. Upon arrival, each neonate is randomly assigned an LOC based on the historical distribution. 3.2.2. Step 3: hospital routing Once a neonate is generated, it is transferred to the closest hospital that offers either the required LOC or a superior LOC. Transfers to hospitals are based on proximity of hospitals with the required LOC (Table 2) and on the availability of beds. In the base case, we assumed there were no dedicated Level I beds and that Level IIA, IIB and III beds were distributed as shown in Table 2. Since our main interest is high-acuity beds, we assumed that each HSDA has one hospital with unlimited capacity for normal neonates. Thus, neonates requiring normal care are always treated in their home region. Neonates requiring higher levels of care are automatically transferred to one of 13 hospitals with NICUs. Neonates that cannot be placed in an NICU are temporarily placed in a queue for an open NICU bed. This was done to address situations where an NICU bed was not immediately available but would become available in a few hours. We assumed that neonates can be treated in their home hospital until they exit the queue. The queue checks for bed availability every 15 min. If a bed is not available within one day, patients are transferred to beds in the

United States for treatment. In reality, mothers are often sent to the US prior to giving birth. We assumed that if a neonate is sent to the US for treatment, it will remain there until it is in a stable condition (defined as LOC Level IIB or lower) and a bed is available anywhere in BC. Otherwise the neonate remains in the US until it is ready to be discharged from the system and can go home. These assumptions may create a bias toward treatment time in Canada versus the US. 3.2.3. Steps 4 and 5: changes in health status A neonate’s LOC may change over time. Using a Markov chain, we reassessed the LOC every 24 h. The Markov chain specifies the probability of a future LOC occurring, given the current LOC. We derived the Markov chain based on a pilot study performed by Perinatal Services BC [49]. The pilot study produced a transition matrix that listed probabilities of movement between levels of care but did not account for discharges, mortality or overall length of stay. We used a weighted least squares procedure to estimate a new transition matrix, using the original (pilot study) matrix along with information on mortality rates and expected length of stay from CIHI. If the neonate’s LOC changes from III to IIB or IIA, then the model attempts to transfer the neonate into a Level IIB bed within the same hospital. If a transfer is not possible, then the neonate remains in the same bed until one becomes available. The availability check is performed every 15 min. If the neonate’s LOC changes from IIB or IIA to Level I within a Level IIA/IIB facility, then the neonate remains in the same bed until it is ready for discharge. To maximize the utilization of beds and avoid unnecessary transfers to the US, we assumed that neonates may be shifted to a lower level of care up to 6 h early. This shift will occur only if the

Table 2 Hospital information and routing matrix.a Region

Births/yearb Hospital

789

12 Kootenay Boundary

654

13 Okanagan

2978

14 Thompson Cariboo Shuswap

2088

21 Fraser East

3394

22 Fraser North 5995

23 Fraser South 8013

31 Richmond

1705

32 Vancouver

6063

33 North Shore/Coast Garibaldi

2382

41 South Vancouver Island

3059

42 Central Vancouver Island

2274

Capacityc 10

24

33

8

6

9

9

6

16

12

8

9

20

10

16

6

LOC

llA

IIB

III

IIA

IIA

IIA

IIA

IIA

IIB

III

IIB

llA

IIB

IIB

IIB

III

LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III LVL I LVL IIA LVL IIB LVL III

e 3 e e e 3 e e e 3 e e e 5 e e 1 1 e e 4 10 e e 2 3 e e e 10 e e e 10 e e e 10 e e e 13 e e e 13 e e

e 9 4 e e 10 5 e e 9 4 e e 11 5 e e 8 3 e e 7 3 e e 8 3 e 4 5 1 e 4 4 1 e 4 3 1 e e 7 3 e e 8 3 e

e 12 6 2 e 11 6 2 e 12 6 2 e 13 7 2 e 10 5 2 e 9 5 2 e 10 5 2 e 8 4 1 e 8 4 1 e 8 2 1 e 11 5 2 e 9 6 2

e 5 e e e 4 e e e 7 e e e 6 e e 2 5 e e 1 1 e e 1 5 e e e 4 e e e 5 e e e 5 e e e 8 e e e 7 e e

1 1 e e 1 1 e e 1 1 e e 2 2 e e e 11 e e e 11 e e e 11 e e e 14 e e e 14 e e e 14 e e e 14 e e e 14 e e

e 10 e e e 12 e e e 10 e e e 3 e e e 7 e e e 6 e e e 7 e e 3 3 e e 3 3 e e 1 1 e e e 6 e e e 6 e e

e 15 e e e 15 e e e 15 e e e 16 e e e 15 e e e 15 e e e 15 e e e 13 e e e 13 e e e 13 e e 2 2 e e 1 1 e e

e 7 e e e 8 e e e 6 e e e 9 e e e 4 e e e 4 e e e 4 e e 1 1 e e 2 2 e e 3 4 e e e 5 e e e 5 e e

e 4 2 e e 5 2 e e 4 2 e e 7 3 e 3 9 1 e 3 2 1 e 4 2 2 e e 7 3 e e 7 3 e e 7 4 e e 9 4 e e 10 4 e

e 11 5 1 e 6 3 1 e 11 5 1 e 12 6 1 e 5 4 1 e 8 4 1 e 9 4 1 e 9 5 2 e 9 5 2 e 9 5 2 e 12 6 3 e 11 7 3

2 2 1 e 2 2 1 e 2 2 1 e 1 1 1 e e 12 6 e e 12 6 e e 12 6 e e 15 8 e e 15 8 e e 15 8 e e 15 e e e 15 8 e

e 8 e e e 9 e e e 8 e e e 10 e e e 6 e e e 5 e e e 6 e e 2 2 e e 1 1 e e 2 2 e e e 4 8 e e 4 e e

e 6 3 e e 7 4 e e 5 3 e e 8 4 e 4 2 2 e 2 3 2 e 3 1 1 e e 6 2 e e 6 2 e e 6 3 e e 10 7 e e 12 5 e

e 16 9 e e 16 9 e e 16 9 e e 4 2 e e 16 9 e e 16 9 e e 16 9 e e 16 9 e e 16 9 e e 16 9 e e 16 9 e e 16 9 e

e 13 7 e e 13 7 e e 13 7 e e 14 8 e e 13 7 e e 13 7 e e 13 7 e e 11 6 e e 11 6 e e 11 6 e 1 1 1 e 2 2 1 e

e 14 8 3 e 14 8 3 e 14 8 3 e 15 9 3 e 14 8 3 e 14 8 3 e 14 8 3 e 12 7 3 e 12 7 3 e 12 7 3 e 3 2 1 e 3 2 1

135

(continued on next page)

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11 East Kootenay

Abbotsford BC BC Burnaby Kelowna Lions Nanaimo Richmond Royal Royal Royal St. Paul’s Surrey University Victoria Victoria Regional Children’s Children’s General General Gate Hospital Hospital Columbian Columbian Inland Hospital Memorial Hospital General General Hospital Hospital Hospital Hospital Hospital Hospital Hospital Hospital of the Hospital Hospital North

Numbers in routing matrix indicate priority of order. For example, a neonate born in East Kootenay requiring Level IIB care would first be routed to Royal inland Hospital then to Royal Columbian Hospital, etc. Births per year were obtained from the 2007 BC Vital Statistics Report [55]. Hospital capacity was obtained from the BC Perinatal Services website [56] and discussion with BC Perinatal Services staff. c

a

1050 53 Northeast

1701 52 Northern Interior

902 51 Northwest

b

e 3 2 1 e 15 9 3 e 15 9 3 e 15 9 3 e 16 9 e 1 1 1 e 1 1 1 e 1 1 1 e e 5 e e e 4 e e e 4 e e e 4 e e e 4 e e e 3 e e e 3 e e e 3 e e e 6 3 e e 5 3 e e 5 3 e e 5 3 e e 13 e e e 13 e e e 13 e e e 13 e e 43 North Vancouver Island

1103

I IIA IIB III I IIA IIB III I IIA IIB III I IIA IIB III LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL LVL

e 11 6 2 e 11 4 1 e 11 6 1 e 11 6 1

e 8 e e e 8 e e e 8 e e e 8 e e

e 14 e e e 7 e e e 7 e e e 7 e e

1 1 e e e 16 e e e 16 e e e 16 e e

e 7 e e e 6 e e e 6 e e e 6 e e

e 9 4 e e 9 4 e e 9 4 e e 9 4 e

e 12 7 3 e 12 7 2 e 12 7 2 e 12 7 2

e 15 8 e e 2 2 e e 2 2 e e 2 2 e

e 10 5 e e 10 5 e e 10 5 e e 10 5 e

2 2 1 e e 14 8 e e 14 8 e e 14 8 e

6 16

IIB

10

IIB

20

IIB

9

llA

8

IIB III

12 16

IIB IIA

6 9

IIA

9

IIA

6

IIA IIA

8 33

llA LOC

III

24

IIB

Capacityc 10

Births/yearb Hospital Region

Table 2 (continued )

III

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Abbotsford BC BC Burnaby Kelowna Lions Nanaimo Richmond Royal Royal Royal St. Paul’s Surrey University Victoria Victoria Regional Children’s Children’s General General Gate Hospital Hospital Columbian Columbian Inland Hospital Memorial Hospital General General Hospital Hospital Hospital Hospital Hospital Hospital Hospital Hospital of the Hospital Hospital North

136

following three conditions are true: 1. A neonate is assessed to have a future LOC that is less than the current LOC; 2. The neonate is in an NICU that is at 85% capacity or higher; and 3. There is a queue of other neonates waiting for beds. The use of the Markov chain assumes history independence for the patient. This condition is not necessarily true, since a neonate’s future health state may be dependent on its current state. The Markov chain is useful for simulating aggregate occupancy and utilization rates since these can be derived based on the time spent in a particular LOC. However, the history-independence assumption may overestimate the total number of neonates requiring higher levels of care. 3.2.4. Validation The face validity of the model was confirmed by staff at Perinatal Services BC. We also compared base-case results (i.e., no additional capacity) versus historical data from the Discharge Abstract Database (DAD) for the years 2007e2008 and 2008e2009. This comparison was performed for the number of neonates sent to the US, the proportion of neonates requiring different levels of care, the LOS of each type of neonate and the total number of neonates. 3.3. Cost Costs included physician fees and bed costs. In BC, physician fees for NICU services vary according to patient acuity and time since birth [50]. We estimated the average physician fee per day stratified by LOC. The estimate was based on physician fees from the BC Medical Services Commission Physician Payment Schedule and length-of-stay data from CIHI. We estimated fixed and variable bed costs using detailed accounting data provided by an Ontario hospital. The accounting data showed the distribution of costs by functional center, including nurseries, pharmacy, allied health professionals, diagnostics and other sources. The fixed costs of a bed include equipment depreciation, facility depreciation, utilities and other costs. The total yearly per-bed operating cost, stratified by LOC, was the sum of three components: the annual fixed bed cost, the annual variable bed cost multiplied by the bed utilization, and the average daily physician cost multiplied by the bed utilization. The total cost for each simulation run was the sum of all costs incurred. 3.4. Scenarios We developed and tested five scenarios. In scenario 1, we added Level I beds to all HSDAs. In scenarios 2, 3 and 4, we added beds in all Level IIA, IIB and III hospitals, respectively. In scenario 5, we performed a “bottleneck” analysis and individually added beds to the hospitals with the highest utilization, in decreasing order of utilization. This action was performed by calculating the utilization of bed types at each hospital, identifying the bed type and hospital combination with the highest utilization, and adding a single bed of that type to the appropriate hospital. This calculation was repeated 30 times as more beds were added. We evaluated all scenarios over a period of 10 years with an additional two years of warm-up. The scenarios were each replicated 10 times with a different random number seed. For each scenario, we estimated the bed utilization, probability of transfer to the US, and total provincial NICU costs. 4. Results We used the model developed in Section 3 to answer the following questions about NICU capacity: What are the tradeoffs between cost and probability of patient transfer? If new NICU beds should be added, where should the new bed space be located, and what level of care should these beds offer? What is the optimal number of BC NICU beds from the perspective of total system cost?

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Fig. 2. Bed utilization and incremental beds. (a) Bed utilization when incrementing LVL I beds in each HSDA (scenario 1). (b) Bed utilization when incrementing LVL IIA beds in LVL IIA hospitals (scenario 2). (c) Bed utilization when incrementing LVL IIB beds in LVL IIB hospitals (scenario 3). (d) Bed utilization when incrementing LVL III beds in LVL III hospitals (scenario 4). (e) Bed utilization when incrementing beds in high-utilization hospitals (scenario 5).

4.1. Base case The average number of babies born per year in the province was 44,100. In the base case, the average utilization was 82% for Level IIA beds, 94% for Level IIB beds and 89% for Level III beds. The average number of babies transferred to the US per year was calculated to be 7.54 resulting in a probability of treatment in the US at 0.0171%. The total system cost was approximately $110,528,000. 4.2. Utilization We measured bed utilization in each scenario because staff at Perinatal Service BC indicated that there was an 80% target

utilization rate. In scenario 1, the utilization of Level 1 beds dropped rapidly as Level I beds were added (Fig. 2a). When one Level I bed was added to each hospital, the utilization of Level I beds was 63%. If a second bed was added, utilization fell to 49%. Utilization of Level I beds fell below 25% when there were six or more Level I beds per region. The addition of Level I beds also reduced the utilization of Level IIA, IIB and III beds since these were not occupied as often by Level I patients. For instance, adding one Level I bed reduced utilization of Level IIA beds from 82% to 76%. The effect was more modest for Level IIB and Level III beds. Regardless of the number of Level I beds added, utilization of Level IIA, IIB and III beds never fell below 63%, 87% and 90%, respectively.

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Table 3 Bottleneck analysis. Allocation of beds in highest utilized hospitals Round

Hospital

Type of bed

Round

Hospital

Type of bed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BC Children’s BC Children’s BC Children’s BC Children’s BC Children’s Royal Columbian BC Children’s Royal Columbian BC Children’s Royal Columbian Royal Columbian BC Children’s Royal Columbian Royal Inland Royal Columbian

Level Level Level Level Level Level Level Level Level Level Level Level Level Level Level

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Royal Inland BC Children’s Royal Inland Royal Columbian Royal Columbian Royal Columbian Burnaby General Royal Inland Royal Columbian Royal Columbian Royal Columbian Royal Columbian Burnaby General Royal Inland Royal Columbian

Level Level Level Level Level Level Level Level Level Level Level Level Level Level Level

IIB IIB IIB IIB IIB IIB IIB IIB IIB IIB IIB IIB IIB IIB IIB

IIB IIB IIB IIB III IIB IIA IIB III III IIB IIB IIA IIB III

In scenario 2, as the number of Level IIA beds in designated Level IIA hospitals increased, the utilization of Level II and Level III beds decreased (Fig. 2b). Adding two beds per hospital (14 beds across the province) reduced total utilization for Level IIB beds to just above 92% and Level III beds to just above 82%. In scenario 3, as the number of Level IIB beds in designated Level IIB hospitals increased, the utilization of Level II and Level III beds decreased (Fig. 2c). Adding three beds per hospital (18 beds across the province) reduced total utilization for Level IIB beds to just above 87%. The addition of Level IIB beds also had a significant effect on the utilization of Level IIA and III beds. In scenario 4, as the number of Level III beds in designated Level III hospitals increased, the utilization of Level III beds decreased

(Fig. 2d). Adding three beds per hospital (nine beds across the province) reduced total utilization for Level III beds below 80%. There was no meaningful effect on Level I, IIA or IIB beds. In scenario 5, we added beds using the bottleneck heuristic. The order of beds added is shown in Table 3. Among the first 30 beds added, there were two Level IIA beds, 24 Level IIB beds, and four Level III beds. The first 19 beds added were all Level IIB; the first five beds added were all at a single hospital; and only two hospitals were represented in the first 13 beds added. As more beds were added, the utilization of Level II and III beds decreased (Fig. 2e). Adding 12 beds to hospitals reduced the total utilization of Level IIB beds to 90% and Level IIA/Level III beds to 80%. 4.3. Probability of transfer to the United States We investigated how the probability of transfer to the US varied, based on the number of beds in the system. This probability decreased rapidly as Level IIB and Level III beds were added (Fig. 3a and b). In the base case, the probability of transfer to the US was 0.0171%. When three beds are added per Level IIB hospital (18 beds province-wide), the probability of transfer to the US was 0.0046% (2.4 transfers per year). We estimated the number of extra beds needed to meet a threshold of one transfer to the US per year (probability of 0.00227%) and found this threshold could be achieved by adding five Level IIB beds per hospital (30 province-wide) or four beds per Level III hospital (12 province-wide). Fig. 3a and b also demonstrates that there would be rapid increases in the probability of transfer to the US if Level IIB or Level III beds were removed. The probability of being treated in the US also decreases rapidly as a result of adding beds during the bottleneck analysis (Fig. 3c). When 16 beds were added, the probability of transfer to the US was 0.00218%, which is slightly below an average of one transfer per year.

Fig. 3. Probability of transfer to the US and incremental beds. (a) Probability of treatment in the US when incrementing LVL IIB beds in LVL IIB hospitals (scenario 3). (b) Probability of treatment in the US when incrementing LVL III beds in LVL III hospitals (scenario 4). (c) Probability of treatment in the US when incrementing beds in high-utilization hospitals (scenario 5).

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Fig. 4. Yearly provincial NICU costs and incremental beds. (a) Yearly provincial NICU cost when incrementing LVL IIB beds in LVL IIB hospitals (scenario 3)*. (b) Yearly provincial NICU cost when incrementing LVL III beds in LVL III hospitals (scenario 4)*. (c) Yearly provincial NICU cost when incrementing beds in high-utilization hospitals (scenario 5)*. *Trend lines added for illustrative purposes only.

4.4. Impact of adding beds on system cost We investigated the effect on system cost of changing the number of Level IIB and Level III beds (Fig. 4a and b, respectively). In both cases, total costs increased approximately linearly as beds were added. In the bottleneck analysis, we found that by adding four Level IIB beds at BC Children’s Hospital, the total system cost was minimized to $110,414,000 (Fig. 4c). We analyzed the relationship between the probability of transfer to the US and system cost for scenario 5 (Fig. 5a). To reduce the probability of transfer from 0.0171% (7.5 neonates per year) to 0.0044% (1.9 neonates per year), total system costs would increase by $408,000. To further reduce the probability of transfer from 0.0044% (1.9 neonates per year) to 0.00227% (one neonate per year), total system costs would increase by $916,000. We also analyzed the relationship between bed utilization by LOC and system cost for scenario 5 (Fig. 5b). This figure demonstrates that in order to reduce bed utilization to 80% in Level IIA and Level III hospitals, total system costs will increase from $110,528,000 to $111,412,000 (representing an additional 12 beds). This figure also indicates that to reduce Level IIB bed utilization to just above 85%, total system costs would increase to 114,196,000. 4.5. Sensitivity analysis We conducted extensive sensitivity analysis. The hospital case costing data used to estimate daily bed costs classified all costs as variable or fixed. It is possible, however, that some costs classified as variable are, in fact, fixed. For example, it may be necessary to always have a minimal number of staff present to be ready for emergencies, and contracts with hospital staff may restrict some

flexibility in reducing staff hours. We found that the proportion of variable costs treated as fixed had an important impact on the results. In the base case, we assumed that no portion of the variable costs was accounted as fixed costs. When we treated 10% of variable costs as fixed costs, only two beds could be added at BC Children’s to minimize operating costs to $111,512,000. When we treated 20% of variable costs as fixed costs, the system was optimized and no beds could be added to reduce operating costs. 5. Discussion We developed a discrete-event simulation model to examine NICU capacity and cost in BC. Our analysis suggests that BC is close to an optimal configuration. The addition of a small number of beds does have an impact on the system as a whole. Adding the suggested Level IIB beds will also further minimize the probability of patient transfers to the US, with a small reduction in system-wide cost. To our knowledge, this is the first use of discrete-event simulation to analyze NICU bed allocation with explicit consideration of cost tradeoffs. Although our model was tailored specifically to investigate NICU capacity in BC, a model like the one developed in this paper could be useful for investigating other health system capacity decisions. For example, there may be other conditions, such as cancer treatment or certain high-demand surgeries, in which sending patients out-ofprovince for care is a viable policy option. A model similar to ours could help policy makers to assess the tradeoffs between capacity, cost, resource utilization, and use of out-of-province services. It is not surprising that adding beds reduces utilization and the probability of transfer to the US. However, our analysis does yield three important insights for planners. First, not all beds are equal. Some beds have a greater marginal impact on the probability of transfer (Fig. 3),

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includes these social costs may suggest that it is optimal to increase the number of beds even further. Acknowledgments Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). Gregory Zaric is supported by the Canada Research Chairs Program. References

Fig. 5. Probability of treatment in the US and total utilization versus total cost for scenario 5. (a) Probability of treatment in the US versus yearly provincial NICU cost (scenario 5)*. (b) Bed utilization versus yearly provincial NICU cost (scenario 5)*. *Trend lines added for illustrative purposes only.

and, if resources are limited, some hospitals and bed types should be given highest priority (Table 3). Second, adding a small number of high-priority beds can actually reduce system-wide costs (Fig. 4). The incremental costs of the new beds are offset by the reduced costs of transfers out of country and by having fewer Level II patients occupy the more expensive Level III beds. Third, even a relatively simple heuristic like the bottleneck analysis performed in this paper can be useful in determining which bed types should have highest priority. Much of the NICU data recorded by hospitals and stored in the CIHI Discharge Abstract Database is based on the level of care provided by the facility in which the patient is being treated and not on the level of care required by the patient. As a result, this categorization of LOS makes it difficult to segment the time a neonate spends in each level of care. This level-of-care issue also makes it harder for hospitals and provinces to use the data for more precise bed planning. Since our study highlights the importance of the various LOC beds, collecting data around LOC required certainly should be considered. Our model cannot account for all aspects of human decisionmaking. We approximated decisions with probability distributions, programmed rules and routing matrices. We have tried to program the model with as much flexibility and as close to reality as possible; however, it cannot fully replicate the clinical environment of a hospital nor can it fully emulate the decision-making process of neonatologists and other health-care professionals in the BC Health System. Some challenges related to incorporating human behavior in health-care simulation models have recently been addressed by Brailsford et al. [51]. Our model attempts to transfer neonates as efficiently as possible. However, checks for bed availability are not performed on the same frequency and in the same manner as in real life. Our analysis looks at costs from the perspective of the provincial government of British Columbia only. We do not include the social costs associated with sending mothers, neonates and families away from their home HSDA to another country. A full analysis that

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Derrick Fournier is a manager at Accenture in the Toronto office. He holds MBA, HBA and B.Eng.Sci. degrees from the University of Western Ontario.

Gregory Zaric is an Associate Professor of Management Science at the Ivey Business School, University of Western Ontario. His research focuses on health economics and health-care management science. He holds a Canada Research Chair in Health Care Management Science.