Monday, March 30, 2009

Patients = Patience

You hear at all the time: the problem with socialized healthcare is that it leads to waiting lists, people waiting too long for operations. Months, I hear, people have to wait months for operations you shouldn’t have to wait for, and sometimes they even die before the operation can happen.

Well, I say that’s crap.

Let’s start with some mathematics. Let’s say that we have a population P, and D, the rate occurrence of a particular condition that requires treatment.

Now let’s, for the sake of argument, assume that P is large enough – major city size,> 1,000,000 – to provide some constancy in statistics. So you can tell right away that we’re dismissing rural medicine. Stupid hillbillies who still live out in the boondocks, what the hell do we care about them anyway? All decent people live in slums cities with at least that number of people in it.

A P that large means that the rate of D is basically fairly constant, with the daily rate of Dd having a standard distribution around the mean D, and an approximate Standard Deviation of √D.

Look, these are rough statistics, and you know the drill: lies, lies, and statistics. But if I had a polished statistician go over this stuff, instead of the weird Health IT Nerd, the picture wouldn’t change that much.

So we have this condition occurring Dd number of times per day in the city. Now let’s say that this condition requires treatment on the same day. If this treatment is not provided, the patient will die. Perhaps the condition is extreme exhaustion from exposure to the political shenanigans associated with the bail-out, and the treatment is to be forced to read the War Nerd. Or we could try taking life seriously and posit that the condition is a renal stone, and the treatment is ultrasonic destruction of the stone. (Not that this is generally highly successful, but I’ve always though it’s the perfect procedure: we’ve got a problem – a real painful one, so what we’re going to do is have a good scream at it for a little while, and see if it goes away all by itself.)

Whatever, there’s a rate T, the number of treatments for the condition that can be provided in a day. Unlike D, this number is not subject to a normal statistical variation. Instead, it’s influenced by the availability of staff and long term institutional policies (which often produce unexpected results on the value of T). So for the sake of argument, let’s assume that T is a fixed constant.

If T is less than D, then this is a disastrous outcome - the queue for services will rapidly grow longer and people will die. The queue will get shorter on some days, but in general it will grow longer. However the length of the queue is limited by the number of people who die before they get to the front of the queue. So eventually the queue will stop growing. (So next time you hear of a long queue, understand: the people waiting aren't dying like flies while they're waiting...)

If T = D, then the queue will quickly reach a steady state – but roughly 50% of people will still have to wait until the next day. (Actually, it starts out much lower than that – a small number miss out on some days, say when Dd = D + 1 * √D. And they get carried over to the next day, where they compete with Dd for that day. The eventual outcome of this, what the average carry over is, depends on a variety of modeling and simulation assumptions, but as a rule of thumb, about 50% get carried over the next iteration.)

So when T = D, only 50% of the target is met. Note that like the previous case, the actual length of the queue depends on the number of people who die before treatment.

As T > D, and the gap increases, the percentage chance that a patient will have to wait until the next day drops – but T has to be quite a bit bigger than D before it approaches 0. (How much bigger depends on the value of D, given that the standard deviation of D was posited to be √D, but a useful rule of thumb is T = D + (3 x √D) gives 1% missed targets)

This is well and good, but what does it mean?

If you want to have immediate treatment available, you have to build considerably more than the average required treatment capacity into the system.

This is true for almost all kinds of treatment, whether obstetrics, oncology, cardiology, or what. You just plug different numbers in, and different requirements, but the same basic principles are in play.

Note that it’s mostly not as bad as it sounds because many treatments share a common set of resources, particularly facilities and staff. By pooling these things, the overall size of D increases, and the ratio of D/√D goes up, and the built in waste is ameliorated.

Nevertheless, you need to have excess capacity built into the system. Now this is hardly a radical conclusion – it arises in other industries all the time, particularly in telecommunications and transportation, and it’s a pretty well understood problem.

But people seem to forget this when they start talking about health, and we have these stupid debates about resources and waiting lists. In these, people not only ignore the simple principles above, they also ignore the fact that no society on earth can afford to pay for unlimited healthcare, let alone have excess capacity in the system.

So, how do you limit the resources available without creating waiting queues? Want a hint?

You can’t.

Well, actually, I lie. You can. But only if you deny some people access to the queue at all. Then they turn into a “totally negative healthcare outcome” instead of screwing up your statistics (i.e. they screw someone else’s stats up. Since funding is linked to statistics in most jurisdictions, this is just a way of externalizing the costs).

So, you choose: the immoral or the distasteful? Which is it to be?

Though there’s a third option. The way this works is simple: You know that a queue has to exist, but you personally don’t want to wait. So you create a two-tier system that ensures you don’t have to wait when you need the treatment, that someone else will wait. Or miss out altogether.

This only really works well if you can arrange that everyone who matters is in the top tier, and people in the second tier are such losers that they either don’t have representation (e.g. communist paradises)  or don’t have the wit or leverage to be heard anyway (say, UAW members ;-). Note that this can only work if the second-tier people fund the first tier some way or other (kind of socialism in reverse).

I’ll leave it to you to decide for yourself how well your country manages this issue, whether you’re happy with the way the case-by-case decision is made, whether it’s going to be the immoral or the distasteful for you and your loved ones.§

But next time you hear someone discussing the disgraceful state of waiting lists in [country/system/state] as compared to [other country/system/state], ask yourself: how are the statistics lying this time? How many people had a totally negative outcome before the possibly positive outcome got counted? And who were they?

§ The correct answer to the question above is ‘no, I’m not happy’. It doesn’t matter which country you live in. Tricky huh?

p.s. Here’s an excellent example of this stuff in practice, quoted from
“It's important to ask this question, because this is precisely the situation where the Canadian-type health care system -- much touted by reform advocates -- tends to fail Canadians.”
Yes, the Canadian government makes one set of decisions. These weight some situations preferentially over others. And then:
“In the United States if someone falls and hits her head and then an hour later is rushed to the emergency room you can bet she will get a STAT CT scan and immediate neurosurgical attention.”
This is another set of decisions. Because there’s a word or two missing from this paragraph – this doesn’t apply to all citizens, only to those with “coverage” – a number steadily decreasing at this time. Both of these are two-tier systems. The Canadians just outsource their first tier to USA – works well for everything but emergency medicine.