For all the faults of its roll out, the Affordable Care Act should ultimately provide more people with health insurance and thus a way to pay for basic health care. That implicitly assumes that there is enough health-care capacity to go around. There is a very real concern that there is not enough capacity — particularly in primary care — to properly cope with an influx of newly insured patients who will want to do basic things like see a doctor.
If capacity is going to be tight, then there is a premium on making sure it is not wasted. That, as Marketplace reports, means that clinics are experimenting with overbooking (How post-ACA health care is like the airline business, Dec 5).
Here is the part I want to talk about:
Cooper University Hospital is expecting a huge wave of patients starting next month, as millions of consumers get health insurance, some for the first time. The question for hospital executives in Camden, and around the country, is how to manage this new population. For one, there is a chance this new patient population will exacerbate existing problems at Cooper.
Today, “the patient no-show rate is in high 20s, 25, 30 percent,” says Jonathan Vogan, the associate director for financial and performance measurement at Cooper’s outpatient clinic, the Urban Health Institute.
The Urban Health Institute serves more than 8,000 patients, virtually all of them low-income. Vogan says the poorer the patients, the more likely they’ll miss their appointments. And that’s an expensive problem. But Vogan says the solution is simple.
“If not all of your patients show up then the easiest thing to do is, well, just book more of them,” he says.
I should note that I have posted on this before (which is why this reporter called me) but this is an interesting problem to think about and is worth revisiting. Part of this is simple to think about. Suppose that a physician has 20 slots available in a clinic session and that all patients have a 25% chance of not showing up. If only 20 patients are booked, then the chance that the doctor is idled for at least one time slot is 99.7%. (If you want to work through the details, note that the number of people showing up will have a binomial distribution. The number of no shows will also have a binomial distribution.) Thus the clinic is all certain to waste some of a scarce resource, physician time.
So how do we figure out by how much to overbook? One can approach this as a newsvendor problem. Suppose that the clinic receives a $80 for seeing a patient but incurs $40 in cost. Further suppose that all of the costs are labor related. (Note I am just making up numbers for the sake of illustration and will have some caveats on them below.) Also, we need to figure out what happens when too many people show up. Let’s suppose that everyone is seen but the clinic runs overtime so our labor costs go by 50%. We would then have that “wasting” one appointment slot because we haven’t overbooked enough costs $80 – $40 = $40. On the other hand, overbooking one too many patients means the clinic has to work overtime that increases costs by 0.5*$40 = $20 relatively to doing the appointment on regular time.
The best policy is found by using these numbers for, respectively, the marginal benefit and marginal cost of overbooking. We can envision every appointment slot for which there is a no show demanding an overbooked patient. The question is what fraction of that demand we should cover. It turns out that we should target 40/(40+20) or 67%. (For more on why, see here.)
If we try to covert that into an overbooking level, we run into a complication: The distribution of no shows is going to depend on the total number of no shows. (To convince yourself of this, note that if we give out 20 appointments, we can have at most 20 no shows. If we give out 21, we could have 21 no shows.) That means that I don’t have a simple formula to neatly solve everything. Still it can easily be done in Excel. Suppose we overbook our 20 slot session by N patients. The Excel function BINOM.INV(N+20,0.25,0.667) then gives us the number, say, X such that the chance that the probability that the number of no shows is at most X is at least 67%. We just need to find the point such that X = N, i.e., the level of overbooking such that the 67th percentile is our level of overbooking. In our example, that works out to 8. That is, we should take 28 appointments for our 20 slots.
Now for the aforementioned caveats. I ground through this by assuming that the clinic cared about its profitability. Not that that’s a bad objective, but it may not capture everything that the people running the clinic care about. For example, we may have 29 people who want appointments today. If we cap appointments at 28, we are pushing someone out to a later day. That may have health consequences for them. Said another way, if we don’t factor in the benefit to the patient on top of the clinic’s financial gain, we may be understating the cost of having a doctor sitting around with no one to see.
Also, we have taken the cost of overbooking too much as just the extra overtime cost and we have assumed that those don’t vary over time. But what do you think the staff is going to say when they have to work extra time for the fourth or fifth day in a row? That is likely to happen. There is only going to be a one-third chance that there is so many no shows that we can see all of our overbooked patients without overtime. Our recommendation may not be sustainable in the long run simply because of personnel issues.
It’s also going to cause problems for patients. Overbooking here is going to mean people wait and we haven’t included any measure of customer waiting. If we care about customer waiting, we are going to pick a lower overbooking level.
Thinking about customer waits highlights one of the biggest problems with overbooking in service setting like a medical clinic in which customers arrive overtime. I have been implicitly assuming that our patients are all scheduled to arrive at the start of our session so the clinic instantly knows whether it has enough capacity. That’s not how clinics (or, for that matter, restaurants and golf courses) work. If customers arrive over time, overbooking may be for naught. We might have an extra patient scheduled for 2:00PM but experience a no show in the morning. This is the worst of all worlds — we are going to waste doctor time and force a patient to wait. My newsvendor analysis is totally standard and is a pretty good fit for the airline industry. However, it is problematic as a model for a medical clinic. I don’t know of any comparable, general approach for scheduling overbooked patient over a service interval as we have at a medical clinic.
So what can the clinic do?
The report mentions that the clinic’s longterm goal is to reduce the number of no shows. There are concrete steps that can be taken. For example, it is often argued that no shows go up the farther out appointments are made. That is, you are more likely to keep an appointment schedule for this afternoon than one that you make for next month. So moving to something like an open access appointment schedule may be desirable. Open access scheduling favors doing “today’s work today” so patients don’t have to wait extended periods in order to get an appointment. You can see how that could improve patient satisfaction as well as overall care. However, it doesn’t necessarily address the overtime problem inherent in overbooking. Doing today’s work today means at least on occasion working extra hours to get today’s patients through.
There is also the question of whether better matching of patients and time slots can lead to fewer no shows. For example, parents have to accompany kids to appointments. Pediatric appointments then need to accommodate parents’ work schedules. To the extent that a clinic can offer flexibility (e.g., more hours in the evening), the fewer no shows it will see.
A clinic could also impose penalties for not showing up or not canceling in a timely manner. From a modeling perspective, that will clearly work. There is a penalty big enough that patients will always call two days out when they know they cannot keep their appointment. So, in theory, this is great. In practice, it may not work so well. Some no shows may well be beyond the patient’s control. A bus runs late or a manager collars the patient as she is leaving work. How much is the clinic going to fight to collect a fee that the patient was forced into?
Finally, there is a question of how a clinic could do a better job of managing overbooking. My analysis assumed that all patients are equally like to not show up. But suppose that the clinic has some idea of which kind of patients are likely not to show up. Arguably, those with higher no-show rates should be scheduled later in the session. The overbooked patients should be added later as well. This will keep overbooking from affecting more reliable patients (although it adds uncertainty to the clinic since it won’t now until late in the day whether overtime will be necessary).
My analysis also assumed that there was only one doctor. Things get better if we have multiple physicians and overbooked patients can be seen by anyone. If a patient has a chronic condition, there may be real value in continuity of care and always seeing one’s primary physician. However, if it just a question of whether a kid has an ear infection, having the flexibility to have that patient be seen by any available doctor is valuable. If we have multiple doctors, the total amount we overbook will go up but the level of overbooking will be a smaller fraction of available regular capacity. For example, if our clinic had three doctors all of whom can see 20 patients today, we would want to overbook by 22 patients while if we manage their schedules separately we would need to overbook by 24 patients.
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