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A systematic literature review of operational research methods for modelling patient flow and outcomes within community healthcare and other settings

  • Ryan PalmerEmail author
  • Naomi J. Fulop
  • Martin Utley
Open Access
Review Article

Abstract

An ambition of healthcare policy has been to move more acute services into community settings. This systematic literature review presents analysis of published operational research methods for modelling patient flow within community healthcare, and for modelling the combination of patient flow and outcomes in all settings. Assessed for inclusion at three levels – with the references from included papers also assessed – 25 “Patient flow within community care”, 23 “Patient flow and outcomes” papers and 5 papers within the intersection are included for review. Comparisons are made between each paper’s setting, definition of states, factors considered to influence flow, output measures and implementation of results. Common complexities and characteristics of community service models are discussed with directions for future work suggested. We found that in developing patient flow models for community services that use outcomes, transplant waiting list may have transferable benefits.

Keywords

literature review community healthcare patient flow outcomes operational research 

Introduction

In recent decades, an ambition of healthcare policy has been to deliver more care in the community by moving acute services closer to patient homes (Munton et al, 2011; NHS England, 2014). This is often motivated by assumed benefits such as reduced healthcare costs, improved access to services, improved quality of care, a greater ability to cope with an increasing number of patients, and improved operational performance in relation to patient health and time (Munton et al, 2011).

A scoping review analysed the evidence regarding the impact that shifting services may have on the quality and efficiency of care (Sibbald et al, 2007). It found that under certain conditions moving services into the community may help to increase patient access and reduce waiting times. Across multiple types of care, however (minor surgery, care of chronic disease, outpatient services and GP access to diagnostic tests), the quality of care and health outcomes may be compromised if a patient requires competencies – such as minor surgery – that are considered beyond those of the average primary care clinician. On the evidence for the effect on the monetary cost of services, Sibbald et al (2007) stated that it was generally expected that community care would be cheaper when offset against acute savings; however, increases in the overall volume of care (Hensher, 1997) and reductions in economies of scale (Powell, 2002; Whitten et al, 2002) may lead to an increase in overall cost in certain instances.

Considering the questions that remain over the impact of shifting services from acute to community sector, it is important to understand how community services may be best delivered. This is where applying operational research (OR) methods to community care services can contribute. For instance, services may be modelled to evaluate how goals, such as better patient access and improved outcomes, may be achieved considering constraints and objectives, such as fixed capacity or reducing operational costs. An example of one such method is patient flow modelling, the focus of this review.

Modelling patient flow

In a model of flow, the relevant system is viewed as comprising a set of distinct compartments or states, through which continuous matter or discrete entities move. Within healthcare applications, the entities of interest are commonly patients (although some applications may consider blood samples or forms of information). Côté (2000) identified two viewpoints from which patient flow has been understood, an operational perspective and, less commonly, a clinical perspective. From an operational perspective, the states that patients enter, leave and move between are defined by clinical and administrative activities and interactions with the care system, such as consulting a physician or being on the waiting list for surgery. Such states may be each associated with a specific care setting or some other form of resource but this need not be the case. In the clinical perspective of patient flow, the states that patients enter, leave and move between are defined by some aspect of the patient’s health, for instance by whether the patient has symptomatic heart disease, or the clinical stage of a patient’s tumour. A more generic view is that the states within a flow model can represent any amalgam of activity, location, patient health and changeable demographics, say, patient age (Utley et al, 2009). A key characteristic is that the set of states and the set of transitions between states comprise a complete description of the system as modelled.

Within the modelling process, characteristics of the patient population and of the states of the system are incorporated to evaluate how such factors influence flow. Examples of the former include patient demographics or healthcare requirements, whilst for the latter, capacity constraints relating to staffing, resources, time and budgets may be considered. The characteristics used depend upon the modelled system, modelling technique and questions being addressed. Considering these, the performance of a system may be evaluated through the use of output measures such as resource utilisation (Cochran & Roche, 2009), average physician overtime (Cayirli et al, 2006) and patient waiting times (Zhang et al, 2009).The output measures calculated within an application depends upon the modelled problem, modelling technique and the factors that are consider to influence flow.

Within acute care settings patient flow modelling has been applied to various scenarios – see Bhattacharjee & Ray (2014). There are also several publications for community care settings; however, no published literature review exists. This systematic literature review was undertaken to gather and analyse two types of patient flow modelling literature relevant for community services. The first were publications that present models of operational patient flow within a community healthcare context, denoted as “Patient flow within community care”. The second were publications that present combinations of patient outcomes and patient flow modelling in any setting, denoted as “Patient flow and outcomes”. Incorporating patient outcomes within the patient flow modelling process is increasingly pertinent within community healthcare. Patient outcomes are used not only to track, monitor and evaluate patient health throughout a care pathway, but also assess the quality of care and inform improvement. The justification for increasing the provision of community care includes improved patient outcomes and satisfaction, thus in combining outcomes and patient flow modelling new and helpful metrics may be developed to evaluate this assertion. Furthermore, such methods help to inform the organisation of healthcare services according to operational capability and the clinical impact on the patient population, unifying two main concerns of providers and patients with a single modelling framework. No specific setting was sought in the “Patient flow and outcomes” to find potentially transferable knowledge and methods for community settings.

To the best of our knowledge, this is the first literature review focussing on OR methods for modelling patient flow applied to community healthcare services and the first to review methods for modelling patient flow and outcomes in combination. This review has been undertaken as part of a project in which OR methods will be developed that combine patient flow modelling and patient outcomes for community care services. The aim of this review was thus twofold. Firstly, to explore different applications of OR methods to community services. Secondly, to understand how patient outcomes have been previously incorporated within flow models. In the discussion section of this paper, we suggest directions for the future of patient flow modelling applied to community care.

Method of review

We conducted a configurative systematic literature review (Gough et al, 2012), an approach intended to gather and analyse a heterogeneous literature with the aim of identifying patterns and developing new concepts. Two searches were performed to find peer-reviewed operational research (OR) publications, relating to “Patient flow within community care” and “Patient flow and outcomes” as previously detailed. We considered all papers published in English before November 2016 with no lower bound publication date, and searched the electronic databases Scopus, PubMed and Web of Science. Using a combination of the search terms listed in Table 1, to find papers related to “Patient flow within community care” we sought records with at least one operational research method term in the article title, journal title or keywords AND at least one patient flow term in the article title, journal title, keywords or abstract AND at least one community health setting term in the article title, journal title, keywords or abstract. Likewise, to find papers related to “Patient flow and outcomes” we sought records with at least operational research method term in the article title, journal title or keywords AND at least one patient flow term in the article title, journal title, keywords or abstract AND at least one outcome term in the article title, journal title, keywords or abstract.
Table 1

Final terms for literature searches

OR method terms

Patient flow terms

Setting terms

Outcome terms

Computer simulation

Discrete event simulation

Heuristics

Markov chain

Markov decision

Markov model

Mathematical model

Mathematical programming

Metaheuristics

Operational management

Operational research

Operations management

Operations research

Optimisation

Optimization

Queueing

Queuing

Simulation model

System dynamics

Integer programming

Linear programming

Modelling patient

Network analysis

Stochastic analysis

Stochastic modelling

Stochastic processes

Visual simulation

Access time

Bed occupancy

Capacity allocation

Capacity management

Capacity planning

Care management

Patient flow

Patient pathway

Patient process

Patient route

Patient throughput

Process flow

Wait time

Waiting list

Waiting time

Care access

Demand management

Flow of patients

Patients’ flow

Flow of care

Community based

Community clinic

Community facility

Community level

Diagnostic facilities

Health care center

Health care centre

Health care clinic

Health care practice

Health care service

Health center

Health centre

Health clinic

Health facility

Healthcare center

Healthcare centre

Healthcare clinic

Healthcare facility

Healthcare practice

Healthcare service

Home care

Home health care

Long term care

Mental health

Primary care

Care facility

Community care

Community health

Community healthcare

Homecare

Medical center

Medical centre

Multi facility

Multiservice

Residential care

Walk in

Outcome

Patient class

Patient type

Quality of life

Readmission

Referral

Disease progression

Health status

Initial sets of search terms relating to community healthcare settings and OR methods were informed by Hulshof et al (2012). Synonyms were added to these lists prior to the preliminary searches for papers. For patient flow terms and outcome terms, we formed initial lists that we considered relevant. The first batch of papers found using these lists was examined for further applicable search terms. The initial search terms are highlighted in bold in Table 1.

Papers obtained from the final searches were assessed for inclusion for full review at three levels. If a paper was not a literature review it was required to meet all the inclusion and none of the exclusion criteria outlined in Table 2. For each included paper, references were assessed using the same inclusion and exclusion process to find any papers that may have been missed in the searches.
Table 2

Inclusion and exclusion criteria for assessing papers presenting models of patient flow

Assessment level

Criteria

Patient flow within community care

Patient flow and outcomes

Title and journal

Inclusion

At least one operational research method term in the article title, journal title or keywords

AND

At least one patient flow term in the article title, journal title, keywords or abstract

AND

At least one community health setting term in the article title, journal title, keywords or abstract

At least one operational research method term in the article title, journal title or keywords

AND

At least one term patient flow term in the article title, journal title, keywords or abstract

AND

At least one outcome term in the article title, journal title, keywords or abstract

English language; published before November 2016 in peer-reviewed journals

Exclusion

Title or journal of publication had no relevance to OR, healthcare or patient flow

Abstract

Inclusion

Abstract suggested that the paper focussed on operational processes of healthcare and that OR methods were used to model patient flow

Exclusion

Papers based within management settings other than operational management

The delivery of healthcare was not evaluated

Only different scheduling policies were evaluated

Abstract indicated that the paper was not based in community care

Abstract indicated that the paper did not use patient outcomes

Full text

Inclusion

Abstract level inclusion criteria met in the full text

A model was presented using mathematical concepts and language

The model was well specified and reproducible

Quantitative analysis of a healthcare system was conducted within the paper

Exclusion

Criteria for exclusion at abstract level met in the full text

A model was viewed only in terms of its inputs and outputs without knowledge of its internal workings

A model was formulated as a composition of concepts that could not be used for analysis

A model was not rooted in analysis

Literature reviews were included at each level if they were concerned with OR methods for evaluating patient flow; focussed on operational processes of healthcare and no equivalent systematic review was included. Within the “Patient flow within community care” literature, review pieces were included if they focussed on community settings; whilst within the “Patient flow and outcome” literature, review pieces were included if they focussed on uses of patient outcomes in modelling processes.

Data tables were constructed to present key characteristics of the literature and shape our analysis. Informed by the initial readings, papers were grouped into five categories based on analytical method with five key characteristics of each model extracted and tabulated for comparison, given in Tables 4, 5 and 6.

Results of literature searches

The results of the final searches for and selection of papers are shown in an adapted PRISMA flow chart (Moher et al, 2009), Figure 1. Reasons for the exclusion of texts at full text assessment are shown in Table 3.
Figure 1

Flow chart of literature search results – 53 papers were eligible for review.

Table 3

Reasons for exclusion at full text assessment

Number of papers excluded at full text assessment

Reason for exclusion

No OR/patient flow modelling

Non-community settings

Model not reproducible/specified//quantitative

Analysis of different scheduling policies

No patient outcomes

23 “Patient flow within community care” literature

5

8

7

3

N/A

14 “Patient flow within community care” references

2

8

3

1

N/A

30 “Patient flow and outcomes” literature

8

N/A

2

7

13

27 “Patient flow and outcomes” references

4

N/A

1

22

Overall 25 “Patient flow within community” papers, 23 “Patient flow and outcomes” papers and 5 papers in the intersection entered the full review. An analysis of this literature is now presented with in the intersection of the two searches included in the “Patient flow within community care” section.

Analysis

Papers found within the “Patient flow within community care” search

Markovian models

A Markovian model views flow within a system as a random process within which the future movement of an entity is dependent only upon its present state and is independent of time spent in that state or the pathway it previously travelled. Whilst systems of healthcare are not truly Markovian, in using these methods, a steady-state analysis of a system may be formulated from which meaningful long-run averages of system metrics can be calculated.

The settings of these publications, presented in Tables 4 and 5, include residential mental healthcare (Koizumi et al, 2005), post-hospital care pathways (Kucukyazici et al, 2011), community services and hospital care (Song et al, 2012) and community-based services for elderly patients with diabetes (Chao et al, 2014).
Table 4

Papers included from “Patient flow within community care” search only

Title

Authors

Setting

States

Factors considered to influence flow

Method output

Implementation of results

Markovian models

 Modeling patient flows using a queuing network with blocking

Koizumi et al (2005)

Community care – mental health

–Physical queues

Multiple residential services

Service capacity

Traffic intensity per service

Congestive blocking

Queue lengths and wait times – with and without blocking

Not explicitly stated

 A block queueing network model for control patients flow congestion in urban healthcare system

Song et al (2012)

Community and hospital pathways

–Physical queues

Community services

Hospital registration

General hospitals

Service capacity

Traffic intensity per service

Congestive blocking

Batch arrival process

Queue lengths and wait times – with and without blocking

Not explicitly stated

Non-Markovian steady state analysis

 A model for planning resource requirements in health care organizations

Bretthauer & Côté (1998)

General approach, examples: blood bank, health maintenance organisation

–Physical queues

Different services

Stages of care

Resource constraints

e.g. Number of clinicians

Performance constraints

e.g. Wait time

Multiple time period extension

Optimised total capacity costs

Not explicitly stated

System dynamics analysis

 A patient flow perspective of U.K. health services: exploring the case for new “immediate care” initiatives

Wolstenholme (1999)

UK health service

–Physical and non–physical queues

Primary care

Secondary care

Community care

NHS continuing care

Volume of patients arriving

Service capacity

Queue lengths

Waiting times

Bed occupation

Scenario analysis

Long run use of services

Some insights shared with NHS staff

 Simulation analysis of the consequences of shifting the balance of health care: A system dynamics approach

Taylor et al (2005)

Community and acute care

Non-physical queues

Cardiac services in community

Wait time

Size of waiting list

Feedback mechanism

Clinical guidelines

Service capacity

Average wait times

Cumulative patient referrals and activity

Overall cost of care

Scenario analysis

Collaboration noted

Analytical methods featuring time dependence

 A continuous time Markov model for the length of stay of elderly people in institutional long-term care

Xie et al (2005)

Long-term care

–Physical queues

Residential home care

Nursing home care

–Long stay

–Short stay

Maximum likelihood estimation (MLE) of model parameters

Sojourn time

Estimation of LOS

Patterns of care usage

Not explicitly stated

 A model-based approach to the analysis of patterns of length of stay in institutional long-term care

Xie et al (2006)

Long-term care

–Physical queues

Residential home care

Nursing home care

–Long stay

–Short stay

MLE of model parameters

Left truncated data

Right censored data

Patient characteristics:

–Previous care

–Gender

Sojourn time

Estimation of LOS

Patterns of care usage

Not explicitly stated

 Analytical methods for calculating the distribution of the occupancy of each state within a multi-state flow system

Utley et al (2009)

Community mental health care

–Uncapacitated demand

General states

Illustrated with states as different stages of care

Time spent in state

Time dependent distribution for occupancy of states

Suggestions made to stake holders

 A deterministic model of home and community

care client counts in British Columbia

Hare et al (2009)

Long-term care

–Uncapacitated demand

Different aspects of LTC:

–Home care

–Accommodation

Care environment

–Publicly funded/

non-publicly funded

Time varying population characteristics:

–Patient age

–Wealth

–Health status

Initial conditions

Future demand for each aspect of LTC

Model used for planning future care

 A mathematical modelling approach for systems where the servers are almost always busy

Pagel et al (2012)

Community mental health care

–Non-physical queues

Different services

Capacity constraints

e.g. Appointment slots

Servers must always be busy (no steady state)

Optimal appointment allocation subject to wait time and capacity constraints

Formulation of a tool

 Appointment capacity planning in specialty clinics: a queueing approach

Izady (2015)

Specialty clinics

–Physical queues

Waiting

In service

Abandonment

–Fixed

–Backlog dependent

Patients able to re-join queue

Capacity

Appointment type

Patient wait time

Queue length

Size of appointment queues

No-show probability

Referral variance

Panel size

Not explicitly stated

Simulation Analysis

 Improving outpatient clinic efficiency using computer simulation

Clague et al (1997)

Outpatient-genito urinary medical clinic

–Physical queues

Stages of care

Patient groups:

–Clinical staff required

–New or returning

Mixed arrivals

No shows

Staffing constraints

Patient wait time

Doctor wait time

Clinic overtime

Scenario analysis

Application of method in response to a feedback survey

 Evaluating the design of a family practice healthcare clinic using discrete-event simulation

Swisher & Jacobson (2002)

Family Practice Healthcare Clinic

–Physical queues

Stages of care

Locations in the clinic

Patient groups:

–Health

Mixed arrivals

No shows

Staffing constraints

Patient wait time

Staffing costs

Revenue

Clinician overtime

Scenario analysis

Staff utilisation

Facility utilisation

Not explicitly stated

 Improving patient flow at an outpatient clinic: Study of sources of variability and improvement factors

Chand et al (2009)

Outpatient clinic

–Physical queues

Stages of care

Stages of patient information flow

Variability in task times

Patient characteristics:

–New or returning

–Administrative characteristics

Patient wait time

Physician overtime:

–AM and PM

Scenario analysis

Some suggested changes have been implemented

 Reducing patient wait times and improving resource utilization at British Columbia Cancer Agency’s ambulatory care unit through simulation

Santibáñez et al (2009)

Community care-ambulatory care unit

–Physical queues

Stages of care process

Shared resources

Appointment type

Capacity constraints

Scheduling policy

Scenario analysis

Patient wait time

Appointment duration

Resource utilisation

Time in system

Clinician utilisation

Suggestions made to senior management

 Facilitating stroke care planning through simulation modelling

Bayer et al (2010)

Stroke services

–Physical and non-physical queues

Stages of a stoke pathway

–Acute

–Community

Patient groups:

–Health related

Probabilistic:

–Death rate

–Length of stay

Capacity constraints

Scenario analysis

Predicted bed days

–Acute

–Care home

Cost of providing resource

Not explicitly stated

 Using discrete event simulation to compare the performance of family health unit and primary health care centre organizational models in Portugal

Fialho et al (2011)

Primary healthcare

–Non-physical queues

Stages of clinic care

Administrative characteristics

Consultation type

Opening hours

Duration of appointment

Routes of care

Days to arrange a GP consultation

Annual number of different consultations

Waiting time

Financial costs

Not explicitly stated

 Modeling the demand for long-term care services

under uncertain information

Cardoso et al (2012)

Long-term care

–Uncapacitated demand

Different aspects of LTC:

–Home based

–Ambulatory

–Institutional

Patient groups:

–Demographics

–Chronic disease

–Level of dependency

Mortality rates

Capacity

Scenario analysis

Future demand

Resources required to meet demand for each aspect of LTC

Cost

Not explicitly stated

 A simulation Optimization Approach to Long-Term Care Capacity Planning

Zhang et al (2012)

Long-term care

–Uncapacitated demand

Waiting

In service

Patient characteristics:

–Age and gender

–Arrival rate

–LOS

Initial conditions

Scenario analysis

Optimised capacity relating to waiting time targets

Future demand/capacity

Collaboration, training and feedback highlighted

 Applying discrete event simulation (DES) in healthcare: the case for outpatient facility capacity planning

Ponis et al (2013)

Outpatient clinics

–Non-physical queues

Different services

Patient characteristics:

–Administrative

–Medical

Budget constraints

Capacity constraints

Appointment types

Abandonment

Distance from clinic

Resource utilisation

Cost of care

Optimised service provision

Not explicitly stated

 Developing an adaptive policy for long-term care capacity planning

Zhang and Puterman (2013)

Long-term care

–Uncapacitated demand

Waiting

In service

Patient characteristics:

–Age and gender

–Arrival rate

–LOS

Initial conditions

Achievement of wait time targets in previous year

Scenario analysis

Adaptive policy for capacity planning

Optimised capacity relating to waiting time targets

Future demand/capacity

Not explicitly stated

 Simulation analysis on patient visit efficiency of a typical VA primary care clinic with complex characteristics

Shi et al (2014)

Primary healthcare clinic

–Physical queues

Stages of care

Patient groups:

–Arrival type

–Care requirements

No shows

Number of double booked appointments

Service utilisation

Wait time

Factor study

Suggestions made to management

 Patient flow improvement for an ophthalmic specialist outpatient clinic with aid of discrete event simulation and design of experiment

Pan et al (2015)

Specialist outpatient clinic

–Physical queues

Stages of care and information flow

Waiting

Patient characteristics:

–Services required

–Punctuality/no show

Layout of clinic

Resource capacity:

–Staffing levels

–Shared resource

Inter-relation of patient flow and information flow

Batch arrivals in information flow

Scenario analysis

Turnaround time

Waiting time

Allocation of appointment slots

Implementation of results

 A simulation model for capacity planning in community care

Patrick et al (2015)

Acute care

Long-term care

-Physical queues

Different services

Patient groups:

–Care requirements

–Priority

–Preference

Capacity

Reneging

Scenario analysis

Necessary capacity to meet target:

–Wait time/list size

–Percentage of patients who reach their preferred facility

Not explicitly stated

 A simulation optimisation on the hierarchical health care delivery system patient flow based on multi-fidelity models

Qiu et al (2016)

Community care

General hospitals

–Physical queues

Community services

General hospitals

Stages of care

Patient groups:

–Care requirements

Profit

Priority

Inter-hospital flow

Queueing network: Optimised resources to achieve maximum profit

Simulation:

Evaluation of feasible solutions regarding:

–Profit

–Use of services

–Cured patients

Not explicitly stated

Table 5

Papers included from “Patient flow within community care” search and “Patient flow and outcomes” search

Title

Authors

Setting

States

Factors considered to influence flow

Method output

Implementation of results

Markovian models

 An analytical framework for designing community-based care for chronic diseases

Kucukyazici et al (2011)

Community care-post acute services

–Non-physical queues

Different services

Post care outcomes

Demographics of inter service flow

Scenario analysis

Likely post care outcomes for common pathways

Not explicitly stated

 The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling

Chao et al (2014)

Community services for diabetes

Health states

Treatment pathway

Based on the results of a randomized controlled

trial

Variable health:

–Severity of disease

Probability of a patients belonging to a given outcome state as time progresses

Not explicitly stated

Analytical methods featuring time dependence

 Intelligent patient management and resource planning for complex, heterogeneous, and stochastic healthcare systems

Garg et al (2012)

Integrated care system including hospital, social, and community services

–Non-physical queues

Post hospital services

Patient groups:

–Demographics

–Care requirements

–Length of stay

Forecast number of patients in post care outcome

Forecast daily/total cost of care

Not explicitly stated

 Improving health outcomes through better capacity allocation in a community–based chronic care model

Deo et al (2013)

Community care-for asthmatic patients

–Non-physical queues

In service-appointment

Waiting state

Health states

Variable health

Time between appointment

Service capacity

Health benefit of treatment

Optimised appointment allocation subject to health benefit and capacity

Not explicitly stated

Simulation analysis

 Evaluating multiple performance measures across several dimensions at a multi–facility outpatient center

Matta & Patterson (2007)

Outpatient services

–Physical queues

Different services

Day of week

Patient groups:

–Care requirements

Patient pathway

Patient throughput

Frequency of clinician overtime

Single parameter for analysing multiple, stratified performance measures

Scenario analysis

Some suggested changes have been implemented

Within these models, states were defined as different services or stages of care. Kucukyazici et al (2011) and Chao et al (2014) also defined states of post-care outcomes. In the former these included patient mortality, admission to long-term care and re-hospitalisation, whilst the latter defined states of subsequent health progression.

Two main factors were considered to influence flow within these models: the effect of congestive blocking caused by limited waiting space (Koizumi et al, 2005; Song et al, 2012) and the diversity of patients: demographics (Kucukyazici et al, 2011) and severity of disease (Chao et al, 2014). In considering blocking, flow was influenced by the available capacity and average occupancy of each service.

The output measures were queue lengths and wait times for each state – with and without congestive blocking (Koizumi et al, 2005; Song et al, 2012) and the probability that patients would be in a given post-care outcome state (Kucukyazici et al, 2011; Chao et al, 2014). An analysis of different scenarios was undertaken in both latter papers to identify how alternative treatments may help improve post-care outcomes.

None of the papers explicitly reported implementation of their results. We consider implementation to include any action to share or use the results of the work within the modelled setting.

Non-Markovian steady-state models

An optimisation approach for resource allocation by Bretthauer & Côté (1998) defined states as services within specified pathways. The aim was to minimise overall costs whilst maintaining a certain level of care as measured by metrics such as desired waiting. Within the model, flow was influenced by capacity constraints, such as number of beds.

System dynamics analysis

System dynamics is a modelling method whereby computer simulations of complex systems can be built and used to design more effective policies and organisations (Sterman, 2000). Two applications were found, modelling systems of markedly different sizes. Taylor et al (2005) evaluated the uses of community care services to bolster acute cardiac services whilst Wolstenholme (1999) evaluated the UK’s NHS.

States were defined as community or acute services (Taylor et al, 2005) and different sectors of care, namely primary, acute, NHS continuing care and community care (Wolstenholme, 1999).

Capacity and rate variables, such as waiting list size and clinical referral guidelines were considered to influence flow within both models. A feedback mechanism was used by Taylor et al (2005) to evaluate how changes in these variables may stimulate and effect demand.

The main metrics of these models related to demand and access, namely waiting times and patient activity – for example, long-run use of services and length of queues (Wolstenholme, 1999). In both papers, a scenario analysis was performed to evaluate how changes within the model affected its output.

Wolstenholme (1999) reported that some findings were shared with NHS staff.

Analytical methods including time dependence

Applications of analytical methods with time dependence included specialist clinics (Deo et al, 2013, Izady, 2015), care after discharge from an acute stroke unit (Garg et al, 2012), long-term institutional care (Xie et al, 2005, 2006), community mental health services (Utley et al, 2009; Pagel et al, 2012) and home/community care in British Columbia (Hare et al, 2009).

The state definitions within these models related to stages of care/different services (Xie et al, 2005, 2006; Hare et al, 2009; Utley et al, 2009; Pagel et al, 2012; Garg et al, 2012); “waiting” or “in service” (Deo et al, 2013; Izady, 2015) and health states – in particular stages of health progression (Deo et al, 2013) or post-care outcomes (Garg et al, 2012).

The factors considered to influence flow included capacity of services (Pagel et al, 2012, Izady, 2015); patient demographics and care requirements (Xie et al, 2005, 2006; Hare et al, 2009; Garg et al, 2012); patient health between recurrent appointments (Deo et al, 2013) and the length of time in which a person occupied a state (Utley et al, 2009).

Commonly, the system metrics used in these papers related to the time a patient spent interacting with parts of the system – such as expected length of stay, waiting times and time spent in states. Garg et al (2012) calculated the daily cost of care and likely post-care outcome states for patients of different demographic groups. Pagel et al (2012) and Deo et al (2013) identified optimal capacity allocations subject to desired levels of queue lengths and wait times, and impact on patient health, respectively. Hare et al (2009) evaluated the possible future demand for services under different scenarios and situations.

Of these applications, Pagel et al (2012) and Utley et al (2009) reported steps towards implementation. In the former, a software tool was created, whilst in the latter the findings of the model were shared with key stakeholders. Hare et al (2009) also noted the use of their model for care planning within their given setting.

Simulation methods

The settings of these papers included long-term care (Cardoso et al, 2012; Zhang et al, 2012; Zhang and Puterman, 2013), outpatient services (Clague et al, 1997; Swisher & Jacobson, 2002; Matta & Patterson, 2007; Chand et al, 2009; Ponis et al, 2013; Pan et al, 2015), primary care and ambulatory clinics (Santibáñez et al, 2009; Fialho et al, 2011; Shi et al, 2014) and provisions of integrated acute and community services (Bayer et al, 2010; Patrick et al, 2015; Qiu et al, 2016).

States were defined as different services, clinics or sectors of care; or healthcare tasks within single clinics (Clague et al, 1997; Swisher & Jacobson, 2002; Santibáñez et al, 2009; Chand et al, 2009; Fialho et al, 2011; Shi et al, 2014). Chand et al (2009) and Pan et al (2015) modelled the flow of patient information alongside patient flow and thus defined states of information flow.

Factors considered to influence flow commonly included the healthcare requirements/demographics of patients (Clague et al, 1997; Swisher & Jacobson, 2002; Chand et al, 2009; Fialho et al, 2011; Shi et al, 2014), constrained capacity and rates of no show/reneging (Clague et al, 1997; Swisher & Jacobson, 2002; Shi et al, 2014). Bayer et al (2010), Cardoso et al (2012), Ponis et al (2013) and Qiu et al (2016) considered monetary influences such as budgetary constraints, cost of care and profitability. Chand et al (2009) used the variability of time in completing care tasks.

Common metrics related to the time that a patient spent waiting in a state or in the system as whole. Optimised capacity levels relating to key performance measures were also widely considered (Zhang et al, 2012; Zhang and Puterman, 2013; Ponis et al, 2013). Matta & Patterson (2007) calculated a single system metric – an aggregate of multiple performance measures stratified by day, facility routing and patient group. This single metric was formed of measures such as average throughput, average system time and average queue time.

The implementation of suggested changes was recorded in several applications (Clague et al, 1997; Matta & Patterson, 2007; Chand et al, 2009; Santibáñez et al, 2009; Zhang et al, 2012; Pan et al, 2015; Shi et al, 2014).

Papers found within the “Patient flow and outcomes” search

Markovian models

As outlined in Tables 5 and 6, seven publications used Markovian methods and outcomes, two of which were also included within the “Patient flow within community care” section. The five new papers modelled transplant waiting lists (Zenios, 1999; Wang, 2004; Drekic et al, 2015), intensive care units (Shmueli et al, 2003) and emergency care (Kim and Kim, 2015).
Table 6

Papers included from “patient flow and outcomes” search only

Title

Authors

Setting

States

Factors considered to influence flow

Method output

Implementation of results

Markovian models

 Modeling the transplant waiting list: A queueing model with reneging

Zenios (1999)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Patient groups:

-Demographic

-Transplant type

Organ groups

Reneging - death

Wait time in system and until transplant-per group

Fraction of patients who receive transplant per group

Not explicitly stated

 Optimizing admissions to an intensive care unit

Shmueli et al (2003)

Intensive Care Unit

-Physical queues

ICU beds

Waiting for service

In service

Variable health:

-Survival probability

Capacity-beds

Loss model

Expected number of statistical lives saved by implementing an outcome based admission policy

Not explicitly stated

 Modeling and analysis of high risk patient queues

Wang (2004)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Patient priority:

-Health related

Risk of death

List size

Queue lengths and wait time-per group

Expected number of deaths

Not explicitly stated

 Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing

Kim and Kim (2015)

Emergency care centre

-Physical queues

Waiting for service

In service

Patient groups:

-Acuity level

Admission policy

Patient group pooling

Infinite waiting space

Waiting time

-FCFS

-Hybrid (FCFS and priority)

-Hybrid with pooled groups

None explicitly stated

 A model for deceased–donor transplant queue waiting times

Drekic et al (2015)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Patient priority

-Health related

Variable health

Prioritisation

Reneging

List size

Blocking probability

Queue length and wait time

Reneging probabilities-per group

Not explicitly stated

Non-Markovian steady state analysis

 Efficiency and welfare implications of managed public sector hospital waiting lists

Goddard & Tavakoli (2008)

Waiting list-hospital care

-Non-physical queues

Number of people on the waiting list

Service capacity

Rationing system

Proportion of sick patients admitted

Wait time

-All patients

-For least ill patients

Not explicitly stated

 A multi-class queuing network analysis methodology for improving hospital emergency department performance

Cochran & Roche (2009)

Emergency department

-Physical queues

Stages of care

Patient group:

-Care requirements

Seasonality

Number of beds

Queue lengths and wait time

Service utilisation

Requirements for a desired level of utilisation

Software made available to EDs

Feedback to clinicians and ED managers

 A queueing model to address wait time inconsistency in solid–organ transplantation

Stanford et al (2014)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Patient groups:

-Care requirements

Organ groups

Compatibility

Wait time per patient type

Not explicitly stated

System dynamics analysis

 Modeling chronic disease patient flows diverted from emergency departments to patient–centered medical homes

Diaz et al (2015)

Care for chronic disease

Stages of care

-Emergency departments

-Ambulatory services

Patient groups:

-Insured and uninsured

-Care requirements

Resource capacity

Death

Congestion

Scenario analysis

Impact on demand for services and required capacity

Resource utilisation

Cost

Health impact

Not explicitly stated

Analytical methods featuring time dependence

 Dynamic allocation of kidneys to candidates on the transplant waiting list

Zenios & Wein (2000)

Waiting list-transplant

-Non-physical queues

Transplant queue

Obtained transplant

Variable health

Patient demographic

Organ groups

Availability of organ

Transplant failure/re-join

Quality of life measure

Wait time in system and until transplant

-per group

Fraction of patients who receive transplant per group

Not explicitly stated

 The optimal timing of living-donor liver transplantation

Alagoz et al (2004)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Health states

-Transplant in time period

-Waiting in time period

Variable health

Organ quality

Post–transplant survival rate

Optimal timing of transplant

Not explicitly stated

A model for managing patient booking in a radiotherapy department with differentiated waiting times

Thomsen & Nørrevang (2009)

Radiotherapy

-Non-physical queues

Radiotherapy slots

Patient groups:

-Care requirements

-Waiting time guarantee

Capacity

Lower and upper limits for slot allocation per group

Suggested use within department

 Investigating hospital heterogeneity with a multi-state frailty model: application to nosocomial pneumonia disease in intensive care units

Liquet et al (2012)

Intensive care

Admission

Infection

Death

Discharge

Patient groups:

-Frailty

-Type of admission

-Infection

Number of patients with infection

-Death

-Discharge

None explicitly stated

 Optimizing intensive care unit discharge decisions with patient readmissions

Chan et al (2012)

Intensive care

-Non-physical queues

ICU beds

Number of people in the system

Variable health

Demand driven discharge

-Cost such as loss in QUALY

Congestion

Optimisation of cost incurred by demand dependent discharge

Readmission load and mortality rates

-Low congestion

-High congestion

Not explicitly stated

 Planning for HIV screening, testing, and care at the veterans health administration

Deo et al (2015)

Community care-for HIV patients

-Non-physical queues

Stages of care

Health states

Variable health

Allocation of screening

Budgetary constraints

Service constraints

Optimal screening policy with regards to health benefit, budget and capacity

Staffing levels

Several suggestions influenced decision making

 Radiation Queue: meeting patient waiting time targets

Li et al (2015)

Radiotherapy

-Non-physical queues

Types of treatment slot for radiotherapy machines

Patient groups:

–Care requirements

-Service times

Capacity

Patient pooling

Required capacity to meet set waiting time targets

Optimal allocation of capacity for different patient groups

Utilisation

Not explicitly stated

Simulation analysis

 Simulating hospital emergency departments queuing systems:

\( (GI/G/m(t)) :(IHFF/N/\infty ) \)

Panayiotopoulos & Vassilacopoulos (1984)

Emergency department-Physical queues

Waiting list

In service

Variable clinician capacity

Waiting capacity

Variable patient priority:-Health related

Average number of patients-in system and queue

Average time-in system and queue

Some suggested changes have been implemented

 Development of a Central Matching System for the Allocation of Cadaveric Kidneys: A simulation of Clinical Effectiveness versus Equity

Yuan et al (1994)

Transplant waiting list

-Non-physical queues

Waiting list

Received transplant

Patient groups

Organ groups

Compatibility

Availability of organs

Time spent waiting

Assessment of different allocation algorithms

-Time until transplant

-Time waiting if no transplant by year end

Number of unused organs

Not explicitly stated

 Patient flows and optimal health-care resource allocation at the macro-level: a dynamic linear programming approach

van Zon & Kommer (1999)

General method for resource allocation

Stages of care

Health states

Variable health

Duration of medical activity

Patient pathway

Health benefit

Scenario analysis

Optimisation of resources:

-Health of patients

-Wait time

Not explicitly stated

 A simulation model to investigate the impact of cardiovascular risk

in renal transplantation

McLean & Jardine (2005)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Transplant failure

Patient mortality rate

Patient characteristics:

-Demographics

-Health risk

Post-transplant survival rate

Scenario analysis

Not explicitly stated

 A clinically based discrete-event simulation

of end-stage liver disease and the organ allocation

Shechter et al (2005)

Waiting list-transplant

-Non-physical queues

Waiting list

Obtained transplant

Patient characteristics:

-Demographics

-Care requirements

Organ type

Variable health

Graft failure

Post-transplant survival rate

-1 year

-3 year

Not explicitly stated

 Capacity planning for cardiac catheterization: a case study

Gupta et al (2007)

Cardiac catheterization clinic

-Physical queues

Stages of care

Patient group:

-Care requirements

Clinician case load

Wait times

Optimised capacity allocation subject to

desired wait times

Scenario analysis

Some suggested changes have been implemented

 A discrete event simulation tool to support and predict hospital and clinic staffing

DeRienzo et al (2016)

Neonatal intensive care

-Physical queues

Intensive care beds

Patient groups:

-Admission type

-Acuity

-Health

Resource capacity

Estimated staffing allocation

Forecast future demand

Cost of provision

Not explicitly stated

In these models, states related to whether patients were “waiting” or had obtained a service/transplant. Drekic et al (2015) defined patient priority states to reflect health deterioration.

The factors that influenced flow related to patient health with groups or states used to assign priorities (Wang, 2004; Drekic et al, 2015) or, represent patient demographics and care requirements. The reneging characteristics of different groups of patients were also considered in each transplant paper with patients modelled as leaving the waiting list due to death or for other reasons. (Zenios, 1999; Drekic et al, 2015).

The output measures of these papers commonly related to the wait time faced by patients. Other metrics included the probability of reneging per patient group (Drekic et al, 2015) and the expected number of deaths for waiting patients (Wang, 2004) or lives saved by an admission policy (Shmueli et al, 2003). Zenios (1999) calculated the average time spent in the system and in the queue for each demographic group, and the fraction of patients from each group who received a transplant.

None of the papers reported an implementation of their results within their care setting.

Non-Markovian steady-state models

The modelled settings and applications included an emergency department (Cochran & Roche, 2009) and two waiting lists, one for hospital care (Goddard & Tavakoli, 2008), the other for transplant patients (Stanford et al, 2014). States were defined as stages of hospital care and as “waiting” or “in service”.

The factors considered to influence flow were patient group and seasonality (Cochran & Roche, 2009) and resource availability and patient health (Goddard & Tavakoli, 2008; Stanford et al, 2014). Each model used metrics relating to the amount of time a patient spent within parts of the system.

Cochran & Roche (2009) reported an implementation of their results with software developed and made available for clinicians and care managers. Feedback and educational sessions were also organised to help key stakeholders to understand the work.

System dynamics analysis

Diaz et al (2015) evaluated patient flow between states of acute care and home care for patients with chronic disease. The factors considered to influence flow related to patient groups based on their care requirements and whether they possessed insurance. Congestion and capacity of resources were also considered. A scenario analysis was performed to evaluate the impact of different patient routes and resource allocations on the level of demand for services and the cost of providing care.

Analytical methods including time dependence

Nine papers were found, two of which were included in the “Patient flow within community care” section. Of the seven remaining, the settings were care for chronic diseases (Deo et al, 2015), two intensive care models (Liquet et al, 2012; Chan et al, 2012), two radiotherapy models (Thomsen & Nørrevang, 2009; Li et al, 2015) and two transplant waiting lists (Zenios & Wein, 2000; Alagoz et al, 2004).

States were defined as “in service” or “waiting”, different services or different appointment slots (Thomsen & Nørrevang, 2009; Li et al, 2015). Alagoz et al (2004), Liquet et al (2012) and Deo et al (2015) also defined multiple health states.

The factors considered to influence flow were commonly related to differences within the patient population pertaining to health (Alagoz et al, 2004; Deo et al, 2015); care requirements or demographic/health-related groups (Zenios & Wein, 2000) and the availability of resources such as organs (Zenios & Wein, 2000; Alagoz et al, 2004) or appointment slots (Thomsen & Nørrevang, 2009; Deo et al, 2015, Li et al, 2015).

Common metrics used by these methods focussed on the amount of time a patient spent waiting for a service – for example, the optimal timing of appointments (Deo et al, 2015) or transplants (Alagoz et al, 2004) subject to changes in patient health. Zenios & Wein (2000) calculated output measures for different groups of patients to evaluate equity within the process of organ allocation. Forecasts of capacity requirements and optimal allocation of resources based on patient groups were also common.

Thomsen & Nørrevang (2009) and Deo et al (2015) reported that some of their suggestions had influenced decision making.

Simulation methods

Eight applications were found with one included in the “Patient flow within community care” (Matta & Patterson, 2007). Of the seven remaining, applications included a cardiac catheterisation clinic (Gupta et al, 2007), three transplant waiting lists (Yuan et al, 1994; McLean & Jardine, 2005; Shechter et al, 2005), an evaluation of an emergency department (Panayiotopoulos & Vassilacopoulos, 1984), neonatal intensive care (DeRienzo et al, 2016) and a healthcare resource allocation model (van Zon & Kommer, 1999).

Within these papers, states were defined as healthcare tasks (van Zon & Kommer, 1999; Gupta et al, 2007), number of beds and “waiting” or “in service”.

The factors considered to influence flow within these models included demographics/care requirements (van Zon & Kommer, 1999; McLean & Jardine, 2005; Shechter et al, 2005; Gupta et al, 2007); the health, mortality and survival rates of patients (van Zon & Kommer, 1999; McLean & Jardine, 2005; Shechter et al, 2005) and resource capacity.

Several metrics were calculated within these methods, with the time patients spent interacting with or waiting within parts of the system a common measure. Other outputs of interest included capacity allocation (Yuan et al, 1994; Gupta et al, 2007; DeRienzo et al, 2016); the cost of care, health benefits of service (van Zon & Kommer, 1999) and the expected survival rate of patients (McLean & Jardine, 2005; Shechter et al, 2005).

Panayiotopoulos & Vassilacopoulos (1984) and Gupta et al (2007) both noted that some of their suggested changes had been implemented.

Summary of findings and discussion across literatures

Findings from across the literature will now be summarised and discussed, drawing together common themes and key characteristics as presented in Tables 4, 5 and 6. In combination, we reviewed 53 papers presenting models of patient flow. 30 applied to community care services which included mental health services, physical health services, outpatient care and patient flow within acute and community settings. Furthermore, 32 applications used, in some form, either queue lengths or the amount of time that a patient spent within states as output measures. The next most common metrics were monetary costs in relation to patient use and the allocation of capacity-related resources.

Within the “Patient flow and community care” literature a range of flow characteristics were considered. For instance, patients access and arrivals to community services were modelled as unscheduled (e.g. Taylor et al, 2005), by appointment (e.g. Deo et al, 2013, 2015), by external referral (e.g. Koizumi et al, 2005), or a mixture of the above (e.g. Chand et al, 2009; Song et al, 2012). Furthermore, multiple care interactions were modelled as either sequential visits to different services (e.g. Koizumi et al, 2005; Song et al, 2012) or as single visits where multiple tasks were carried out (e.g. Chand et al, 2009). In either instance patients were sometimes modelled as being able to recurrently visit the same service over time with some patients using the service more frequently (e.g. Shi et al, 2014; Deo et al, 2013).

Within the “Patient flow and outcome” literature, there were 10 models of transplant/waiting lists, 8 of community, ambulatory and outpatient services, 3 of emergency departments, 4 for intensive care, 2 for radiotherapy and 1 general model of resource allocation. Outcome measures were incorporated within the outputs of these models in three broad ways: (1) system metrics were stratified by outcome related groups; (2) variable patient or population level health was used as an objective or constraint within a model to influence resource allocation or (3) health outcomes – such as patient mortality or future use of care – were used as system metrics. Notably, 15 papers used patient groups to represent differing health/outcomes, whilst 13 papers incorporated variable health/outcome which could change during a course of care. By including variable health/outcome, a model’s output was informed by the effect of a care interaction, or absence of a care interaction, on patient outcomes and on the operation of the system.

Patient groups relating to health/outcome were used in models of each method and were commonly used in resource and service capacity allocations. Notably, their application within steady-state methods is limited since it is difficult to model differing group-dependent variables, such as service times, since the order of patients within these queues is unknown.

Variable health/outcome which could change during a course of care was commonly used within time-dependent methods. They were used to model the effect of care on a population where the modelled time period was large, such as stays with residential care or where multiple interactions were considered.

Across both literatures, queues could be categorised as either physical – constrained demand – or non-physical – unconstrained demand, as per Tables 4, 5 and 6. Physical queues form when patients wait for service within a fixed physical space. Examples include, arrivals forming a queue within a clinic or emergency care (e.g. Chand et al, 2009; Santibáñez et al, 2009; Shi et al, 2014) or when patients move between care interactions and immediately wait within another single physical location (e.g. Xie et al, 2005, 2006; Cochran & Roche, 2009). When physical queues occur, the time a patient spends waiting for service is typically of the order of their expected service time. These queues are constrained and patient demand is modelled from the point when they physically arrive to the service.

Given these dynamics, the most common analysis of physical queues related to the daily operation of single services. Such models were used to gain insight into the delivery of care (e.g. flow between multiple treatments/consultations in a single visit). Studies of physical queues were carried out using each type of method. The choice of method depended on the desired insight, factors considered to influence flow and size of the system. Steady-state methods were sufficient if queue lengths and wait times were of primary concern. However, if variability in input parameters or periodic influences were important, time variable methods were more appropriate. These models typically focus on shorter time frames of care, therefore health/outcome groups were used within these models.

Alternatively, non-physical queues occur when patients may wait in any location away from the service such as their place of residence-e.g. when care is scheduled (Deo et al, 2013) or a patients wait is potentially long and unknown (Zenios & Wein, 2000). Non-physical queues represent unconstrained demand which begins from the point when a patient is referred to a service. A patient’s wait is therefore typically of an order larger than their expected service time. Such models are commonly used to model the demand and access at a system level.

The most common analysis of non-physical queues related to waiting lists and multiple uses of a single or multiple services. Studies of these scenarios were carried out using steady-state analysis or time-dependent methods. Due to the long-run nature of steady-state models these models were appropriate for such situations, especially when variability and differences within the patient population were negligible. In scenarios of scarce appointment or resource allocation, time variable methods were increasingly used. Within these models, variable health/outcome was widely considered due to the longer time frames of care, possible multiple interactions and the benefits stated previously.

It should be noted that this work is limited due to the difficulty of systematically reviewing this literature. In particular, we found two main difficulties. Firstly, these papers are published within a wide range of journals, some within healthcare journals, others in operational research (OR) journals, whilst a proportion was found within journals that were neither health-specific nor OR specific. Secondly, we found that patient flow is described and referred to in myriad ways within literature. No clear standards were found; thus, locating these papers was particularly difficult.

Due to the complexity of finding literature, we cannot claim our findings to be exhaustive. However, by following an iterative process of literature searching our findings are representative of this literature, allowing us to draw meaningful conclusions in the next section.

As a final observation, the reporting of implementation and collaboration varied greatly within each group of analytical method.

Conclusions and directions for future work

Community healthcare consists of a diverse range of geographically disparate services, each providing treatment to patients with specific health needs. As a result, the factors that are considered to influence patient flow are often markedly different to acute services and vary from one service to another. Considering the characteristics discussed in this review, it is common for a mixture of complex dynamics to be modelled within community care applications. Modelling these services can thus become complicated, requiring innovative methods to include all or some of these dynamics. This is highlighted by the range of different methods presented in this review.

Future directions for patient flow modelling within community care are now explored motivated by known challenges for community care, gaps found within the literature and any transferable knowledge between the two sets of literature.

Few models considered patient flow within systems of differing community services with most studies focussing on single services. Likewise, few also considered the mix of patients within these services. Consider, however, a diabetes pathway where patients may require treatment for comorbidities from multiple services based in the community. Each of these services will also provide care to a range of patients, not just those with diabetes. This example highlights a significant challenge in the management of community services. Namely, how to co-ordinate and deliver care within physically distributed, co-dependent services considering increasing episodic use by patients with differing needs. With a shift of focus towards care for the increasing number of patients with multiple long-term illnesses (NHS England, 2014), the patient mix within each service further exacerbates this challenge. Therefore, it would be beneficial to develop methods for modelling patient flow through multiple services to investigate these scenarios.

Considering the above, another useful direction would be to develop time-dependent analytical methods and simulation models for these scenarios. Whilst often analytically difficult, there are important benefits in using these methods as shown by the wide range of applications within this review. Given the characteristics of community services previously discussed, a helpful addition to the research landscape would be models of systems for which steady-state assumptions do not hold or where capacity, demand and timing of patient use vary. This would be helpful in community care where – due to the decentralisation – it can be hard to measure and interpret the impact that changes to one part of the system have on the whole system over short-term and long-term time periods. In considering flow in a system of inter-related services, or situations where patients may re-use the same service over a time period, the development of system level, time-dependent methods would be beneficial in analysing the time variable impact of changes in the immediate, short term and long term for the whole system.

Finally, 13 papers used variable health/outcomes, of which 5 applied to multiple care interactions. Again considering the purpose and nature of community care, we suggest that methods which use multiple health states to model the improvement and decline of patient health throughout a course of care would be a useful direction for future study. A good example of these methods is presented by Deo et al (2013, 2015). Having otherwise not been widely explored, methods that quantify and evaluate the quality of care and include an interaction between patient outcomes, care pathways and flow within the system would be valuable and appropriate for community care modelling.

In considering OR methods for community services which combine patient flow modelling and patient outcomes, there may be some transferable knowledge from transplant models. For situations where non-physical are modelled, transplant list models may provide a useful basis as they share some distinct similarities to community care services – such as reneging, time-varying demand, limited resources and in some cases re-entrant patients. Transplant models may be informative for both scheduled care and unscheduled care.

Notes

Acknowledgements

This research was supported by the National Institute for Health Research (NIHR) Collaboration for Leadership in Applied Health Research and Care North Thames at Barts Health NHS Trust. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health. The first author was supported by the Health Foundation as part of the Improvement Science PhD programme. The Health Foundation is an independent charity committed to bringing about better health and healthcare for people in the UK.

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Copyright information

© The OR Society 2017

Authors and Affiliations

  1. 1.Clinical Operational Research Unit, Department of MathematicsUniversity College LondonLondonUK
  2. 2.Department of Applied Health ResearchUniversity College LondonLondonUK

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