Optimising the complete care pathway for cerebrovascular accident patients

Computers & Industrial Engineering 93 (2016) 236–251

Contents lists available at ScienceDirect

Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie

Optimising the complete care pathway for cerebrovascular accident patients Peter Chemweno a,⇑, Laurent Brackenier a, Vincent Thijs b,c, Liliane Pintelon a, Adriaan Van Horenbeek a, Dominik Michiels d a

Centre for Industrial Management/Traffic and Infrastructure, KU Leuven, Celestijnenlaan 300A, 3001 Heverlee, Belgium Research Group Experimental Neurology, University Hospitals Leuven, Herestraat 49, B3000 Leuven, Belgium VIB Vesalius Research Center, University Hospitals Leuven, Herestraat 49, B3000 Leuven, Belgium d Care Program Management, University Hospitals Leuven, Herestraat 49, B3000 Leuven, Belgium b c

a r t i c l e

i n f o

Article history: Received 17 June 2015 Received in revised form 1 January 2016 Accepted 14 January 2016 Available online 22 January 2016 Keywords: Stroke Diagnostic-therapy care pathway Bed-blocking problem Length of hospital stay Simulation modelling Buffer management

a b s t r a c t Cerebrovascular accidents or stroke is an important healthcare concern. For this reason, the need to optimise waiting times along the patient’s diagnostic-therapy care pathway has gained considerable attention in operations management. In this context, the bed-blocking problem is perceived as an important healthcare logistical bottleneck where, although medically ready, the patient cannot transit upstream their care pathway due to unavailable bed resources. In addition, the care pathway is characterised by shifting bottle-necks whereby, optimising resources at downstream departments often yields considerable waiting time delays for patients transiting further upstream for rehabilitation and nursing home care. This paper addresses these concerns by simulating the stroke patient’s complete pathway, right from arrival at the emergency department and ending at the nursing homes for terminal care. A case study of a large university hospital is presented where intervention strategies aimed at minimizing patient waiting time delays for available bed resources at upstream departments, such rehabilitation wards, and nursing homes are evaluated. The simulation outcomes show that implementing intervention strategies that maximise the bed resource utility, and moreover, implementing buffer management yields considerable improvements in the patients’ waiting time delays. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Background Cerebrovascular accident or stroke occurs when blood flow to a part of the brain is prevented due to blockage, or rupture of blood vessels (Sacco et al., 2013). Recent statistics on European cardiovascular diseases indicate that stroke is responsible for 4 million deaths, with over 1.9 million deaths recorded in the European Union (Nichols et al., 2012). In 75% of the cases, the stroke attack is attributed to blood clot, i.e. ischemic stroke. The remaining cases are attributed to ruptured blood vessel in the brain, i.e. hemorrhagic stroke.

⇑ Corresponding author. Tel.: +32 16 372804. E-mail addresses: [email protected] (P. Chemweno), [email protected] (L. Brackenier), [email protected] (V. Thijs), [email protected] (L. Pintelon), [email protected] (A. Van Horenbeek), [email protected] (D. Michiels). http://dx.doi.org/10.1016/j.cie.2016.01.008 0360-8352/Ó 2016 Elsevier Ltd. All rights reserved.

Stroke survivors often remain disabled, both mentally and/or physically. In particular, the elderly are more prone to stroke attacks. Since the ageing population in the European Union is increasing rapidly, stroke care is becoming an important health care problem (Nichols et al., 2012). In recent years, considerable research has focused on improving the stroke patient’s clinical pathway. One important concern relates to bottlenecks in the patient’s diagnostic-therapy care pathway, and often attributed to sub-optimal resource allocation or use. De Bleser et al. (2006), defines the term ‘care pathway’ as; ‘‘a method for the patientcare management, for a well-defined group of patients during a well-defined period of time, with the objective of improving the quality of care, reduce risks, increase patient satisfaction and enhance the efficient use of resources”. Such resources may include diagnostic equipment, healthcare personnel, or hospital beds. In many hospitals, the average bed occupancy rate is widely used as a decision variable for allocating and analysing bed resource supply and often, these occupancy rates are derived from historical usage data (Halpern & Pastores, 2015). Although costs are also included in bed allocation decisions, determining bed

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

supply sorely on occupancy and costs is considered as sub-optimal approach, because balance with other resources, for instance, diagnostic capacity is hardly achieved (Green, 2012). The resulting inefficiencies often affects the quality of the healthcare delivery system, as often characterised by extended length of stay for stroke patients, and here, the bed-blocking problem is an important contributor (Lewis & Purdie, 1988; Manzano-Santaella, 2010). From a logistical and healthcare perspective, the bed-blocking problem is viewed as an important problem, and has drawn considerable attention, especially from the logistical perspective (Bhattacharjee & Ray, 2014). For the stroke patient, the typical care pathway integrates several departments, starting with arrival at the emergency department, diagnosis and treatment at the stroke unit, rehabilitation at specialized centres, and for patients whom rehabilitation is not possible, transit to the nursing homes for terminal care. From the healthcare perspective, the bed-blocking problem, apart from extending the patient length of stay, places considerable strain on hospital resources (Halpern & Pastores, 2015). However, how can hospital managers minimize the patient length of stay without necessarily compromising resource utilisation in the patient care pathway? To answer this question, Green (2012) argues that there is the need for implementing operations management concepts and models for evaluating care pathways. Such models, she argues, would yield the much needed managerial insights and decision support on better resource utility. Nonetheless, modelling such care pathway is not straightforward because often, optimising resources in one department in the care pathway causes a shift of the bottleneck either downstream, or upstream the pathway. For instance, optimising the diagnostic test capacity at the stroke unit may minimise medical length of stay at the unit, but may shift the bottleneck to the upstream department, especially in instances where the upstream department, e.g. the rehabilitation centre is under-capacitated. In addition, modelling such pathway where multiple institutions are involved is often challenging for several reasons. For instance, mapping the care pathway for patients across department in the pathway requires identifiable logistical attributes such as the unique patient identifier (Chemweno, Thijs, Pintelon, & Van Horenbeek, 2014; Jeremic et al., 2012). In addition, modelling the care pathway requires a careful identification of model parameters and relevancy for the specific modelling task, and the identification process can be daunting since patient attribute data often consists of a large number of feasible modelling attributes (Green, 2012). 1.2. Study aim and motivation for the research Thus, to address the need for decision support with respect to optimising resource use in the stroke patient’s care pathway, a simulation modelling approach is proposed. Specifically, this paper is motivated by the need to provide a tool for decision support for bed resource allocation in the uncertain environment that characterises the stroke patient’s care pathway. The uncertainties include; varying diagnostic capacity, bed resource utilisation, stochastic patient arrival patterns, shifting bed-blocking problem, either downstream or upstream the care pathway, and competition for bed-resources at the post-acute facilities by both the stroke and non-stroke patients. In this study, the post-acute facilities include the designated rehabilitation centres and nursing homes. As is often the case, optimising resources in one department, for instance, the diagnostic test capacity in the stroke unit, would likely lead to a bottle-neck shift upstream in under-capacitated departments, for instance, the rehabilitation centres. Thus, the resource optimisation problem should focus on the entire pathway rather than specific departments. Modelling the complete pathway is, however, challenging especially in a multi-institutional set-up

237

as is the case in this research. Thus, modelling the aforementioned aspects in a way that integrates the complete stroke patient care pathway is considered an important contribution of this research. It should be mentioned that such modelling approaches in which the complete stroke patient care pathway is integrated is underreported the literature. The proposed simulation modelling approach evaluates the feasibility of implementing operational strategies that minimize average waiting time delays for stroke patient in their respective pathway. This is achieved through implementing simulation experiments that mimic alternative and more realistic improvement strategies in the care pathway such implementing buffer management at the rehabilitation centre or adding bed resources at upstream departments. In simulation modelling, evaluating the impact of the alternative improvement strategies is achieved without implementing physical changes in the care pathway. As a consequence, the decision makers are in a better position of evaluating the alternative strategies more cost-effectively, and in a less disruptive manner. Thus, the intuitive applicability of the simulation model as the basis for evaluating alternative improvement actions in a practical set-up is also viewed as an important contribution. Apart from the integrated care pathway modelling outlook, the simulation model validity is demonstrated using the case study of stroke patient flow in a multi-institutional set-up that consists of a large university hospital, rehabilitation centre and a nursing home. The remaining sections of this paper are organised as follows: Section 2 presents a comprehensive review of previous related studies evaluating the bed-blocking problem. The review highlights gaps in existing work, and provides a further justification for the proposed simulation modelling approach. Section 3 evaluates the integrated stroke care pathway and discusses modelling aspects as included in the simulation model. Section 4 discusses the model design and verification where sensitivity analysis is performed. Section 5 evaluates alternative improvement strategies aimed at optimising bed resources with a view of minimizing stroke patient waiting delay times attributed to the bed-blocking problem. The results of the case study are further presented in this section. Section 6 discusses the results where operational insights on the bed-blocking problem are drawn from the simulation modelling approach. Moreover, the applicability of the modelling approach for decision support is also discussed. A general outlook is also presented where applicability of the simulation methodology approach for care pathway resource optimisation is discussed in-depth. Section 7 draws important conclusions, study limitations and possible directions for future work.

2. Literature review In recent years, the applications of operations management models for evaluating the bed-blocking problem in the patient pathway are discussed in the literature. The models are largely analytical, for instance, queuing models or based on simulation approaches. Analytical models have been applied, for instance in Green (2002), where queuing models are applied for estimating the optimal bed resource allocation for intensive care and obstetrics units for New York state hospitals. Osorio and Bierlaine (2009) models patient flow as a finite capacity queuing network where patient congestion attributable to bed-blocking is evaluated based on impact on the queue waiting times. Asaduzzaman, Chaussalet, and Robertson (2010) propose a queuing model for evaluating optimal bed resource capacities in a hospital’s neonatal facility. More recently, Wiler, Bolandifar, Griffey, Poirier, and Olsen (2013) models the patient flows to the emergency department of a hospital, but also notes the following deficiencies generally

238

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

associated with queue models; (1) assumption of uni-directional patient flow, that is, from one service station to the next which is not usually the case in practice, more so, for stroke patient care pathway where patient flow is dynamic and seldom unidirectional; (2) assumption of exponentially distributed patient inter-arrival times, which is also not realistic in practice. Often, depending on empirical patient inflow data, the patient arrival process may be characterised by more complex distributions, e.g. Weibull, Beta, or Gamma. These distributions, however, are seldom incorporated in queue models. Given the aforementioned limitations, simulation modelling approaches are proposed for evaluating the bed-blocking problem in complex care pathways of which, system dynamics and discrete event simulation are the most commonly applied approaches. Heinrichs, Beekman, and Limburg (1999), for instance, apply a systems dynamics modelling approach to evaluate bed resource and personnel staffing constraints at the stroke unit of a Dutch hospital. Lane, Monefeldt, and Rosenhead (2000) explores using a system dynamics model, factors contributing to patient waiting time delays at the accident and emergency department of a hospital. In the study, bed resource capacity constraints are identified as an important contributor to the waiting time delay. More recently, Rashwan, Abo-Hamad, and Arisha (2015) evaluate waiting time delays occasioned by acute bed blocking in the emergency department of Irish hospitals, and likewise, use a systems dynamic modeling approach. Systems dynamic modelling approaches such as discussed above are, however, primarily suited for instance where a holistic view of the process is required (Caro, Briggs, Siebert, & Kuntz, 2012). Thus, rather than focusing of patient attributes and individual patient care pathway, such attributes are aggregated in the system dynamics model. As a result, modelling operational details where individualised attributes, e.g. care pathway, or type of stroke attack is usually daunting in the systems dynamics modelling approach. Since the objective of this study is to gain operational insights on the bed-blocking problem, a system dynamics modelling approach is inappropriate. Thus, the discrete event simulation is proposed as an alternative modelling approach and specifically suited for modelling the operational aspects at a more detailed level. In literature, El-Darzi, Vasilakis, Chaussalet, and Millard (1998), for instance, presents one of the earliest application of discrete event simulation for analysing the bed-blocking problem in a hospital’s geriatric department. Using the simulation model, the authors’ are able to quantify the impact of waiting time delays attributable to the bed-blocking and consequently suggest remedial managerial strategies targeting bed resource allocation. Wang, Belaidi, Guinet, and Besombes (2007) evaluate bottlenecks causing waiting time delays at the emergency department of a hospital, where the

Cat. E

delays are partly attributed to bed capacity constraints upstream the care pathway. The authors, however, largely optimise resource use at the emergency department, thus resource use at upstream departments are not evaluated. Baril, Gascon, and Cartier (2014) model patient flow and resource utilisation in an orthopaedic clinic using discrete event simulation and although the bed blocking problem is not explicitly modelled, the impact of resource constraints, here, the number of consulting rooms and available nurses on waiting time delays is evaluated in the study. In the study, however, the influence of upstream resources on patient waiting time delays is also not evaluated. More recently, Chemweno et al. (2014) model the stroke patient care pathway and diagnostic test resource use in the stroke unit of a university hospital. Using the model, the authors evaluate the influence of diagnostic test capacity on waiting time delays for stroke patients. The study, however, focuses on optimising diagnostic test resources at the stroke unit. Thus, the influence of upstream resources on waiting time delays is also not evaluated. This article addresses these gaps, and in particular models stroke patient flow through their integrated care pathway, right from the emergency department to post-acute facilities that include the rehabilitation and nursing home facilities. The simulation modelling approach takes into account diagnostic test capacities, and bed resource utilisation within the care pathway. Moreover, the stroke patient attributes such as age or type of stroke are taken into account, and their influence on waiting time delays evaluated. The simulation model, upon verification and validation is used to evaluate alternative improvement strategies such as varying bed resources and rehabilitation treatment times.

3. The integrated stroke care pathway In this section, the integrated care pathway is discussed and typically, the pathway depends on the stroke severity and as such varies from one patient to another. Consequently, individual patients follow unique trajectories that can be classified into one of five categories depicted in Fig. 1. The categories are as follows; categories A consist of patients with transient ischemic attack (TIA) of which, the patients undergo diagnostic tests at the stroke unit prior to discharge and allowed to go home. The TIA attack is often mild, although, may point out to a potentially more severe stroke attack if not treated. Patients in category B are classified as suffering from hemorrhagic or ischemic strokes, and here, the patients undergo diagnostic tests and stabilization at the stroke unit prior to discharge. Patients in category C are classified as suffering from severe stroke attacks that often necessitate rehabilitation after treatment and stabilization at the stroke unit. The rehabilitation process is

Cat. E

Cat. D Input Emergency department

Cat. C

Stroke Unit

Rehabilitaon center

Diagnosc tests

Paent rehabilitaon

Nursing home Cat. D

Terminal care

Cat. B Cat. A Acute

Neurology unit Hemorrhagic paents

Cat. B

Cat. C

Cat. A

University Hospital

External instuons Fig. 1. The integrated stroke care pathway.

Home - Rehabilitated; - Terminal care

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

undertaken at specialized centres where the patients recover lost motor skills, e.g. speaking, eating, etc. In case of unavailable bed at these centres, patients in this category wait at the stroke unit until a bed resource is availed. Once fully rehabilitated, the patients are discharged and allowed to go home. Patients in category D exhibit similar clinical pathologies to those of category C; however, patients in category D often fail to fully recover even after rehabilitation thus transit to the nursing homes for terminal care. Category E includes patients for whom rehabilitation is not possible and these patients often stay at the stroke unit for a time equivalent to their respective stabilization time, and afterwards, transit to the nursing homes for terminal care. Although not explicitly categorised, some hemorrhagic patients (i.e. ‘acute’ in Fig. 1) are immediately referred for neurosurgery to repair the raptured blood vessel and afterwards, stabilized prior to inclusion in one of the four categories, i.e. B–E. The integrated pathway depicted in Fig. 1 is multi-institutional of which, the emergency department and stroke unit are located within a large university hospital. On the other hand, the rehabilitation centre and nursing home are located outside the hospitals confines, thus extra resources are required, for instance, ambulance for transporting the patient. The rehabilitation centre consists of two separate wards for geriatric and non-geriatric patients. In Fig. 1, the rehabilitation centre and nursing homes are depicted as ‘external institutions’. Fig. 1 also forms the scope of the simulation model and discussed in latter sections. 4. Simulation model design and validation In this section, the simulation modelling approach for the patient flow through the integrated stroke care pathways is discussed. The model is verified and validated for accuracy and realism of which, sensitivity analysis is performed. For validation, theoretical distribution fits are derived from the empirical data of patient attributes, e.g. age, arrival time, discharge time. The theoretical distributions are analysed for variance where the quality of fit is evaluated. Next, the theoretical distributions are included as input to the simulation model and the resulting simulated output validated with the empirical data, and here, the two-sample Kolmogorov–Smirnov test is used. Five simulation experiments are implemented of which, each experiment mimics alternative improvement strategies aimed at optimising waiting time delays in view of patient flow, diagnostic test resources and available bed capacities in the integrated care pathway. The simulation modelling methodology consists of four main steps: (1) model setup; (2) model design; (3) model verification and validation; and (4) design of simulation experiments. 4.1. Model setup The model setup takes into account tradeoffs in relation to modelling complexities associated with the integrated pathway

239

depicted in Fig. 1. Thus, several simplifying assumptions are considered and these assumptions take into account the opinion of the decision makers at the departments in the stroke care pathway. Although these assumptions don’t perfectly match the real life situation, the assumptions are nonetheless viewed as realistic and include: (i) Only the diagnostic test resources at the stroke unit and bed resources situated in the care pathway are modelled. Other resources such as nurses and healthcare practitioners are thus not included. This assumption is considered realistic since the bed-blocking is perceived as the main contributor to the patient waiting time delays. (ii) Patients who pass away in the course of their respective care pathway are modeled as patients going home since these patients do not occupy bed resources. (iii) Patient transfer times from specific departments, e.g. from the stroke unit to the rehabilitation centre, is assumed negligible as compared to their respective length of stay. This assumption seems reasonable because transfer resources, e.g. ambulance, are usually available when requested. (iv) External interactions with departments outside the scope depicted in Fig. 1 are neglected. A detailed modelling of the emergency department is also omitted since its inclusion would add unnecessary complexity to the simulation model. Thus, the patient arrival process at the emergency department is sampled from a theoretical distribution derived from empirical patient inter-arrival times. (v) All patients with diagnosis other than stroke attack are modelled as external patients and patient gender considerations are also ignored. 4.2. Simulation model design The simulation model is developed in the ARENA discrete event simulation software (Kelton, Sadowski, & Zupick, 2014). The model consists of seven modules depicted in Fig. 2 and include; stroke patient arrival process, stroke diagnosis and treatment, patient discharge process, shared ward or buffer zone at the rehabilitation centre, patient rehabilitation process, external (non-stroke) patient arrival process, patient care at the nursing homes. Each module mimics the underlying complex clinical processes, for instance, Fig. 3 depicts the non-stroke patient arrival process. The modules are depicted with the numerical values, nos. 1–8 and discussed as follows: (1) Stroke patient arrival module: In this module, the patient entity arrives at the hospital’s emergency department and assigned patient attributes such as age, arrival time, and patient category. The latter determine the care pathway, thus trajectory followed by the patient. The patient arrival process is generated from theoretical inter-arrival times

Fig. 2. ARENA simulation modules for the stroke integrated care pathway.

240

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

Direct paent to buffer?

Assign medical me (GER)

Route GER paent to buffer zone

True

False

Create external paents

Assign paent aributes

Geriatric paent?

Route GER paent for rehabilitaon

True

False

Direct paent to buffer?

Assign medical me (non-GER)

True

Route non-GER paent to buffer zone

False

Route non-GER paent for rehabilitaon Fig. 3. ARENA modules depicting the flow of external patients to the buffer zone and rehabilitation centre.

derived from the empirical arrival attributes. The patient trajectory, stroke severity and respective percentages are depicted in Fig. 4. (2) Stroke unit module: In this module, the diagnostic and treatment process is initiated and here, the patient length of medical stay (LoS) depends on the stroke severity. Thus, patients in category A undergo diagnostic tests, e.g. MRI and once diagnosed as suffering from a transient ischemic attack, the patients are treated and subsequently discharged. By contrast, patients with severe attacks, e.g. haemorrhagic require diagnostic tests, treatment (surgery) and stabilisation at the stroke unit. Medically ready patients in categories C, D and E wait in queue for an available bed at the rehabilitation centre or nursing homes, and depending on the availability, significant waiting time delays may be experienced. Since only the medical time is recorded in the electronic databases, the additional time components such as stabilisation time are based on expert estimates. (3) Buffer zone module: This zone evaluates the feasibility of creating a shared rehabilitation ward that is accessible by patients irrespective of age. This differs from the current situation where patients are rehabilitated in separate wards based on age, i.e. geriatric ward and non-geriatric ward. Usually, the current configuration assumes that geriatric patients (i.e. more than 70 years) require more specialised care as compared to the younger patients. In literature, buffer management is discussed as a short-term solution for alleviating the bed-blocking problem (Mur-Veeman & Govers, 2011). (4) Geriatric and non-geriatric rehabilitation wards: In this module, the stroke patient rehabilitation process is simulated and here, the bed resource capacities of 33 and 36 beds for the geriatric and non-geriatric wards are modelled.

(5) Non-stroke patient arrival module: In reality, the bed capacities at the rehabilitation wards are shared by both stroke and non-stroke patients alike. Thus, the non-stroke patients are modelled as external patient arrivals and their inclusion is important since they share resource capacities, thus influencing the waiting time delays for rehabilitation. (6) Nursing home module: In this module, the bed resource availability at the nursing homes is simulated. Since several nursing homes exist in the neighbourhood of the hospital and rehabilitation centre, incorporating explicitly all the nursing homes in the simulation model is not feasible. Thus, the rate of bed resource availability is simulated instead. The module also simulates logic that allows patients select a suitable nursing home based on their social preferences, e.g. social environment, or closeness to family. (7) Patient discharge module: This module mimics the patients discharge process from the stroke unit and rehabilitation wards, to either the nursing homes or own homes. Patients at the nursing homes usually stay there for the remainder of their lives. 4.3. Simulation model input parameters Table 1 summarises the statistical input distributions for patient attributes implemented in the integrated care pathway simulation model. The distributions are derived through a statistical data fitting process of which, the empirical patient data is used, and covers a period of three years. The theoretical distribution fits are validated for the ‘goodness-of-fit’, and here, an analysis of variance (ANOVA) is performed. In the ARENA software, the statistical distribution fitting and the evaluation of the ‘goodness-of-fit’ is performed using the input analyzer (Kelton, Sadowski, & Zupick, 2014). Here, the ‘goodness of fit’ is measured through two tests; Nursing home

Hemorrhagic (17%)

6%

16%

100%

CVA paents (100%)

Stabilizaon

17%

52%

Geriatric

84%

48% Ischemic (83%)

84%

77%

Nongeriatric

16%

99%

Home or deceased

1% TIA (tests)

100%

Home or deceased

Fig. 4. Stroke patient flow trajectories and respective percentages.

Nursing home

241

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251 Table 1 Comparison of candidate theoretical distribution for the patient age attribute. Distribution

Distribution parameters

Mean square error

Test statistic

1

Beta

0.00172

71.9

2 3

Triangular Weibull

16.5 + 83  BETA (3.56, 2.15) TRIA (16.5, 83, 99.5) 16.5 + WEIB (57.4, 4.05)

0.00185 0.00211

78.6 106

16.5. These adjustments take into account the patient age because the youngest patient was 17 years of age, while the oldest patient was 99 years of age. A visual analysis of the distribution depicted in Fig. 5 likewise suggests a good fit. A summary of input distributions and corresponding parameters for patient attributes incorporated in the simulation model are depicted in Table 2. 4.4. Model verification and validation

the chi-square test and the Kolmogorov–Smirnov test (Kelton et al., 2014). Essentially, the two tests measure how closely the fitted theoretical distribution is to the empirical distribution derived from the patient attribute data. Consequently, two numerical measures are incorporated for assessing the quality of the fit; the pvalue and the minimum square error (MSE). Of the latter, a small MSE is desirable while for the p-value, a numerical value greater than 0.05 indicates a good statistical fit. Fig. 5 illustrates the distribution fit for the attribute ‘patient age’, of which, the Beta distribution with parameters; b = 3.56, and a = 2.15, is indicated as the best fit. The Beta distribution is also compared to alternative theoretical distributions such as; Triangular, Weibull and Gamma distributions. The results of the comparison are depicted in Table 1 where the Beta distribution is associated with the least MSE and test statistic value. To further improve the fit, the Beta distribution is adjusted by a multiplication factor of 83, and skewed to the right by a factor of

In this section, the output of the simulation model is compared to the patient’s empirical data, and in this way, the validity of the simulation model is evaluated. Moreover, sensitivity analysis is also performed with a view of verifying the simulation model. 4.4.1. Sensitivity analysis In the sensitivity analysis, the input parameters to the simulation model were varied which include, the stroke patient inflow rate, medical length of stay (LoS) at the stroke unit, medical LoS at the geriatric ward, and medical LoS at the non-geriatric wards. The flow trajectory for patients leaving the stroke unit is also modified. The impact of the variations on measures such as average waiting time delay at rehabilitation and at the nursing home care is consequently evaluated. This is addition to evaluating the variation on the impact of bed resource utilisation at the stroke unit, geriatric ward, and non-geriatric wards. Table 3 summarizes the results of the sensitivity analysis.

Fig. 5. Histogram and theoretical distribution fit for the patient age attribute (Distribution: 16.5 + 83  BETA (b = 3.56; a = 2.15); Kolmogorov–Smirnov test p-value > 0.15).

Table 2 Overview of parameters, statistical input distributions and respective p-values. Parameter

Statistical distribution

p-value

Stroke patient inter-arrival time at the Emergency Department Test duration time (h) Stabilization + test time at the Stroke unit Medical length of stay at the geriatric ward Medical length of stay at the non-geriatric ward Inter-arrival times for the external patients

BETA (0.71, 4.73) LOGN (2.57, 2.04) LOGN (7, 9.34) NORM (36.6, 16.8) TRIA (4, 41.9, 163) 5.6  BETA (0.475, 2.3)

0.22 0.13 0.15 0.2 0.15 0.1

242

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

Table 3 Summary of sensitivity analysis results of the average waiting times for available bed resource and percentage utilisation. Parameter

External patients (+20%)

Length of stay (+20%)

Modified trajectory

Stroke unit (%)

Geriatric ward (%)

Non-geriatric ward (%)

Stroke unit (%)

Average waiting time delays (days)

Rehabilitation Nursing home care

+39.7 +25.7

+250.1 +22.02

+40.7 +2.5

+58.7 +2.6

+0.5 +57.2

Percentage bed resource utilisation (%)

Stroke unit Geriatric ward Non-geriatric ward

+90.4 +97.3 +98.3

+26.67 +13.80 +6.91

+6.9 +0.8 +2.9

+9.2 +3.8 +2.8

+10.7 +3.7 +0.9

In the first verification step, the external patient arrival rate at the emergency department is increased by +20%, and as a consequence, a significant increase in the percentage bed resource utilisation at the stroke unit is observed (+90.4%) which is intuitive since the increased inflow at rehabilitation implies that stroke patients have to wait longer for rehabilitation. A significant increase in average waiting time delays is also observed for rehabilitation (+39.7%) and nursing home care (+25.7%). In the second verification step, the medical length of stay for stroke patients is increased by 20%. As a result, a corresponding increase in the percentage bed utilisation is observed at the stroke unit (+26.67%). The increased length of stay also seems to impact the waiting time delays for rehabilitation and nursing home care, and particularly, a significant increase is observed on the waiting time delays for rehabilitation. The increase is intuitive since the stroke patients wait longer at the stroke unit as a result of the extended medical time. By contrast, increasing the length of stay for geriatric and non-geriatric patients by a margin of 20% yields significant waiting time delays, particularly for rehabilitation. Again, this increase is expected since the longer stay at the rehabilitation centre would imply that patients downstream at the stroke unit experience considerable waiting time delays for rehabilitation. In the fourth verification step, the care pathway trajectories for patients leaving the stroke unit is modified where, for instance, it is assumed that a larger proportion of patients transit to rehabilitation, as compared to the nursing homes (i.e. from 6% to 11%) as currently the case. This assumes a hypothetical situation, for instance, improved treatment regime at the stroke unit. Consequently, a slight increase (+3.71%) in bed resource utilisation at geriatric ward is observed and in addition, a significant increase in waiting time delays for nursing home care is also observed (+57.23%).

In the fifth verification step, the bed resource utilisation at the stroke unit is increased by 100%, and this is achieved by increasing the stroke patient arrivals at the emergency department such that, the bed resources at the stroke unit are always utilised. As would be expected, an exponential increase in waiting time delays for stroke treatment is observed as depicted in Fig. 6. In addition, a stagnation of bed resource utilisation at the geriatric and nongeriatric wards is observed, thus implying a corresponding high resource utility at the rehabilitation centre owing to consistent demand for rehabilitation.

4.4.2. Model validation For model validation, the simulation model output is compared to the empirical patient attribute values. Four attributes are thus compared; number and type of stroke patients, medical length of stay, waiting time delays for bed resources, and percentage bed resource utilisation. A simulation run-length of the three years is implemented which corresponds to the logged time in the patient data base. Table 4 presents an overview of the validation results. From the results, the simulation model output closely mimics the empirical data as the deviations are below 5% for most of the evaluated attributes. Although a significant deviation is observed for the waiting time delay for nursing home care, the three day difference between the empirical and simulated values is perceived as realistic and moreover, is not seen to significantly influence the simulation results. Apart from comparing the simulation model output and the empirical attributes, statistical distribution derived from the simulation output and the empirical attributes were also compared. Here, the two-sample Kolmogorov–Smirnov test is performed which returns a null hypothesis in instances where the compared distributions and not significantly different, i.e. the

Fig. 6. Exponential increases in waiting times and stagnation in bed resource utilisation at the rehabilitation centre. Notes: Abbreviations ‘GER’ denotes the geriatric stroke patient; ‘non_GER’ denotes the non-geriatric stroke patient.

243

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251 Table 4 Summary of the comparison between the simulation output and the empirical patient attributes. Parameter

Empirical data

Simulation Model

%D

Number of patients (patient number)

Total stroke patients Transient ischemic attack Ischemic attack Hemorrhagic stroke Geriatric patients Non-geriatric patients

610.8 79.6 427.5 103.6 46.6 41.8

605 76 425 103 46 42

+0.96 +4.74 +0.58 +0.58 +0.87 +0.48

Length of stay (days)

Category Category Category Category Category Category

2.36 6.69 46.5 89 81.9 40.1

2.43 6.34 50 85 86 40

+2.88 5.52 7.00 4.71 4.77 0.17

Average waiting time delays (days)

Rehabilitation Nursing home care

11.34 33

10.95 30

3.56 10.00

Percentage bed resource utilisation (%)

Stroke unit bed resource Geriatric ward bed resource Non-geriatric ward resource

71.35 85.50 91.98

71.99 82.30 89.00

0.64 3.89 3.35

A patients B patients C (Geriatric patients) C (non-geriatric patients) D patients E patients

Fig. 7. Validation for the Length of stay distribution for geriatric patients (LoS GER) (Output: NORM (l = 48.92, r = 17.29); Data: NORM (l = 50.31, r = 23.90); two-sample Kolmogorov–Smirnov test p-value = 0.62.

simulated output and empirical data sets belong to the same distribution. Fig. 7 compares the validation results for the medical length of stay for geriatric patients, and as observed, the simulated output closely mimics the empirical medical length of stay distribution. Moreover, the two-sample Kolmogorov–Smirnov test returns a high p-value, suggesting similar distributions. Thus, from the model validation process, one can conclude that the simulation model validly represents the integrated care pathway, and thus provides a feasible basis for evaluating alternative operational strategies aimed at minimizing the patient waiting time delays. 5. Design of simulation experiments To evaluate the effect of the bed-blocking problem on the integrated stroke care pathway, five simulation experiments are formulated where each experiment evaluates an alternative improvement strategy aimed at minimizing the waiting time delays. The strategies are as follows: 1. Increasing the bed resource capacity at the hospital’s stroke unit. 2. Increasing the bed resource capacities at the geriatric and nongeriatric rehabilitation wards. 3. Implementing a shared ward at the rehabilitation centre accessible by both geriatric and non-geriatric patient.

4. Increasing the bed resource capacity at the nursing homes. 5. Evaluating the effect of reducing the patient’s medical length of stay at the stroke unit, and at the rehabilitation centre. 5.1. Experiment 1: Increasing the bed resource capacity at the stroke unit In this experiment, the bed resources at the stroke unit are gradually increased and the corresponding effect on the waiting time delay for rehabilitation and nursing home care evaluated. The impact of the increase on the percentage bed resource utilisation is also evaluated. In this strategy, the bed resources capacities are varied, from an increase of one bed, to a maximum of four beds. The corresponding impact of the increase is compared to the base case, or the situation without any bed resource increases in the care pathway. Table 5 summarizes the results of the effects of the capacity increases on the average waiting time delays for rehabilitation, and nursing home care for medically ready patients. In Table 5, the abbreviation ‘Su_B (+x)’ denotes an increase of bed resources at the stroke unit by x units. As an example, the abbreviation ‘Su_B (+1)’ denotes an increase of one bed resource at the stroke unit, as compared to the current, or as-is situation. Fig. 8 illustrates the corresponding graphical depiction as derived from Table 5 where the numerical values for the average waiting times are depicted on the box plot.

244

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

Table 5 Simulation experiment results for increase in stroke unit bed resource capacity. Strategy

Base case Su_B (+1) Su_B (+2) Su_B (+3) Su_B (+4)

Average waiting time delays (days)

Percentage bed resource utilisation (%)

Rehabilitation

Nursing home care

Stroke unit

Geriatric ward

Non-geriatric ward

11.34 10.26 12.02 9.08 10.40

33.4 28.5 33.3 31.8 37.8

71.35 66.60 66.40 61.30 62.30

85.50 85.20 85.00 85.20 85.50

91.98 91.50 92.50 91.40 90.90

20

50

18

45

16 14 12 10

12.02 11.3 10.4

10.26

9.08

8

6 4

Waing me for nursing home care [days]

Waing me for rehabilitaon [days]

Notes: Abbreviations ‘Su_B (+x)’ denotes addition of bed resources at the stroke unit by x units.

40 37.8

35

33.4

33.3 31.8

30

28.5

25 20 15 10

2

5

0

0

Fig. 8. Impact of additional bed resource capacity on the average waiting time delays for rehabilitation and nursing home care.

From the results, one can observe that adding bed resources at the stroke unit does not yield a significant reduction in average waiting time delays for rehabilitation and nursing home care, thus would seem counter intuitive. For instance, although adding four extra bed resources at the stroke unit reduces the waiting time delays for rehabilitation by 9% (i.e. from 11.34 days to 10.4 days), the increase is counter intuitive as it subsequently increases the waiting times for nursing home care by 13.15% (i.e. 33.4 days to 37.8 days). A similar depiction is evident in Fig. 8 where no notable trend decreases in patient waiting times are observed for the rehabilitation and nursing home care. The insignificant reduction in the delays could be explained by the high percentage bed resource utilisation upstream the stroke unit, that is, at the rehabilitation wards. For instance, the resource utilisation at the non-geriatric ward is as high as 92.5% which points to a potential bed-blocking problem at this ward thereby negating the need for extra resource additions at the stroke unit. Rather, a more meaningful strategy could entail adding additional capacity at the rehabilitation centre which is explored in the next simulation experiment. 5.2. Experiment 2: Increasing the bed capacity at the rehabilitation centre In this experiment, the bed resource capacities at the geriatric and non-geriatric rehabilitation wards are varied separately. Three strategies are thus implemented; (1) adding bed resources at the geriatric ward, (2) adding bed resources at the non-geriatric ward, and (3) reshuffling bed resources between the stroke unit, geriatric, and non-geriatric wards. In each strategy, the bed resources at other sections are maintained constant. For instance, the geriatric ward bed capacity is added while at the same time, resources at

the stroke unit, non-geriatric ward, and nursing homes are maintained at current levels. The experimental results are compared to the base case, i.e. all bed resources are maintained at current levels. 5.2.1. Experiment 2.1: Bed capacity increase at the geriatric ward In this experiment, the bed capacity at the geriatric ward (Ger_B) is varied from one bed to five beds, and the effect of this increase on the average waiting time delays for rehabilitation and nursing home care is evaluated. Table 6 depicts the effects of the capacity increases on the average waiting time delays. From the results, the additional capacities are observed as positively influencing the average waiting time delays for rehabilitation for geriatric stroke patients of which, a downward trend is observed with each additional bed resource. For instance, adding five bed resources, i.e. ‘Ger_B (+5)’, reduces the waiting time delays for rehabilitation of non-geriatric stroke patients by as much as 33.5% as compared to the base case (i.e. from 15.48 to 10.3 days). This decrease may be attributed to reduced percentage bed utilisation at the geriatric ward as a response to increasing bed resources at this ward. Here, adding the five bed resources reduces the utility by 11% as compared to the base case (i.e. from 85.5% to 74.5%), of which, the utility decrease could point to a potential bottleneck at the geriatric ward. By contrast, the capacity increase negatively impacts the waiting time delays for nursing home care of which, an increasing trend in delays is noted with each additional increase. For instance, adding five bed resources marginally increases the delays by 5% (from 33.4 days to 35.1 days). This may be because, the additional resources at the geriatric ward facilitates the rehabilitation of more elderly patients. However, since a high proportion of the geriatric patients eventually require nursing home care, capacity

245

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251 Table 6 Simulation results for increase in the geriatric bed capacity. Strategy

Average waiting time delays (days)

Base case Ger_B (+1) Ger_B (+2) Ger_B (+3) Ger_B (+4) Ger_B (+5)

Percentage utilisation (%)

Geriatric ward

Non-geriatric ward

Rehabilitation centre

Nursing home

Geriatric ward

1.84 1.17 0.68 0.56 0.33 0.25

15.48 12.00 11.10 13.25 11.01 10.30

11.34 8.71 7.94 9.40 7.78 7.25

33.4 37.4 35.9 33.5 35.6 35.1

85.50 83.00 80.60 78.70 76.20 74.50

Notes: Abbreviations ‘Ger_B (+x)’ denotes the addition of bed resources at the geriatric rehabilitation ward by x units.

Table 7 Simulation results for increase in non-geriatric bed capacity. Strategy

Base case Nger_B (+1) Nger_B (+2) Nger_B (+3) Nger_B (+4) Nger_B (+5)

Average waiting time delays (days)

Percentage utilisation (%)

Non-geriatric ward

Rehabilitation centre

Nursing home

Non-geriatric ward

15.48 10.95 5.94 2.86 2.03 1.39

11.34 8.15 4.78 2.77 2.65 2.12

33.4 32.6 35.9 34.1 37.3 35.7

92.00 89.00 87.80 84.20 83.70 81.90

Notes: Abbreviations ‘Nger_B (+x)’ denotes addition of bed resources at the non-geriatric rehabilitation ward by x units.

5.2.2. Experiment 2.2: Bed capacity increase at the non-geriatric ward In this experiment, bed resource capacities at the non-geriatric ward ‘Nger_B’ are increased, and the effect of this increase on the waiting time delays evaluated. Table 7 summarizes the results, where minimal increases are observed. For instance, adding two extra beds is observed as significantly decreasing the average waiting time delays for rehabilitation, by as much as 57.8% (i.e. from 11.34 days to 4.78 days) as compared to the base case. Additionally, adding the five bed resources reduces the waiting time delays at the non-geriatric ward by as much as 91% as compared to the base case (from 15.48 days to 1.39 days as depicted in Fig. 9). As also observed in Fig. 9, the resource increases results in a corresponding decrease in the resource utilisation at the non-geriatric

Waing me for rehabilitaon [days]

30

25

20 15.4

15 10.9

10 5.94

5 2.86

0

2.03

1.39

ward, and here, the bed utility reduces by 11%, i.e., from 92% in the current situation to 81.9% in the instance where five resources are added. The positive influence of the resource additions, both on bed resource utility at the non-geriatric ward, and also on correspondingly reducing the waiting time delays at the non-geriatric ward points to a bed-blocking problem at this ward. More interestingly, the capacity increase only marginally increases the waiting time delays for nursing home care, which could be attributed to the lower proportion of non-geriatric patients eventually seeking nursing home care as compared to more elderly patients (see Fig. 4). Thus, it would seem that adding extra capacity at the nongeriatric wards is an interesting proposition. 5.2.3. Experiment 2.3: Reshuffling bed resources at the stroke unit, geriatric ward, and non-geriatric ward In this experiment, a strategy in which the bed capacities are shuffled at the stroke unit, the geriatric ward and non-geriatric Perecntage bed resource utilisaon at the non geriatric ward

constraints are consequently experienced at the nursing homes. Thus, effecting capacity increase at the geriatric ward without corresponding resource increases at the nursing homes would seem counter intuitive in this instance.

120

100 92.0 89.0

80

87.8 84.2

83.7

81.9

60

40

20

0

Fig. 9. Average waiting time delays for rehabilitation for non-geriatric patients, and corresponding percentage bed resource utilisation at the non-geriatric ward.

246

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

Table 8 Simulation results for reshuffled bed capacities. Strategy

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Base case Ger_B ( 2) Nger_B (+2) Ger_B ( 3) Nger_B (+3) Su_B ( 1) Ger_B ( 1) Nger_B (+2) Su_B ( 1) Ger_B ( 1) Nger_B (+2) NH_B (+10) Su_B ( 1) Ger_B ( 2) Nger_B (+3) Su_B ( 2) Nger_B (+2) Su_B ( 3) Nger_B (+3) NH_B (+10) Su_B ( 2) Ger_B ( 1) Nger_B (+3) Su_B ( 3) Nger_B (+3) Su_B ( 2) Ger_B ( 1) Nger_B (+3) NH_B (+10)

Average waiting time delays (days) Rehabilitation centre

Nursing home

11.34 6.00 5.70 5.24 4.50

33.4 35.3 33.9 36.5 20.5

4.00 3.60 3.60 3.50 3.00 2.70

30.9 37.2 20.7 34.8 31.9 21.4

Notes: Abbreviations ‘Su_B (+x) denotes addition of bed resources at the stroke unit by x units; ‘Ger_B (+x)’ denotes addition of geriatric bed resources by x units; ‘Nger (+x)’ the addition of non-geriatric bed resources by x units; ‘NH_B (+x)’ denotes addition of bed resources at the nursing home by x units.

ward is implemented. In this way, the beds resources are shifted amongst the departments, with or without net capacity increases at the specific departments, e.g. at the nursing home. During the reshuffling process, no more than three extra beds are added to any specific department, since as observed in the previous simulation experiments, for instance, experiment 2.1, adding more than three beds does not significantly reduce the average waiting time delays. The results for the simulation experiment are summarized in Table 8, and here, shifting a bed resource from a specific department is indicated as a subtraction, while the department to which the resource is shifted to is indicated by an addition. For instance, in strategy 2, two bed resources are shifted from the geriatric ward

‘Ger_B ( 2)’, and the capacity added to the non-geriatric ward ‘Nger_B (+2)’, thus no net extra capacity is added to the care pathway in this strategy. By contrast, in strategy 5, one bed resource each is shifted from the stroke unit ‘Su_B ( 1)’ and geriatric ward ‘Ger_B ( 1)’ and consequently added to the non-geriatric ward ‘Nger_B (+2). In addition, in this strategy, ten extra beds are added at the nursing home ‘NH_B (+10)’, thus a net increase of ten beds are added to the care pathway. From the results, for strategies where net capacity is not added to care pathway, strategy 9 where two bed resources and one bed resource are respectively shifted from the stroke unit and the geriatric ward, and consequently added to the non-geriatric ward, is observed as yielding the best outcome in terms of reducing the average waiting time delays. Here, a percentage reduction of 69% in waiting time delay for rehabilitation is observed (i.e. from 11.34 days to 3.50 days). Strategy 9, however, minimally impacts the waiting time delay for nursing home care, where in fact, an increase is noted (i.e. from 33.4 days to 34.8 days). For strategies where net resources are added to the care pathway, strategy 5 yields the best outcome since a reduction of waiting time delays for nursing home care by 35.9% (i.e. from 33.4 days to 20.5 days) is observed, although requires ten extra resource additions at the nursing home. 5.3. Experiment 3: Implementing buffer zone In this experiment, a strategy where bed resources are shifted from other departments to the buffer ward (B) is evaluated. Fig. 10 compares the impact of the resource shift strategies on the average waiting time delays. In the figure, strategies in which net capacity is added are represented on the x-axis, i.e. positive net number of extra beds, while the effect of the shift strategies on the average waiting time delays for rehabilitation is depicted along the y-axis. For experimental purposes, the strategies are compared with respect to two hypothetical maximum allowable

Fig. 10. Effect of implementing buffer strategy on the average waiting times for rehabilitation. Notes: Abbreviations ‘S’ denote the stroke unit; ‘G’ the geriatric ward; ‘nG’ the non-geriatric ward; ‘B’ the buffer; ‘NH’ the nursing home; ‘rehab,’ rehabilitation.

247

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

threshold; (1) waiting time delay for rehabilitation and (2) net extra resources. From the results, implementing strategies where the bed resources are shifted from the stroke unit and geriatric ward, and consequently added to the buffer zone are observed as yielding lower average waiting time delays for rehabilitation. In particular, the strategy, ‘S ( 2)G ( 2)B (+6)’, in which two beds each are shifted from the stroke unit and geriatric wards respectively, and consequently added to the buffer zone, yields the lowest waiting time delay. Additionally, in this strategy, two extra bed resources are added at the buffer ward, thus yielding a net increase of two bed resources. By contrast, implementing a bed shift strategy while adding extra resources at the nursing home likewise yields significant reduction in waiting time delays. For instance, the strategy S ( 2)G ( 2)B (+4)NH (+10) in which ten net capacity is added at the nursing home is observed as yielding a significant reduction in average waiting time delays for rehabilitation. Thus, the effect

of the extra capacity at the nursing home is analysed in a more detailed way in the next experiment. 5.4. Experiment 4: Increasing bed capacity at the nursing homes In this experiment, the number of bed resource capacities is varied from 5% (NH_B (+5%)) to 50% (NH_B (+50%)), and compared to a strategy in which the ideal situation is mimicked, and here, infinite bed resource availability is assumed at the nursing home, i.e. always available on demand. The corresponding numerical values for the average waiting time delays are depicted on the box plots in Figs. 11 and 12. Figs. 11 and 12 illustrate the results from which, significant reduction in waiting time delays is observed for nursing home care. As an example, increasing the resource capacity by 15% (NH_B (+15%)) yields as much as 44.5% reduction in average waiting time delay (33.2 days to 18.3 days), especially for category D and category E patients, described earlier on in Section 3. In particular, as

45

18 16 14 12.5

12

10.9

10.5

10.6

10

9.5

10.1 9.1 8.1

8 6 4 2

Waing me for nursing home care [days]

Waing me for rehabilitaon [days]

20

40 35

33.2

30 25.1

25 23.1

20

18.3 15.1

15

9.5

10 5

4.3 1.1

0

0

Average waing me from geriatric ward to the nursing home [days]

60

50

40

40.1

33.3

30 28.1 25.5

20

20.9 16.6

10

11.1 7.9

0

Average waing me from stroke unit to the nursing home [days]

Fig. 11. Effect of increasing nursing homes bed capacity. Notes: Abbreviations NH_B (+x%)’ denotes addition of bed resources by x% at the nursing home.

100 90 80

80.4 73.3

70 60

68.1

65.2 61.1 56.4 50.7

50

47.0

40 30 20 10 0

Fig. 12. Effect of increasing nursing homes bed capacity on the average waiting time delay. Notes: Abbreviations ‘NH (+x%)’ denotes adding bed resource capacity by x% at the nursing home.

248

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

depicted in Fig. 12, a significant improvement in waiting time delay is observed for patients transiting from the geriatric ward to the nursing homes, and here, a decreasing trend is observed with each resource increase. By contrast, the influence of the additional capacity seems to diminish beyond 25% where the average waiting time delay converges towards steady state and further increases does not substantially reduce the waiting time delays. 5.5. Experiment 5: reducing the medical time at the stroke unit and rehabilitation wards In this experiment, a strategy where a reduction in the medical length of stay for stroke treatment and rehabilitation is explored. In real life, such reductions would correlate to policy initiatives such increasing the number of medical personnel, procuring extra diagnostic capacity at the stroke unit, or improvements in the medical therapy. Two simulation experiments are further implemented; (1) reducing the medical time at the stroke unit and (2) reducing the rehabilitation time. 5.5.1. Experiment 5.1: Reducing patient medical time at the stroke unit Fig. 13 illustrates the influence of the reduced stroke treatment time (or medical length of stay ‘LoS’) on the waiting time delays for rehabilitation and nursing home care. In the figure, the abbreviation ‘LoS 0.95’ implies a strategy mimicking a treatment reduction time of 5% as compared to the base case. From the results, reducing the patient’s medical time at the stroke unit does not seemingly yield significant reduction in waiting time delays for both rehabilitation and nursing home care. Here, a clear reduction trend is not evident in waiting times in both instances despite the increases, which further emphasises the fact that the stroke unit is not the bottleneck. Thus, reducing the medical length of stay at the stroke unit is counter intuitive as it increases the patient outflow to upstream post-acute facilities, i.e. the rehabilitation centre and nursing homes. However, reducing the medical time would positively influence patients in category A and B who suffer from mild stroke attacks, thus go home after discharge from the stroke unit. A more effective approach would be to implement strategies aimed at reducing

medical length of stay upstream, here, at the rehabilitation centre and this is explored next. 5.5.2. Reducing patient medical time at the rehabilitation centre Fig. 14 summarize the effects of reducing the medical length of stay for rehabilitation. Likewise, in this experiment, the abbreviation ‘LoS 0.95’ implies a medical reduction time of 5%. A summary of the simulation results are also depicted in Table 9. From the results, reducing the medical length of stay in this instance marginally, by as low as 5%, seemingly reduces the waiting time delays for rehabilitation by as much 61% (11.3 days to 4.4 days) as compared to the base case. As also observed in Table 9, reducing the rehabilitation time also seems to positively influence the percentage bed resource utilisation at the geriatric and non-geriatric wards of which, a decreasing trend is observed. Here, the utility reduces from 85.5% to 61% at the geriatric ward, and from 92% to 66.7% at the non-geriatric ward. Reducing the rehabilitation medical length of stay, however, results in more demand for nursing home care since more patients now transit from the rehabilitation centre to the nursing homes. Despite the expected increased patient outflow, no discernable increasing trend is observed in waiting time delays for nursing home care (see Fig. 14). For instance, reducing the rehabilitation time by 40% (LoS 0.60) marginally increases the waiting time delay for rehabilitation by 10% (from 33.4 days to 36.8 days). Looking at the influence of the reduced rehabilitation time on bed occupancy at the stroke unit, a slight decrease in bed occupancy of 6% is observed with a 30% reduction in the rehabilitation time (LoS 0.70). As earlier depicted in Fig. 4, the marginal decrease here may be attributed to the comparatively lower proportion of stroke patients eventually requiring rehabilitation after treatment at the stroke unit. 6. Discussion and limitations 6.1. Managerial decision support From the simulation study, several insights and recommendation for improving care extended to stroke patient can be derived. Moreover, the study shows that often, as opposed to common

60

20

15 11.4

10

11.5 9.1

9.9

11.3 9.2

10.1 8.6

5

0

Waing me for nursing home care [days]

Waing me for rehabilitaon [days]

25

50 42.3

38.4

40

33.4

35.5 35.3 36.1

32.4 29.3

30

20

10

0

Fig. 13. Effects of reducing the medical length of stay at the stroke unit. Notes: Abbreviations ‘LoS x’ denotes a reduction in the patient length of medical stay at the stroke unit by a factor of (1 x).

249

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

70

Waing me for nursing home care [days]

Waing me for rehabilitaon [days]

25

20

15 11.3

10

5

4.4 2.9 0.9 0.3

0.2

0.1

60

50 45.6

40

37.4

35.9

35.0

35.3

38.6 36.8

33.4

30

20

10

0.05

0

0

Fig. 14. Trend analysis for the effects of reduced patient rehabilitation time. Notes: Abbreviations ‘LoS_x’ denotes reducing the medical length of stay at the rehabilitation centre by a factor of (1 x).

Table 9 Simulation results for reduction in patient rehabilitation time (length of stay). Strategy

1 2 4 5 7 8 10

Base case LoS 0.95 LoS 0.90 LoS 0.85 LoS 0.80 LoS 0.75 LoS 0.70

Average waiting time delays (days)

Percentage utilisation (%)

Rehabilitation

Nursing home care

Stroke unit

Geriatric ward

Non-geriatric ward

11.34 5.31 2.93 1.32 0.37 0.18 0.05

33.4 30.3 35.9 37.2 36.9 43.2 38.8

71.30 66.30 66.10 65.90 64.40 67.10 65.30

85.50 83.70 77.00 74.40 68.80 67.15 61.00

92.00 88.50 84.40 80.40 74.60 72.40 66.70

postulates in the literature, optimising the average waiting times in view of resource constraints requires a multi-strategy approach that takes into account resource allocation within the patient’s integrated care pathway. Importantly, formulating the strategy requires a careful understanding of the operational aspects, for instance, the diagnostic-therapy trajectory followed by patients in different stroke categories, patient inflow rates, diagnostic test capacities, and available bed resources. However, the above aspects raises an important fundamental question; how can the organisation translate operational aspects within the stroke care pathway into quantifiable decision variables such as the medical length of stay, average waiting time delays, or optimal bed resource allocation along the care pathway? In this regard, correctly identifying and quantifying the critical parameters that can feasibly be included in the simulation model is a considerable challenge. Often, the decision makers may rely on patient data, but an in-depth understanding of the patient trajectories is also important. As observed from the simulation study, and also from the literature, hospitals often collect patient data, but largely for clinical purposes, and often, not from the logistical view point (Baril, Gascon, & Cartier, 2014; Green, 2002). Yet, the latter is very relevant for modelling and decision support purposes, more so, with regards to modelling operational aspects in the care pathway. Thus, a translation of the ‘clinical data’ to ‘operational data’ is necessary, yet not straightforward. For instance, extracting the patient attributes in this study required considerable effort since the data was often recorded in different data bases, thus required attribute aggregation based on a common identifier, in this instance, the unique patient index. Such interpretation challenges

are not unique to the case discussed in this article, but are also highlighted in the literature, for instance, in Rashwan et al. (2015) where clinical patient data from hospitals in the Irish healthcare system were evaluated. Apart from interpretive challenges, clinical data consists of perhaps hundreds of patient attributes, given the dynamic healthcare environment. Thus, patients’ attributes vary widely based on gender, clinical pathologies, or treatment regimes. Therefore, this raises another fundamental question, how can the decision makers identify the relevancy of the important patient attributes specific for the modelling problem? This question is partly addressed by the simulation modelling approach because by modelling the care pathway, the decision makers are availed with an opportunity of critically reviewing the scope of the problem. From the scope, the relevancy of modeling attributes is established more clearly and thus, the attributes forms a plausible basis for formulating a concise structure for collecting relevant operational-related parameters. Closely linked to interpretative challenge is the question, how can the decision makers map the patients’ diagnostic-therapy care pathway? The answer is, unfortunately, not straightforward more so, for stroke patients transiting multiple-institutions in their care pathway. Although patient data may give insights on plausible care pathways, often, patients’ exhibiting similar pathologies may follow different trajectories, and statistically combining the different trajectories is often daunting. A similar challenge is also highlighted in Chemweno et al. (2014). In this study, this challenge is addressed by implementing the stroke patient categories as a decision variable, which differs from studies in the literature where

250

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251

often, the patient care pathways are aggregated, and assumed as following a well-defined pathway. However, aggregating care pathways in this way limits the extent to which operation insights can be derived and improvement strategies evaluated through the simulation model. For instance, Rashwan et al. (2015) aggregates care pathways for geriatric patients, and as a result, their model yielded a holistic view of the bed-blocking problem for postacute patients, and expectedly, long term systemic interventions are proposed as opposed to short and medium term operational improvements. The authors, for instance, propose flow interventions such as enhancing home care for elderly patients. By contrast, by segregating stroke patients based on unique attributes, operational improvements such as buffer management and bed shuffling were evaluated and observed to reduce waiting time delays. In addition, the impact of long term strategies such as reducing the medical length of stay through improved clinical protocols can be evaluated as well, but not at the expense of the more short term operational improvements. From the simulation modelling approach, interesting operational insights could be derived. For instance, contrary to common postulates where geriatric patients are viewed as bed-blockers, e.g. see (Lewis & Purdie, 1988; Manzano-Santaella, 2010), non-geriatric patients were highlighted as potential bed-blockers as well. Particularly, the non-geriatric ward was observed as under-capacitated and an important bottleneck as compared to the geriatric ward. This may explain an important bed resource planning flaw. By prioritizing resource allocation at the geriatric post-acute facilities in view of geriatric patients as bed-blockers, sub-optimal resource allocation at non-geriatric post-acute facilities may emerge as a result. This emphasises the importance of evaluating operational aspects as opposed to a holistic view of the care pathway as often the case in bed resource planning (Halpern & Pastores, 2015). Finally, modelling the integrated care pathway is seen as beneficial for decision support as opposed to optimising resources at specific departments, e.g. the emergency department, or stroke unit. As observed from the results, optimising bed resources at the stroke unit, for instance, does not significantly reduce waiting time delays for post-acute stroke patients. In fact, optimising downstream resources, e.g. at the stroke unit, significantly increases the waiting time delay for patients in need of postacute nursing home care by as much as 13.2%. Adding capacities downstream is similar to the strategies adopted in Chemweno et al. (2014) where additional diagnostic capacities at the stroke unit are evaluated. 6.2. Limitations Three main limitations should be emphasised. Firstly, the data collection and interpretation process was a particular concern, since the care pathway was multi-institutional and as one would expect, clinical data is stored at separate data bases. As such extra interpretive effort was required, as was also the process of verifying and validating the modeling input distributions and care pathway trajectories. Secondly, the simulation model was limited to two types of resources; diagnostic capacity, and bed resources. Focusing on the bed resources was particularly informed by the trend in literature where the bed blocking problem is viewed as an important logistical problem. Additional resources such as nurses or medical practitioners could yield additional insights and thus proposed for future work. Thirdly, the proposed strategies invariably require financing and for this reason, an economic analysis would be important. The economic analysis could yield insights on possible cost implications of the alternative strategies since increasingly; cost is often included as a decision variable in the care pathway planning (Halpern & Pastores, 2015). The economic evaluation is considered for future work.

7. Conclusion In this article, a discrete event simulation approach for modelling the stroke patients integrated care pathway is presented. The proposed approach is implemented in the case study where multiple institutions forming the stroke patient care pathway are taken into account. The study evaluates the impact of the bedblocking problem which is often considered an important logistical problem in the stroke care pathway. The simulation model is verified and validated based on empirical patient data of the concerned institutions. Five simulation experiments are implemented and a comparison made with the current situation of the existing stroke care pathway. The experiments evaluate alternative improvement actions aimed at optimising patient waiting times within the stroke’s diagnostic-therapy care pathway. From the study, implementing buffer management at the rehabilitation centre and shuffling bed resources based on utilisation are observed as significantly reducing the waiting time delays for post-acute stroke patients. Acknowledgments The authors wish to thank in the first place, the university hospital and the rehabilitation centre that made it possible to perform the extensive case study reported in this article. The authors also wish to thank three anonymous reviewers for their remarks that considerably improved the quality of this article. References Asaduzzaman, M., Chaussalet, T. J., & Robertson, N. J. (2010). A loss network model with overflow for capacity planning of a neonatal unit. Annals of Operations Research, 178(1), 67–76. Baril, C., Gascon, V., & Cartier, S. (2014). Design and analysis of an outpatient orthopaedic clinic performance with discrete event simulation and design of experiments. Computers & Industrial Engineering, 78, 285–298. Bhattacharjee, P., & Ray, P. K. (2014). Patient flow modelling and performance analysis of healthcare delivery processes in hospitals: A review and reflections. Computers & Industrial Engineering, 78, 299–312. Caro, J. J., Briggs, A. H., Siebert, U., & Kuntz, K. M. (2012). Modelling good research practices – Overview report of the ISPOR-SMDM ‘modelling good research practices task force one. Medical Decision Making, 32(5), 667–677. Chemweno, P., Thijs, V., Pintelon, L., & Van Horenbeek, A. (2014). Discrete event simulation case study: Diagnostic path for stroke patients in a stroke unit. Simulation Modelling Practice and Theory, 48, 45–57. De Bleser, L., Depreitere, R., Waele, K. D., Vanhaecht, K., Vlayen, J., & Sermeus, W. (2006). Defining pathways. Journal of Nursing Management, 14, 553–563. El-Darzi, E., Vasilakis, C., Chaussalet, T., & Millard, P. (1998). A simulation modelling approach to evaluating length of stay, occupancy, emptiness and bed blocking in a hospital geriatric department. Health Care Management Science, 1, 143–149. Green, L. V. (2002). How many hospital beds? INQUIRY: The Journal of Heath Care Organisation, Provision, and Financing, 39(4), 400–412. Green, L. V. (2012). OM forum – The vital role of operations analysis in improving healthcare delivery. Manufacturing and Service Operations Management, 14(4), 488–494. Halpern, N. A., & Pastores, S. M. (2015). Critical care medicine beds, use, occupancy, and costs in the United States: A methodological review. Critical Care Medicine, 43(11), 2452–2459. Heinrichs, M., Beekman, R., & Limburg, M. (1999). Simulation to estimate the capacity of a stroke unit. Studies in Health Technology and Informatics, 77, 47–50. Jeremic, V., Bulajic, M., Martic, M., Markovic, A., Savic, G., Jeremic, D., & Radojicic, Z. (2012). An evaluation of European countries’ health systems through distance based analysis. Hippokratia, 16(2), 170. Kelton, W. D., Sadowski, R., & Zupick, N. (2014). Simulation with ARENA. McGrawHill Education. Lane, D. C., Monefeldt, C., & Rosenhead, J. (2000). Looking in the wrong place for healthcare improvements: A system dynamics study of an accident and emergency department. Journal of Operational Research Society, 518–531. Lewis, H., & Purdie, G. (1988). The blocked bed: A prospective study. The New Zealand Medical Journal, 101(853), 575–577. Manzano-Santaella, A. (2010). From bed-blocking to delayed discharges: Precursors and interpretations of a contested concept. Health Services Management Research, 23(3), 121–127. Mur-Veeman, I., & Govers, M. (2011). Buffer management to solve bed-blocking in the Netherlands 2000–2010. Cooperation from an integrated care chain perspective as a key success factor for managing patient flows. International journal of integrated care, 11 (Special 10th Anniversary Edition).

P. Chemweno et al. / Computers & Industrial Engineering 93 (2016) 236–251 Nichols, J., Townsend, N., Luengo-Fernandez, R., Gray, A., Scarborough, P., & Rayner, M. (2012). European cardiovascular disease statistics. Brussels, Sophia – Antipolis: European Heart Network and European Society of Cardiology. Osorio, C., & Bierlaine, M. (2009). An analytic finite capacity queuing network model capturing the propagation of congestion and blocking. European Journal of Operations Research, 196(3), 996–1007. Rashwan, W., Abo-Hamad, W., & Arisha, A. (2015). A system dynamic view of the acute bed blockage problem in the Irish healthcare system. European Journal of Operational Research.

251

Sacco, R., Kasner, S., Broderick, J., Caplan, L., Connors, J., Culebras, A., ... Higashida, R. (2013). Stroke imaging comes of age: An updated definition of stroke for the 21st century from the American Heart Association and American Stroke Association. Stroke, 44, 2064–2089. Wang, T., Belaidi, A., Guinet, A., Besombes, B., 2007. Modeling and simulation of emergency services with ARIS and ARENA. In Proceeding of international conference on industrial engineering and systems management. Beijing, China. Wiler, J. L., Bolandifar, E., Griffey, R. T., Poirier, R. F., & Olsen, T. (2013). An emergency department patient flow model based on queueing theory principles. Academic Emergency Medicine, 20(9), 939–946.