Family Practice Advance Access originally published online on April 6, 2005
Family Practice 2005 22(3):347-352; doi:10.1093/fampra/cmi023
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General practice as a complex system: a novel analysis of consultation data
a Department of General Practice, Wellington School of Medicine, University of Otago, PO Box 7343, Wellington, New Zealand, b Health Informatics Centre, University of Dundee, Dundee DD2 4AD and c Community Health Sciences—General Practice, University of Edinburgh, 20 West Richmond Street, Edinburgh EH8 9DX, UK
Correspondence to Tom Love, Health Informatics Centre, University of Dundee, Dundee DD2 4AD, UK; Email: t.love{at}chs.dundee.ac.uk
Received 28 October 2004; Accepted 30 December 2004.
Love T and Burton C. General practice as a complex system: a novel analysis of consultation data. Family Practice 2005; 22: 347–352.
 |
Abstract |
|---|
 Top Abstract IntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
Background. Complex systems have specific properties of robustness and self organisation which arise from interacting components within the overall system and which govern the system's behaviour. These are typically associated with a power law distribution of event sizes. Commentators have suggested that health systems are complex, but there has been limited quantitative investigation of this issue.
Objectives. To test the hypothesis that consultation patterns in primary care follow a power law distribution typical of a complex system.
Methods. Analysis of 142 050 episodes of non-pathological back pain in routinely collected New Zealand national data. Calculation of the distribution of the duration and number of GP consultations for each illness episode. Secondary analysis of a published UK dataset of consultation rates for 44 000 patients in four general practices.
Results. Number of consultations per episode of back pain demonstrated excellent fit with a power law in the full dataset (r2 = 0.96) and all but one subgroups (r2 = 0.90–0.99). The number of consultations per patient from four UK practices was suggestive of a power law distribution (r2 = 0.88–0.93).
Conclusions. Consultation patterns in general practice show measurable properties of a complex system. The consistency of the distribution across different population groups suggests that attempts to manage consultation patterns should focus on the whole system of patients, rather than upon individuals or subgroups of the patient population.
Keywords. Behavioural sciences, complex systems, consultations, health service management, primary health care.
|
Introduction |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
Complexity and primary care
Complexity science is the generic title for the study of systems whose properties and behaviours arise primarily from the interactions between their individual elements rather than the elements themselves. Complex systems have been observed in a very wide range of settings, from animal biology and ecology, to forest fires traffic jams and the spread of infectious disease.1
Because the behaviour of the system as a whole results from the interacting individuals within it, patterns across the system can appear unpredictable. For instance power supply networks (which depend on redistribution of load between interconnected substations) usually adapt well to minor failures in the grid but occasionally a small incident can set off a cascade which overwhelms the system and causes huge areas to lose power. Retrospective analysis of large events typically fails to show any recurring characteristic of their location or timing. Nonetheless at the level of the system, typical statistical properties can be detected.2
Enthusiasm for these ideas from systems theory has led to suggestions that the properties of complex systems might apply to primary care.3 It seems plausible that the large scale patterns seen across primary care as a whole, such as consulting or prescribing distributions, might reflect a complex system. Moreover, the health system is notorious for responding unpredictably to interventions for change. Hospital waiting lists appear to behave as such a complex system.4
Patients are known to consult their GP at widely differing rates, only partly explained by differences between individuals in illness, concern about symptoms, and socio-economic factors.5–7 The healthcare system itself influences consultation through accessibility, feedback and cost, while patients' behaviour is influenced by past consultation patterns7,8 and their sense of what is appropriate and fair.9 The multiple interactions and feedback between individual patients and practitioners, and the healthcare and social systems they comprise, meets the requirements for a theoretical complex system.
Statistical characteristics of complex systems
Analysis of complex systems has identified a characteristic statistical property of complex systems, namely the power law distribution,1,10 which relates the magnitude of some value to the frequency of its occurrence within the system. For instance in the case of power networks, the frequency distribution of failures by number of consumers affected shows a characteristic distribution with the great majority of events being very small, but a consistent relationship between frequency and magnitude.
In a power law distribution, the probability p of an event (in this case an episode of illness requiring a particular number of healthcare consultations n) is inversely related to its magnitude n raised to a constant power a, represented as p 
1/na. When plotted on a logarithmic scale, power law distributions form a characteristic straight line with the slope corresponding to the exponent a from the above equation. In addition to suggesting the presence of a complex system, two other features make power law distributions notable in the context of healthcare. Firstly the shape of the distribution is consistent across the entire dataset, suggesting that a common mechanism underlies the effect under study across the range of the data. Secondly, extremely large events (in the case of our hypothesis very high numbers of consultations), while still rare, occur much more frequently in a power law distribution than is the case with an exponential or normal distribution.
We hypothesised that if primary health care constitutes a complex system it should be possible to observe a power law in the distribution of consultation activity. We analysed two datasets: a primary analysis of national data comprising a consecutive series of all patient consultation episodes for back pain beginning in one year, to examine the distributions of duration and number of GP consultations per episode, and a secondary analysis of published consultation rates for patients of four UK general practices.11
We expected that the duration of episodes of illness would be largely determined by factors operating at the level of the individual (such as illness severity and personal obstacles to recovery) but that the number of consultations would be heavily influenced by the system comprising patients, healthcare providers and their respective cultures and social networks and so would show a power law.
|
Methods |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
Primary data analysis, New Zealand national back pain data
The Accident Compensation Corporation (ACC) is the statutory funder of accident related health services for the whole of New Zealand. Unlike commercial insurance systems, ACC fund all accident related treatment on a no-fault basis, and without regard to whether lump sum compensation is paid to the injured party. The organisation therefore collects payment data for every item of accident related care in the country, regardless of age, sex or workforce status and includes even minor accidental injuries and strains.
We analysed all episodes of back pain in the New Zealand national accident insurance database which were initiated during 1998. The data included a measure of the number of GP consultations funded under each episode of care and whether the patient had been referred for radiology, physiotherapy or a specialist opinion. Data was stored in Microsoft Access and Excel. Analysis was carried out with these and with custom scripts written in the Python computing language.
For each episode of back pain we estimated the duration, as the time between the first consultation and closure of the claim, and the number of consultations. We then derived frequency distributions for both duration and number of consultations per episode. Data were binned in increasingly spaced groups derived from rounding to the nearest integer of the series (
2)1, (2)2 ... (2)n then converted to logarithms. The resulting data series was plotted and the slope of the regression line and its correlation coefficient r2 were calculated. The results were tested for sensitivity to different binning schemes. A similar process was carried out for episode duration (measured in weeks and including uncompleted weeks).
The analysis was carried out on the full dataset and by subgroups of patient age and sex. We also used two proxies for episode severity to test their influence on the consultation distribution: whether the episode was managed entirely within primary care or referred and whether the episode resulted in paid time off work.
Secondary analysis of four practice consultation data
To test whether our observations could be replicated in another dataset we took the published data of Neal and colleagues describing consultation rates for four UK general practices.11 This dataset referred to all consultations of 44 146 patients in four practices over a period of 41 months, and was originally a study of the distribution of attendance frequency in UK general practice. We binned the published frequency data into 10 groups by the number of consultations per patient and plots of log(consultations per patient) versus log(number of patients) made for each practice and for the pooled data.
|
Results |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
New Zealand national back pain data
The dataset contained 148 514 entries. 6564 (4.4%) had insufficient data to calculate duration of claim and number of consultations so were discarded leaving 142 050 episodes of back pain for which at least one GP consultation had been made. 787 episodes of care were still active at the time of data collection in July 2001 but are included in the analysis. The effect of these episodes of care is to make some data points underestimate the number of consultations per claim. These represent 0.55% of the total dataset. Analysis with the 787 episodes excluded made a negligible difference to the results.
Of the 142 050 episodes of back pain, 92 617 (65.2%) involved only a single consultation; 25 084 (17.7%) involved two; 17 533 (12.3%) episodes had three to five consultations; 4717 (3.3%) had six to ten; 1698 (1.2%) had 11 to 20; and 401 (0.3%) had more than 20. Two episodes were for over 90 consultations with the GP. 79 274 (55.7%) episodes were referred outwith the GP surgery: 68 967 to physiotherapy; 22 268 to radiology; 6832 to a hospital specialist and 1492 seen by the GP emergency service).
The consultation count data showed a linear relationship between log(consultations per episode) and log(count of episodes) with slope –2.15 (r2 = 0.96, P < 0.001) characteristic of a power law relationship. In contrast the episode duration data yielded a skewed gaussian curve which did not fit a power law distribution. Figure 1 shows the distributions of consultation count and duration in both natural (a) and log (b) format. Figure 2 shows that the power law relationship was clearly demonstrated in all subgroups apart from patients who were unable to work. Table 1 contains the results of the subgroup analysis.
|
|
|
Episode duration and consultation count were loosely correlated (r2 = 0.24). When episodes with outlying consultation frequencies were excluded (less than one consultation per 120 days) this correlation became stronger (r2 = 0.55).
UK practice data
Figure 3 shows the individual distributions for the four individual practices and for the pooled data. The correlation coefficient r2 for the pooled data was 0.91, with individual practices ranged between 0.88 and 0.93.
|
|
Discussion |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
Summary of key findings
The data for consultations per episode of back pain showed an excellent fit with the hypothesised power law distribution; in contrast, the distribution of episode duration did not fit the power law. The UK data for consultations per patient fitted less well, but still approximated to a power law distribution. These results are in keeping with our hypothesis that consultation patterns of individuals generate properties at the level of the healthcare system, as predicted from the theory of complex systems1,12 while the duration of each back pain episode was not a function of complex interactions.
Strengths and limitations of the study
The study addresses the knowledge gap between the theory of complex systems and its increasing application in healthcare management. As one property of complex systems is that they can only be fully understood as a whole, the study design runs the risk of artefact due to measuring only one aspect. We addressed that in three ways, by using large and complete samples, by including a measure we predicted would not have a power law distribution (back pain duration), and by corroborating our primary analysis with a secondary analysis of a published dataset.
The unusual nature of the New Zealand ACC, in which GPs are funded on a fee per consultation basis, means that the organisation's data on GP consultations can be easily linked to a specific episode of accident related care covered by the scheme. In the case of musculo-skeletal problems such as back pain, ACC funding covers the medical costs of any episode where there is an acute onset due to an external cause (for instance acute lumbar pain brought on by lifting one's own furniture would be eligible) and in effect represents all non-pathological back pain.
We considered a number of sources of error in the back pain dataset by excluding incomplete data and testing for the effect of outlying data. We identified 11 989 (8.4%) episodes which averaged less than one GP consultation for every four months of the episode. Of these 7211 had been referred to specialists or physiotherapists and were assumed to be receiving continuing treatment under their care; the remaining 4778 (3.3%) probably represented late completion of claims; these data were retained in the analysis for completeness but recalculation of distributions after their exclusion did not significantly alter the results. 102 (0.07%) episodes involving consultation more often than once every three days were identified, exclusion of these did not significantly change the results.
Both authors analysed the data independently using different methods and software. To reduce bias due to categorisation, we tested a variety of scales for data binning, to find a series which gave sufficient integers of increasing separation within the range of values. Although the r2 and slope of the power law distribution varied slightly according to choice of categorisation (by less than 5% and 10% of presented values respectively) the overall pattern was unchanged.
The New Zealand data is collected within the context of a rather unusual primary care funding system which could limit the generalisability of the findings, although we have tried to address this by using UK data to compare the results. It is possible that, in our primary dataset, some of the episodes of back pain represented injuries which included additional factors such as legal compensation to prolong the case. The unique no-fault scheme by which ACC insurance operates minimises this effect. Payment to patients of earnings related compensation when back pain prevented them working could provide an incentive to keep returning to the GP, thereby distorting the consultation patterns observed under this unusual funding scheme. However such earnings related compensation was paid in only 4.8% of the episodes of care in our dataset, so any distorting effects are likely to be small.
While the data on back pain was for episodes of a single condition, that from Neal and colleagues included consultations for any reason, including planned follow up of chronic conditions, health promotion, antenatal care and, in some practices nurse and health visitor contacts. Although we assumed the back pain consultations to be primarily patient-led, it is likely that the managed care aspects of general practice, with planned recall for both illness management and health promotion, will have constrained the natural consultation pattern in the UK practice data. We suggest that this explains why the our second data set fits less well to a power law distribution.
Interpretation in the context of existing evidence
There have only been two published demonstrations of the power law distribution in healthcare, both relating to outpatient waiting lists. Nevertheless, power laws have been observed in a wide range of other natural and social settings and can be generated by simulations of complex systems. We suggest that the demonstration of the power law in two separate sets of consultation data provides new evidence to support the notion of primary care as a complex system.
Our analyses add further weight to the argument, supported by the original authors of the UK practice data, that so called ‘frequent attenders’ are not a discrete group of healthcare users.11 The consistency of the power law distribution across a wide range of consultation behaviour suggests common processes underlying the decision to consult among both high and low consulters. This finding implies that interventions which are intended to manage the distribution of consulting resource across the distribution of patients are a priori more likely to be effective if planned across the whole system of consulting patients, rather than targeted at isolated patient groups.
Implications for research and practice
This study provides the first evidence that, particularly for symptom driven consultations, family practice behaves as a complex adaptive system. This has implications for attempts to understand and shape healthcare. Currently models of consultation rate are based on distributions of predictor variables among independent individuals in a population. Our data suggest that while illness episode duration is distributed at an individual level, use of healthcare is not. Instead, the complex system, comprising patients and their primary healthcare providers, itself strongly influences its own consultation rates.
Such self-organising behaviour is characterised, in experimental models, by an unpredictability in response to stimuli for change. These systems usually respond to change by reconfiguring close to the original state, but occasionally transform: the size of the change often bearing no clear relationship to its trigger. In practical terms, effort to change one part of a system, for instance attempting to address only high users of healthcare, is unlikely to effect long term change as the system will tend to adjust to restore the original distribution. This form of stability has been observed in a number of complex systems including forest fires and traffic flows.1
More generally, the finding that general practice consultations are a complex system, has broader implications for health services management, particularly in light of the previous observation of power laws in secondary care waiting lists.4 At a time when access to primary care in the UK is undergoing major changes and when reductive performance measures are an increasingly common feature of primary care management structures, this study suggests that caution should be exercised in introducing measures which do not recognise the complex nature of primary care, and of health systems more generally.
Conclusion
This is the first study to demonstrate a power law distribution in GP consultation data which is independent of patient characteristics. If consultation patterns in general practice are emergent properties of a self-regulating complex system, then future models for understanding primary healthcare systems need to be capable of explaining this behaviour.
|
Declaration |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
Funding: CB and TL are supported by the Chief Scientist's Office of the Scottish Executive Health Department.
Ethical approval: the analysis of anonymised patient back pain data was approved by the Wellington Regional Ethics Committee.
Conflicts of interest: none.
|
Acknowledgments |
|---|
The data were provided by the New Zealand Accident Compensation Corporation. We wish to thank Professors Sally Wyke, Tony Dowell and Aziz Sheikh for their constructive comments on earlier drafts of this paper.
|
References |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionDeclarationReferences |
|---|
1 Bak P. How Nature Works. New York: Oxford University Press; 1998.
2 Watts D. Small worlds: The dynamics of networks between order and randomness. Princeton: Princeton University Press; 1999.
3 Plsek PE, Greenhalgh T. Complexity science: The challenge of complexity in health care. Br Med J 2001; 323: 625–628.
4 Smethurst D, Williams H. Are hospital waiting lists self-regulating? Nature 2001; 410: 652–653.[CrossRef][Medline]
5 Campbell SM, Roland MO. Why do people consult the doctor? Fam Pract 1996; 13: 75–83.
6 Carr-Hill RA, Rice N, Roland M. Socioeconomic determinants of rates of consultation in general practice based on fourth national morbidity survey of general practices. Br Med J 1996; 312: 1008–1012.
7 Jordan K, Ong BN, Croft P. Previous consultation and self reported health status as predictors of future demand for primary care. Journal of Epidemiology & Community Health 2003; 57: 109–113.
8 Neal RD, Heywood PL, Morley S. ‘I always seem to be there’—a qualitative study of frequent attenders. Br J Gen Pract 2000; 50: 716–723.[Web of Science][Medline]
9 Pollock K, Grime J. Patients' perceptions of entitlement to time in general practice consultations for depression: qualitative study. Br Med J 2002; 325: 687.
10 Carlson J, Doyle J. Highly optimized tolerance: A mechanism for power laws in designed systems. Phys Rev E 1999; 60: 1412–1427.[CrossRef]
11 Neal RD, Heywood PL, Morley S, Clayden AD, Dowell AC. Frequency of patients' consulting in general practice and workload generated by frequent attenders: comparisons between practices. Br J Gen Pract 1998; 48: 895–898.[Web of Science][Medline]
12 Turcotte D, JB R. Self-organised complexity in the physical, biological and social sciences. Proceedings of the National Academy of sciences 2002; 99: 2463.
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  D. Rickles, P. Hawe, and A. Shiell A simple guide to chaos and complexity J Epidemiol Community Health, November 1, 2007; 61(11): 933 - 937. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 D. Kernick Wanted--new methodologies for health service research. Is complexity theory the answer? Fam. Pract., June 1, 2006; 23(3): 385 - 390. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||