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- Appendix A: Adapting the efficiency formula to incorporate costs
While numerous reports have sought ways of improving the efficiency of surgical operating lists, none has defined ‘efficiency’. We describe a formula that defines efficiency as incorporating three elements: maximising utilisation, minimising over-running and minimising cancellations on a list. We applied this formula to hypothetical (but realistic) scenarios, and our formula yielded plausible descriptions of these. We also applied the formula to 16 consecutive elective surgical lists from three gynaecology teams (two at a university hospital and one at a non-university hospital). Again, the formula gave useful insights into problems faced by the teams in improving their performance, and it also guided possible solutions. The formula confirmed that a team that schedules cases according to the predicted durations of the operations listed (i.e. the non-university hospital team) suffered fewer cancellations (median 5% vs 8% and 13%) and fewer list over-runs (6% vs 38% and 50%), and performed considerably more efficiently (90% vs 79% and 72%; p = 0.038) than teams that did not do so (i.e. those from the university hospital). We suggest that surgical list performance is more completely described by our formula for efficiency than it is by other conventional measures such as list utilisation or cancellation rate alone.
As healthcare providers strive for better value-for-money from their investments [1, 2], hospital operating theatres have been identified as potential areas for cost reduction, especially as it has been estimated that ∼ 46% of patients discharged from hospital have undergone surgery . Poor scheduling of operations can result in cancellation of procedures [3, 4]. This is costly both to the patient and to the hospital. Two common causes of cancellation are under-optimisation of the patient's medical condition (which can be effectively addressed by good pre-assessment)  and over-running of a surgical list .
Not surprisingly, a number of authoritative reports (e.g. from the Association of Anaesthetists of Great Britain and Ireland, AAGBI , and the Audit Commission [7–9]) have examined how best to manage operating lists. The recommendations made are broadly similar and include measures such as: effective administrative systems, accurate records for analysis and audit, optimally managing staff time, and good pre-assessment of patients to optimise medical conditions. This list is not exhaustive.
Collectively, these recommendations seem very reasonable but one problem remains: none of these reports offers an explicit definition of ‘efficiency’. In the absence of a clear definition, it may not be known, in quantitative terms, that implementing the recommendations has achieved the desired effect. One reason for the deficiency may be that there are potentially many elements contributing to ‘efficiency’. These include: cancellation rate, under-utilisation, over-running, complication rates, low costs, and perhaps some less tangible measures such as patient satisfaction or teamwork and communication .
Any chosen measure of efficiency should ideally have the following attributes: it should be widely applicable and be relatively simple to calculate. The professionals who work in theatre should be able to influence the measure directly through their activity. Thus, crude ‘profitability’ as an index of efficiency may have limited value if it is determined only by re-imbursement rates set elsewhere and not by the activity of the surgical team . In its extensive report , the Audit Commission chose to focus heavily on utilisation of the list as a prime measure (i.e. the proportion of scheduled list time used for anaesthesia and surgery). Unfortunately, it is possible to achieve quite impressive rates of utilisation of > 100% simply by over-running lists. Far from being an accomplishment, over-running is a common – if not the main – cause of cancellations on the day of surgery, which is inefficient . Cancellation rate itself therefore might be thought a useful measure, but excellent figures can be achieved by under-utilisation, which again is not efficient .
In the US, analysis of operating list management has historically been more established and sophisticated than it has in the UK, perhaps because of the more direct financial incentives involved [13–15]. Recently, Dexter and colleagues were invited by a leading anaesthetic journal to summarise their extensive work in this field . They proposed a simple formula for (in)efficiency :
The costs in this formula are in the main influenced by list under- or over-runs because these in turn are related to wage costs. However, we have recently criticised this formula because it yields a quantity whose units of measurement are in absolute dollars: efficiency is instead better thought of in terms of a percentage of an input or of an optimum value . Their formula also is biased against larger institutions since here, the overall costs will be higher and so therefore will the absolute magnitude of the sum in the formula. Even if the formula were modified to take into account the size of institution or prevailing level of costs, as we have suggested , true costs might be difficult to calculate, especially in those countries where much work is still done according to historical or block contracts rather than as fee-for-service.
In the context of such difficulties, it was our aim to describe a new formula for surgical list efficiency. We also wished to test the applicability of our new formula using hypothetical (albeit realistic) scenarios and real data from elective lists of the same surgical specialty.
Appendix A: Adapting the efficiency formula to incorporate costs
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- Appendix A: Adapting the efficiency formula to incorporate costs
Our formula for efficiency is
Eqn 1: Efficiency formula:
There is always a base cost to running an operating theatre (estimated by the Audit Commission as £17 400 as the national average) and in addition there is a cost per hour (for staffing, equipment, maintenance, material, drugs, heating, lighting, etc.) . The cost per hour can be offset by performing cases, as these bring income (either directly as in the US , or indirectly in terms of block contracts or Payment-By-Results in the United Kingdom ). Thus, under-utilisation results in an extra cost to the institution as no income is generated by performing no work. Over-utilisation also incurs extra costs because of staff overtime and unbudgetted costs of additional surgical/anaesthetic materials in the over-run. McIntosh et al. have estimated that over-running is ∼ 1.5–2 times as expensive as under-running . Using these considerations, our Efficiency Formula can be adapted:
Eqn 2; Cost formula:
where £ is the extra cost per hour of under-utilised time. We have used K£ to estimate the cost of over-running (where constant K is the assumed ratio of cost of over- to under-run), but if the actual cost per hour of over-running is known, a different constant can be used for this second term of the equation. For example, Calvert et al.  have estimated that theatres cost ∼ £500 per hour (including staff costs) so that over-running costs ∼ £1000 per hour if the multiplier suggested by McIntosh et al.  is correct. A cancelled operation has numerous additional or detrimental knock-on effects on the institution in terms of wasted tests, cross-matched blood, intensive care beds, etc. . It may be possible to estimate these costs (e.g. one study estimated costs to the institution to be ∼ £600–900 per case over and above under- or over-utilisation costs ; another study reported that in addition to these costs, patients and families may face costs of £250–500 ), or this term may be ignored .
It is interesting that this adaptation of our base formula for efficiency to consider costs closely resembles the ‘cost formula’ of McIntosh et al.  which focused on overall costs:
Eqn 3: McIntosh et al. Cost formula:
Note that Eqn 2, our adapted Cost formula, predicts that over-running as a device to minimise cancellations will be an expensive strategy as it will increase overall costs. As McIntosh et al. state: ‘…inefficiency is minimised by minimising the hours of over-utilised operating room time…what matters is…reducing the hours worked late’.