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There is evidence that hospital waiting lists in the UK are resistant to shortening because reductions in length generate increases in referrals. We explored this concept by examining outpatient data for eight specialties in a large hospital centre over 17 months. Correlation coefficients were calculated by regressing waiting list density (numbers waiting more than 26 weeks) against referral rate.
In three of the eight specialties, with the longest waiting lists, referral rates were significantly related, after one month's delay, to waiting list density (P < 0.01)—dermatology, R=0.68; ear-nose-throat R=0.78; trauma/orthopaedics (R=0.64). These were the three with the longest lists.
These results help to explain why initiatives to shorten waiting lists are commonly ineffective in the long term.
Waiting lists in the UK National Health Service (NHS) are politically sensitive. Though huge resources have been devoted to their reduction, the results have often been disappointing1,2,3,4. This troublesome behaviour has been explained in terms of a complex system where any change tends to be met by countervailing forces1,5,6. An analogy is drawn with ecosystems in which a decline in population increases the food supply and thus promotes survival. There has been much theorizing about complex self-organizing systems, one of the models being chaos theory, but supporting data are scarce2,3,7,8. Our hypothesis is essentially simple—that long waiting lists deter referrals. We have explored the patterns within the referral systems of our hospital and tested the hypothesis that referral rates depend upon waiting list densities.
At Queen's Medical Centre University Hospital NHS Trust, two monthly sources of information refer to waiting lists: an internal publication offers a breakdown of waiting times according to both specialty and consultant; and a synopsis of this, the Waiting Times Report, goes out at about the same time to general practitioners. Referral rates and waiting list sizes from April 1999 to September 2000 were investigated across the Nottingham region for ear-nose-throat (ENT) surgery, dermatology, trauma and orthopaedics (elective)/general surgery, general medicine, cardiology, rheumatology, immunology and histopathology. We examined the degree of covariance between waiting list density (number waiting more than 26 weeks) and referral rate. In determining probabilities we assumed normal distributions. This is not strictly correct when the underlying drivers are unknown. However, we draw upon the ‘chaos paradox’ to justify this methodology. In a complex system with multiple inputs this approach is deemed acceptable for broad analysis9. Waiting list densities were correlated with later referral rates to look for temporal effect. This approach was based on correspondence with local general practitioners, who told us how they responded to waiting list figures; information on this matter has subsequently been published10.
Our primary interest was the specialty of dermatology. Figure 1a shows the monthly rate of referrals to the dermatology department plotted against the density of the waiting population. Density dependence is apparent (Pearson correlation coefficient, R=0.61, P < 0.01). When a delay of one month was inserted (Figure 1b), density dependence became stronger (R=0.68, P < 0.01); and examination of a range of intervals indicated that density dependence was greatest when the lag was one to two months. (Figure 2). Figure 3 shows results for the eight specialties when correlations were determined with a one-month lag. The strongest correlations were seen for the specialties with the longest waiting lists—ENT, dermatology and elective trauma/orthopaedics (all significant at P < 0.01)—and the weakest for immunology and histopathology.
We find that outpatient referral rates decreased as waiting list densities increased and vice versa. It is likely, therefore, that referral rates are density dependent. The correlations are strongest when a delayed response is allowed for, as one would expect in any human system; and the fact that they are evident in several specialties supports our interpretation of a self-regulating system. Specialties with long waiting lists (exemplified by dermatology) show the strongest feedback sensitivity; in those with short lists self-regulation may be completely absent—in other words, the feedback mechanism may turn out to be non-linear. General practitioners receiving the data on waiting lists seem to alter their referral patterns the following month. The observation of some residual correlation between waiting lists and referral rates for several months either side of the published waiting lists suggests that referrals are based upon the overall perception or running average of waiting times and not merely upon an instantaneous measure for one month. At the time general practitioners are contemplating a referral, the Waiting Times Report gives them the previous month's figures, so the time lag of one month reflected by our data suggests that maximum responsiveness to waiting list density occurs around the time of publication.
Could there be some other explanation? One alternative hypothesis is that waiting lists control hospital managers' spending. Thus a short waiting list might invite a change of priorities such that low-referral months are rewarded with fewer resources. If this happened within a monthly time-frame it could account for the negative feedback effect we have observed; but, in our experience, budgetary changes happen much more slowly than this.
Waiting list data are often obstructively ‘noisy’ or ‘scattered’. Pearson's correlation is only a statistical method and can give false positives and negatives. However, our approach is notable for being based on a simple theory—the longer the likely wait, the less likely a general practitioner is to refer. It may be too simple, but tentative evidence for it already exists6. A correlation was not found in all specialties, so it may not be a general phenomenon. We have not allowed for multiple possible influences such as the role of private consultations and referrals from general practitioner to general practitioner. Feedback is very likely to occur at more than one node: for example, our hospital arranges for consultants with the shorter lists to see more patients who have been referred to the department (‘Dear Doctor’) rather than to an individual. In complex systems of this kind, phenomena tend to be highly interdependent and linear relationships are not to be expected.
Our observations provide weight to what might be considered a self-evident relationship. However, the fact that referral rates go up as waiting list statistics come down has important implications. Waiting lists are a major concern and initiatives such as Saturday clinics, specialist nurses and teledermatology receive much attention11,12,13. We suggest that, if these are successful, subsequent months may well see them neutralized. This paper explores only one of the many suggested mechanisms that together generate inertia in waiting list reduction. For example, the demand for medical services is also fuelled by new drugs, medical interventions and diagnostic methods. Such need-generators are more likely to arise in health services that are well funded and not overburdened. If the NHS became a well funded system with low waiting lists and high patient satisfaction, the rise in demand could be massive.
We thank Professor Tony Avery (Department of General Practice Nottingham University), Mr Nicholas Evans (Department of Health) and Dr Jake Burdsall (Department of Gastroenterology Nottingham University) for helpful comments.