Why are waiting lists so common in the medical sector?
David Friedman recently asked a related question on SSC (he asked about why there are waiting lists for surgical procedures), and I decided that as I’d read some stuff about these topics in the past I might as well answer his question. The answer turned out to be somewhat long/detailed, and I decided I might as well post some of this stuff here as well. In a way my answer to David’s question provides belated coverage of a book I read last year, Appointment Planning in Outpatient Clinics and Diagnostic Facilities, which I have covered only in very limited detail here on the blog before (the third paragraph of this post is the only coverage of the book I’ve provided here).
Below I’ve tried to cover these topics in a manner which would make it unnecessary to also read David’s question and related comments.
The brief Springer publication Appointment Planning in Outpatient Clinics and Diagnostic Facilities has some basic stuff about operations research and queueing theory which is useful for making sense of resource allocation decisions made in the medical sector. I think this is the kind of stuff you’ll want to have a look at if you want to understand these things better.
There are many variables which are important here and which may help explain why waiting lists are common in the health care sector (it’s not just surgery). The quotes below are from the book:
“In a walk-in system, patients are seen without an appointment. […] The main advantage of walk-in systems is that access time is reduced to zero. […] A huge disadvantage of patients walking in, however, is that the usually strong fluctuating arrival stream can result in an overcrowded clinic, leading to long waiting times, high peaks in care provider’s working pressure, and patients leaving without treatment (blocking). On other moments of time the waiting room will be practically empty […] In regular appointment systems workload can be dispersed, although appointment planning is usually time consuming. A walk-in system is most suitable for clinics with short service times and multiple care providers, such as blood withdrawal facilities and pre-anesthesia check-ups for non-complex patients. If the service times are longer or the number of care providers is limited, the probability that patients experience a long waiting time becomes too high, and a regular appointment system would be justified”
“Sometimes it is impossible to provide walk-in service for all patients, for example when specific patients need to be prepared for their consultation, or if specific care providers are required, such as anesthesiologists [I noted in my reply to David that these remarks seem highly relevant for the surgery context]. Also, walk-in patients who experience a full waiting room upon arrival may choose to come back at a later point in time. To make sure that they do have access at that point, clinics usually give these patients an appointment. This combination of walk-in and appointment patients requires a specific appointment system that satisfies the following requirements:
1. The access time for appointment patients is below a certain threshold
2. The waiting time for walk-in patients is below a certain threshold
3. The number of walk-in patients who are sent away due to crowding is minimized
To satisfy these requirements, an appointment system should be developed to determine the optimal scheduling of appointments, not only on a day level but also on a week level. Developing such an appointment system is challenging from a mathematical perspective. […] Due to the high variability that is usually observed in healthcare settings, introducing stochasticity in the modeling process is very important to obtain valuable and reasonable results.”
“Most elective patients will ultimately evolve into semi-urgent or even urgent patients if treatment is extensively prolonged.” That’s ‘on the one hand’ – but of course there’s also the related ‘on the other hand’-observation that: “Quite often a long waiting list results in a decrease in demand”. Patients might get better on their own and/or decide it’s not worth the trouble to see a service provider – or they might deteriorate.
“Some planners tend to maintain separate waiting lists for each patient group. However, if capacity is shared among these groups, the waiting list should be considered as a whole as well. Allocating capacity per patient group usually results in inflexibility and poor performance”.
“mean waiting time increases with the load. When the load is low, a small increase therein has a minimal effect on the mean waiting time. However, when the load is high, a small increase has a tremendous effect on the mean waiting time. For instance, […] increasing the load from 50 to 55 % increases the waiting time by 10 %, but increasing the load from 90 to 95 % increases the waiting time by 100 % […] This explains why a minor change (for example, a small increase in the number of patients, a patient arriving in a bed or a wheelchair) can result in a major increase in waiting times as sometimes seen in outpatient clinics.”
“One of the most important goals of this chapter is to show that it is impossible to use all capacity and at the same time maintain a short, manageable waiting list. A common mistake is to reason as follows:
Suppose total capacity is 100 appointments. Unused capacity is commonly used for urgent and inpatients, that can be called in last minute. 83 % of capacity is used, so there is on average 17 % of capacity available for urgent and inpatients. The urgent/inpatient demand is on average 20 appointments per day. Since 17 appointments are on average not used for elective patients, a surplus capacity of only three appointments is required to satisfy all patient demand.
Even though this is true on average, more urgent and inpatient capacity is required. This is due to the variation in the process; on certain days 100 % of capacity is required to satisfy elective patient demand, thus leaving no room for any other patients. Furthermore, since 17 slots are dedicated to urgent and inpatients, only 83 slots are available for elective patients, which means that ρ is again equal to 1, resulting in an uncontrollable waiting list.” [ρ represents the average proportion of time which the server/service provider is occupied – a key stability requirement is that ρ is smaller than one; if it is not, the length of the queue becomes unstable/explodes. See also this related link].
“The challenge is to make a trade-off between maintaining a waiting list which is of acceptable size and the amount of unused capacity. Since the focus in many healthcare facilities is on avoiding unused capacity, waiting lists tend to grow until “something has to be done.” Then, temporarily surplus capacity is deployed, which is usually more expensive than regular capacity […]. Even though waiting lists have a buffer function (i.e., by creating a reservoir of patients that can be planned when demand is low) it is unavoidable that, even in well-organized facilities, over a longer period of time not all capacity is used.”
I think one way to think about the question of whether it makes sense to have a waiting list or whether you can ‘just use the price variable’ is that if it is possible for you as a provider to optimize over both the waiting time variable and the price variable (i.e., people demanding the service find some positive waiting time to be acceptable when it is combined with a non-zero price reduction), the result you’re going to get is always going to be at least as good as an option where you only have the option of optimizing over price – not including waiting time in the implicit pricing mechanism can be thought of as in a sense a weakly dominated strategy.
A lot of the planning stuff relates to how to handle variable demand, and input heterogeneities can be thought of as one of many parameters which may be important to take into account in the context of how best to deal with variable demand; surgeons aren’t perfect substitutes. Perhaps neither are nurses, or different hospitals (relevant if you’re higher up in the decision making hierarchy). An important aspect is the question of whether a surgeon (or a doctor, or a nurse…) might be doing other stuff instead of surgery during down-periods, and what might be the value of that other stuff s/he might be doing instead. In the surgical context, not only is demand variable over time, there are also issues such as that many different inputs need to be coordinated; you need a surgeon and a scrub nurse and an anesthesiologist. The sequential and interdependent nature of many medical procedures and inputs is likely also a factor in terms of adding complexity; whether a condition requires treatment or not, and/or which treatment may be required, may depend upon the results of a test which has to be analyzed before the treatment is started, and so you for example can’t switch the order of test and treatment, or for that matter treat patient X based on patient Y’s test results; there’s some built-in inflexibility here at the outset. This type of thing also means there are more nodes in the network, and more places where things can go wrong, resulting in longer waiting times than planned.
I think the potential gains in terms of capacity utilization, risk reduction and increased flexibility to be derived from implementing waiting schemes of some kind in the surgery context would mediate strongly against a model without waiting lists, and I think that the surgical field is far from unique in that respect in the context of medical care provision.
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