Background
Managing demand for healthcare is a global problem. The science of complex systems [
1,
2] has been proposed as a way of understanding health services [
3,
4], but there has been little quantitative evidence to support this notion. The idea that healthcare services can be considered as complex systems is not new [
4‐
7] and remains current [
3,
8], but it has rarely been tested, particularly in ways that use large-scale data. Healthcare self-evidently possesses many of the characteristics of a complex system [
1,
2,
5] in that there are many component parts (patients, clinicians, services) with many interactions (consultations) which occur in the context of prevailing social attitudes and norms (e.g. ideas about when it is appropriate to seek healthcare). Because of the interactions and the way that characteristics of the system emerge from these interactions, complex systems are different from conventional systems in several ways [
1,
9]. Some of these differences are listed in Table
1. Much current health services research and innovation addresses healthcare as a conventional system rather than as a complex one, with important implications for the development and implementation of complex interventions to change health and healthcare [
1,
3,
9,
10].
Table 1
Comparison of features between a complex system and a conventional system
Relationship of individual to system | System comprises discrete individuals, who are considered as distinct and statistically independent from each other, but who share the system environment | System comprises individuals, each interacting with others in the system; characteristics of the whole system emerge from these interactions |
Context and culture | Context or culture seen as separate from the individuals and may be externally directed or imposed. Treated as a confounder or covariate in analysis | Context or culture seen as emergent properties of the system. In turn, these properties condition the interactions of individuals within the system |
Predictability of response to events | Multiple independent responses to change produce a coherent average value response and an approximately normal distribution | Changes to the system are usually buffered by local interaction (so have minimal effect), but sometimes events spread through the system with unexpectedly large effects |
Statistical Distributions | Normal distribution for continuous measures, Poisson distribution for events | Heavy-tailed distributions for events: typically inverse power law or log-normal |
Despite the resemblance of healthcare to a complex system and the wide recognition that complex systems display characteristic statistical properties [
11,
12], there have been very few studies which have sought to test this by comparing the statistical properties of healthcare use with known properties of complex systems [
13‐
15]. However, robust methods are available for this [
11] which have been widely used in many other areas of science (examples include the size distributions of avalanches, forest fires and human settlements and patterns of Internet activity) [
16].
One aspect of healthcare which is well suited to being examined as a complex system is the use of urgent care [
17,
18]. Urgent care (emergency department (ED) and primary care out-of-hours (PCOOH) services) represents a relatively open system in which use is driven by patients rather than controlled by the service. It also includes the particular problem of high-using, or frequently attending, patients [
17]. These patients take up a disproportionate amount of resources including professional time and treatment costs and are frequently portrayed as problematic individuals for whom initiatives are developed to identify and manage individual frequent attenders [
19,
20]. This action at the level of the individuals carries the implication that tackling these extreme cases will resolve the pressure on urgent care services [
21]. However, frequent attenders comprise a very heterogeneous group [
22], including both patients who appear to need multiple attendances because of severe or complex medical conditions and others who attend for conditions that could be managed elsewhere [
23] or to an extent which is disproportionate to their medical conditions [
19,
24‐
26]. While interventions to tackle specific problems for some frequent attenders are successful at the individual level, there is little evidence that they lead to a substantial reduction in overall demand.
In contrast to the view of frequent attendance as a problem of a few individuals, a complex system perspective could argue that (1) frequent attenders might represent the “black swans [
27]” occurring in the natural heavy-tailed distribution of events [
11], (2) patterns of consultation by individuals over time should show the bursts typically seen in complex systems [
12] and (c) there should be plausible social mechanisms which drive the behaviour of individuals across all levels of attendance from least to most frequent. While social mechanisms have been documented in several qualitative studies of healthcare seeking [
28‐
32], there have been no studies, to our knowledge, which have examined the statistical properties of complex systems in urgent healthcare use. The closest to this have been some reports of the overall population distribution of urgent care use which described non-normal distributions [
33,
34]; however, none have carried out more detailed statistical analyses.
In this study we tested the hypothesis that patterns of attendance at urgent care services should display two typical statistical characteristics of complex systems. Specifically we hypothesised first, that the overall distribution of consultations per individual would follow a power law [
2,
11] and second, that individuals’ consultations would occur in correlated bursts (sequences of consultations clustered in time), with the distribution of burst lengths also approximating to a power law [
12]. The implication of these hypotheses is that if urgent care services do behave as complex systems, then interventions to influence their use need to act in a system-wide fashion rather than focus on problematic individuals.
Methods
We conducted three linked studies to compare the statistical properties of urgent healthcare use with the typical properties of a complex system. First, we defined the total number of contacts per person and compared this to two heavy-tailed distributions, the inverse power law and the log-normal. Second, we used the same data to examine the pattern of bursts of attendance. Third, we conducted a systematic search for and analysis of reports, from other centres, of the distribution of number of contacts per person to compare these results with the findings from our primary data sources.
Data sources
We analysed primary data from two sources: PCOOH data from a study of NHS 24, the service which provides out-of-hours primary care services throughout Scotland (population 5.6 million (M)) [
35] and ED data supplied by Canterbury District Health Board in New Zealand. The data was for the ED of Christchurch Hospital, serving a population of approximately 500,000 people. Both datasets were derived from routine management data and thus included all cases handled by the respective services.
In the PCOOH service, all calls were initially managed through a nurse-based triage system with a range of options including telephone advice by the nurse, consultation with a general practitioner (GP), either at a treatment centre or in the patient’s home, and direct ambulance transfer to an ED. The data included all calls to the NHS 24 service throughout 2011. We excluded calls during office hours (08.00 to 18.00 weekdays except public holidays) because the vast majority of urgent care requests during these hours go directly to the patient’s GP practice. All data was anonymised and handled under a data-sharing agreement between the University of Aberdeen and NHS 24; as no patient-identifiable data was involved, additional research ethical permission was not required. The ED data comprised anonymised data of adult attendance for the period July 2011 to June 2013. Since no identifying patient information was involved, research ethical permission was not required under New Zealand’s Standard Operating Procedures for Health and Disability Ethics Committees.
Definitions of attendance
For both datasets, the unit of analysis was a contact — defined as one or more attendances or phone calls with the service on a given day. While some patients had more than one attendance or call on the same day, we limited data to one contact per day, since most repeated calls on the same day related to the same episode of care (e.g. escalation of a contact from telephone advice to consultation). PCOOH contacts included episodes of care which were managed by telephone, in the urgent care department or at home, and by any healthcare professionals. ED contacts included emergency attendances by any route.
Heavy-tailed statistical distributions and correlated bursts of activity
Heavy tails are a feature of a number of statistical distributions, including the inverse power law and the log-normal, which have been repeatedly observed in large, naturally occurring systems [
11]. The term refers to the long, or thick, “tail” of the distribution, in contrast to the shorter tails of distributions such as the normal, where data points cluster close to the mean (and almost always within a few standard deviations of it). One of the first described heavy-tailed distributions was the Pareto principle whereby 80% of the wealth is held by 20% of the population (and of that wealth, 80% is held by only 20% of the 20%, and so on) [
16]. This observation is mathematically related to the inverse power law. The result of such a distribution is that the range of wealth from poorest to richest is much greater than would occur if individuals were normally distributed around a mean. While plots of the normal distribution produce the familiar bell curve, conventional plots of heavy-tailed distributions are difficult to interpret because of the much larger range of values. A simple solution to this is to plot cumulative distributions with logarithmic axes. Using this format an inverse power law will describe a straight line (from top left to bottom right). Heavy-tailed distributions are typically seen in theoretical complex systems and have been held to be a typical feature, or fingerprint, of complex systems [
11].
While there are many possible explanations for the occurrence of heavy-tailed distributions [
36], and their presence alone is not proof of the presence of a complex system, the more recent description of correlated bursts of activity within a complex system leading to heavy-tailed overall distributions [
12] means that identifying both in the same data strengthens the evidence for the presence of a complex system. Correlated bursts of activity represent clusters of activity in time, with the distribution of burst lengths also following a heavy-tailed distribution [
12]. This distribution of bursts means that long bursts arise more often than would occur by chance, and furthermore that bursts undergo a kindling process, whereby the longer a burst has gone on, the more likely it is to continue.
Study 1: analysis of total contacts per patient
We conducted this analysis using the total number of contacts per patient in 1 year of data from each dataset. We plotted the complementary cumulative distribution function (CDF), defined as the proportion of patients whose total number of contacts was equal to or greater than each number of contacts between 1 and the largest recorded. This is preferable to plotting the probability distribution function, as the CDF is more robust against fluctuations in the tail of the distribution due to finite sample sizes [
11]. Plots of the CDF were made with logarithmic axes, on which a power law distribution displays a straight line. The slope of this line is equal to one minus the scaling parameter of the power law distribution (for example, a scaling parameter of 3 produces a slope of − 2). We fitted inverse power law and log-normal functions to each dataset using maximum likelihood fitting with the poweRlaw package in R 3.3.2. We examined the closeness of fit of the data to a power law distribution, using the Kolmogorov-Smirnoff (KS) test. Where data was deemed different from a power law distribution (
p value < 0.05) we examined whether the data was closer in fit to a power law or log-normal distribution using the Vuong test for non-nested distributions [
37] at a significance level of 0.01. As naturally occurring distributions often include a power law only above a certain threshold [
11], we repeated this analysis with a range of minimum values for the number of contacts per patient.
Subgroup and sensitivity analysis
We conducted a subgroup analysis of the PCOOH data with data split by sex and by age using the median value. For each subgroup we repeated the plotting and model-fitting procedure described above, with the addition of 95% confidence intervals (CIs) derived from a non-parametric bootstrapping procedure (1000 iterations). We did not conduct a subgroup analysis of the ED data because of the smaller number of patients.
We conducted two post hoc sensitivity analyses to test for artefacts arising from the fact that each dataset contained a calendar year but that patients might have their first consultation at any point during the year and thus have different durations of follow-up. In the first sensitivity analysis we limited data to patients consulting within the first half of the year and censored each patient’s data 6 months after their first contact. In the second sensitivity analysis we considered that some patients consulting in the first few weeks of the year would be doing so within a burst of contacts. We thus split the PCOOH data into patients whose first contact was before the 15th day of the time period and those whose first contact was on or after the 15th day. In each of the sensitivity analyses we used the same method for plotting and analysing distributions as described for the whole dataset.
Study 2: analysis of bursts of contacts
We examined bursts of contacts using the method developed by Karsai [
12]. We defined a burst as a sequence of contacts in which the interval between each pair of consecutive contacts is less than a specified time window
∆t. We used a range of values for
∆t of 4 and 7 days for the PCOOH data and 4, 7 and 10 days for the ED data. For each burst we counted the number of contacts within the burst. We pooled the burst patterns across all individuals and limited the analysis to patients with between 4 and 52 contacts in order to exclude data with too few contacts to display bursts, or so many contacts that bursts were inevitable because the PCOOH data comprised only 1 year. We conducted the burst analysis on the PCOOH dataset (1 year) and on the whole ED dataset (2 years).
For each dataset and value of ∆t we plotted the CDF. As for the distribution of total contacts, we plotted the CDFs using logarithmic axes, so that an inverse power law would display as a straight line. In order to assess whether the burst patterns could have arisen by chance, we conducted a bootstrapping procedure in which we compared the actual data with a set of surrogate datasets in which the temporal structure of bursts was broken by randomly allocating the number of contacts for each patient to dates within the time between their first contact and the end of the study period. These surrogate datasets were thus identical to the original dataset except that the bursts they contained arose at random. We conducted this bootstrapping procedure with 250 iterations, meaning that the probability of any observed distribution lying wholly above the bootstrapped range by chance was less than 0.008.
Study 3: review of data from published reports
We systematically identified papers reporting numbers of patients attending EDs, using a structured search of the MEDLINE and Embase databases (Table
2 lists the search terms). Titles, abstracts and full manuscripts were screened by two authors independently to identify usable data. We followed references from, and citations of, eligible papers to identify additional studies.
Emergency department |
1) Emergency Service, Hospital/ |
2) ((emergency or casualty) adj1 department).mp. |
3) (accident adj2 emergency).mp. |
4) 1 or 2 or 3 |
5) (frequen$ adj2 attend$).mp. |
6) “high use$”.mp. |
7) (hig$ adj (utiliz$ or utilis$)).mp. |
8) “frequent flier”.mp. |
9) (frequen$ adj3 use$).mp. |
10) 5 or 6 or 7 or 8 or 9 |
11) 4 and 10 |
Primary care out-of-hours service |
1) General Practice/ |
2) Primary Health Care/ |
3) “General Practi$”.mp. |
4) “GP”.mp. |
5) “primary care”.mp. |
6) 1 or 2 or 3 or 4 or 5 |
7) (out adj2 hours).mp. |
8) “out-of-hours”.mp. |
9) “unscheduled”.mp. |
10) 7 or 8 or 9 |
11) (frequen$ adj2 attend$).mp. |
12) “high use$”.mp. |
13) (hig$ adj (utiliz$ or utilis$)).mp. |
14) “frequent flier”.mp. |
15) (frequen$ adj3 use$).mp. |
16) 11 or 12 or 13 or 14 or 15 |
17) 6 and 10 and 16 |
Inclusion and exclusion criteria
We included studies which reported urgent care attendance data either in EDs or PCOOH services. We required reports to include all of the following: setting (time and place), an unselected population (e.g. “all attenders” or “all adults”, but not “adults with asthma”) and a continuous or categorical (binned) distribution of individual patient attendances over 1 year which included all attenders. We excluded studies which reported less than four categories or where the lower threshold of the highest category was less than 10 episodes of care, in order to ensure a spread of data points and include at least one order of magnitude for the number of episodes of care. Where a study reported more than 1 year or more than one site for care separately, we used the most recent year or the largest site. Where studies reported several sites together, we did not attempt to separate them. Studies varied in the categories they used to report attendance (individual numbers of attendances, ranges of attendances or a mixture of the two). In most cases we kept data in the original format; where studies reported many categories, each with small numbers (< 10) of individuals, we aggregated them into category ranges containing 10 or more individuals. We did not restrict studies on the basis of healthcare system or level of economic development.
Quality assessment of included studies
All studies were observational studies describing similar retrospective data collection of a complete sample. Provided studies met our stringent inclusion and exclusion criteria we did not apply further quality assessments, as the topics for evaluation in common tools (e.g. completeness of sample, sources of bias, etc.) are designed for studies which make inferences based on samples from populations, whereas the studies we included reported on counts of attendance for entire services.
Distributions of attendance per patient in review data
For each study we plotted the complementary CDF: the proportion of patients whose total number of attendances was equal to or greater than the lower boundary of each category. Plots used logarithmic axes to facilitate the display of heavy-tailed data. We plotted data for ED and PCOOH studies separately. In addition, we selected a subset of studies which contained at least 8 data bins, with the highest data bin threshold set ≥ 20. As most studies provided heavily aggregated data with wide categories, we did not attempt to fit distributions to this data.
Discussion
This data provides original and robust evidence that patients using urgent care do so in patterns typical of individuals within a complex system. This evidence is present in both the distribution of bursts of contacts by individuals and in the overall distribution of contacts per individual. Finding both features together is important, as bursts of contact are a plausible generative mechanism for the overall distribution [
12]. Frequent attenders occurred with a frequency which was in keeping with the hypothesised statistical distributions.
Strengths and limitations
This study used large, recent and complete datasets from two different urgent care settings in different healthcare systems. The analysis used established techniques for burst estimation [
12] and model fitting [
11]. We also adjusted for different lengths of follow-up by censoring data and found it had no influence on the findings. Examining the combination of both burst analysis and overall distribution analysis is important, as bursts have been identified as a generative mechanism for power laws in other systems. Furthermore, bursts have been identified in other healthcare research, such as the tendency of exacerbations of chronic obstructive pulmonary disease to cluster in time [
52].
While the ED data showed a close fit to a power law across the whole range of contact numbers, there was some evidence that the PCOOH data contained more very frequent attenders (above 30 contacts) than expected from the best fitting model. This may indicate some excessive or inappropriate use, but the absolute number of patients was small. When we restricted the analysis to patients who did not use the service in the first 2 weeks of the year (and so who were not currently in a burst of consultations), the observed data showed a closer fit to an inverse power law.
The inclusion of the systematic identification of secondary data adds strength to our findings of overall distributions, as heavy-tailed distributions of use, similar to those seen in our primary data, were observed across very different healthcare settings, with generally similar parameters for the proportion of frequent consultation. We were not able to conduct statistical analysis on these secondary sources of data, as they did not have sufficient detail.
Relationship to other research
While complex systems have been hypothesised as a way of describing healthcare services [
3‐
5,
7,
13], this is the first large-scale empirical examination of whether urgent healthcare displays the typical statistical properties of a complex system. No previous studies have reported the population distribution of urgent care attendance in detail; however, non-normal distributions of use have been previously noted but not analysed in the ways we have used in this study [
33,
34].
To be plausible, our finding of the typical statistical properties of a complex system must be compatible with real-life mechanisms, which in modelling of social systems can be considered as rules [
5,
53]. Qualitative studies have already suggested candidate rules: patients simultaneously seek to balance being a prudent user of services [
29] with being “better safe than sorry” [
30], and this balance is influenced by societal processes and norms [
31,
32]. In turn, these rules may be mediated through processes such as candidacy (seeing oneself as an appropriate user of services) and recursivity (a tendency to repeat patterns of help-seeking which have been successful) [
28]. Together, these processes — which are socially mediated — can be seen as comprising system-wide mechanisms which drive, and restrain, urgent care use by individuals.
Frequent attendance is commonly regarded as abnormal and taken to be a sign of an inefficient system, however many frequent attenders appear to use healthcare appropriately [
17], suggesting the system may in fact be operating efficiently. Recent work in information theory suggests that power law distributions may represent an optimal configuration for a system to meet very variable demands [
54]: in the case of urgent care, systems must deal with many patients with minor problems while retaining the capacity to handle a few with intensive ones. Heavy-tailed distributions of attendance may be a feature of well-optimised urgent care rather than a sign that something is wrong.
Implications for policy, practice and research
Our findings of striking similarity between data from urgent care use and statistical features of typical complex systems support the argument that services need to engage more with a complex systems approach [
3]. This means there should be a greater focus on contextual matters across the whole system and a recognition that the mechanisms driving processes such as demand both arise from, and influence, many individual interactions. In turn, this means there is a need for interventions to influence these mechanisms, which are social, both through information channels and media, and through creating and sharing positive patient experiences. A second general consequence of considering healthcare systems as complex is that interventions to change services must recognise that complex systems respond unpredictably to interventions to change them [
3,
5,
15], and that what works in one setting will not necessarily work in another. This dependence on context is still under-acknowledged in the development of “complex interventions” [
3], which should be viewed as “interventions in complex systems” [
55].
In practice, the implication of our findings for frontline care is that there must be a partial shift in thinking from individual frequently attending patients to the workings of the whole system. While each frequently attending individual is unique, the consistent and mathematically predictable frequency with which they occur is highly suggestive of overall system effects. In theoretical models of complex systems, this dependence on system effects means that even if extreme outliers (such as individual frequent attenders) are removed (representing action on individuals), new ones will arise to fill their place [
56]. This phenomenon can be seen in waiting lists — whereby initiatives to shorten them (by bringing forward treatment of individuals) generally lead to them rapidly re-growing through system effects [
57,
58]. Services thus need to provide care which is simultaneously person-centred and system-aware.
For research, our identification of bursts represents a potential target for interventions to identify and respond to individuals with high need. Interventions should be developed to prevent, or shorten, bursts. These interventions must be safe, while addressing the mechanisms by which patients rationalise decisions to consult, such as candidacy and recursivity [
28]. This may involve forms of explanation or sign-posting which make patients more likely to use alternative management the next time a situation occurs rather than more likely to re-attend the urgent care service, as currently happens. A focus on recognising bursts at an early stage may also permit identification of individuals at high risk of frequent attendance. In our ED data, among people who attended at least four times in a year, a burst of 3 consultations each separated by no more than 7 days represented only 1% of bursts. In the PCOOH setting, bursts of 4 consultations each separated by no more than 7 days accounted for 1% of bursts. These may represent useful “early warnings” of emerging problems, and these and other potential signals of ongoing high use should be tested in further analyses.