There’s lots of heat but little light when it comes to the issue about how best to handle volunteers returning to the US after caring for Ebola patients in West Africa.
Front and center right now is Kaci Hickox, a nurse who recently returned from Sierra Leone after a three-week stint taking care of Ebola patients. Officials say her temperature was elevated on arrival at New Jersey’s Liberty International airport, and that landed her in quarantine at a hospital. Although New Jersey arranged for her to travel back to her home in Maine, her home state has a 21-day quarantine as well. Ms. Hickox is protesting and threatening to sue; Maine officials haven’t yet blinked.
It’s a complicated question, but epidemiologists (people who study diseases in populations) have a good way of thinking about such problems: the number needed to treat (or NNT). In the case of a blood pressure medication that reduces the chance of stroke, the NNT is the number of patients who would have to take the medication to prevent one stroke.
We can use the idea of NNT to come up with the NNQ: the number of healthcare workers returning from West Africa that you’d have to quarantine to prevent the spread of Ebola to one member of the public.
There are a number of assumptions in getting to the NNQ, but my back-of-the-envelope calculation suggests that the absolute risk reduction from quarantining healthcare workers instead of enforcing monitoring is on the order of 0.004%. Take one over that number, and you get the NNQ: about 25,000.
That’s right. We would need to quarantine 25,000 healthcare workers to prevent one Ebola infection in the public: that’s roughly equivalent to locking up the half of the city of Cupertino for three weeks.
Seems a wee bit high to me.
Of course, the NNQ is only as good as the assumptions on which it’s based, and folks from the WHO and CDC have better access than do I to the relevant evidence. If my numbers are roughly right, however, it seems that Kaci Hickox is right to tell state officials to go pound sand.
NOTE: You can come up with your own NNQ using this nifty calculator. To see how I got mine, read on.
How I Came Up with the Estimate
We can use the epidemiological idea of “number needed to treat” (or NNT) to come up with the NNQ: the number of healthcare workers returning from West African that you’d have to quarantine to prevent the spread of Ebola to one member of the public. Just as with the NNT, the NNQ the reciprocal of the absolute reduction in the chance of the bad outcome – here, infecting someone else with Ebola – offered by mandatory quarantine instead of monitoring.
To take a shot at estimating the NNQ we need to think about three things:
- The chance that a returning healthcare worker is infected with Ebola,
- The chance the infected healthcare worker will become symptomatic in public, and
- The number of people who would become infected if the healthcare worker became symptomatic in public.
What’s the Chance that a Healthcare Worker Returning from Caring for Ebola Patients in West Africa is Infected with the Virus?
To get a good handle on this, we need to know the total number of workers exposed to these patients, how many times they’d been exposed (and for how long), and how many had become infected. According to NBC News, nearly 50 healthcare workers have returned from caring for Ebola patients; only one was infected. That’s a chance of about 2% (i.e., 1 in 50).
The situation in Dallas provides a bit of evidence as well. There, two nurses caring for Thomas Eric Duncan – the Liberian who inadvertently brought the Ebola virus to the US – became infected. If we assume that 50 clinical staff cared for Mr. Duncan, that would put the risk at about 4%.
The situation in West Africa is quite different than in Dallas, of course, but it’s not clear whether that makes it less or more likely that a healthcare worker would become infected there. Let’s give the benefit of the doubt to protective gear and good practices, and say that the chance that a healthcare worker providing direct care to Ebola patients in Africa becomes infected is 2%.
What’s the Chance an Infected Healthcare Worker Will Become Symptomatic in Public?
The CDC and WHO tell us that the risk of infection is minimal unless the patient is symptomatic and others come in contact with bodily fluids (blood, vomit, feces and other unpleasant things). We’ll assume that quarantine offers a reduction in infection risk is if the infected healthcare worker is out and about, is suddenly stricken with symptoms, and is delayed in getting herself to a hospital or otherwise isolated. Let’s say that of 100 infected healthcare workers, one of them will become symptomatic while mingling with the population. In other words, we will assume this happens 1% of the time. Could be higher; could be lower.
How Many People Should We Expect to Become Infected if a Healthcare Worker Becomes Symptomatic in Public?
Being symptomatic doesn’t necessarily mean others will get infected. Scientists tell us that for every one person infected in West Africa, about two others will be infected. Because this spread happens over days in which the sick person has symptoms, we will need to adjust the risk down; it’s highly unlikely that a symptomatic healthcare worker wouldn’t attempt to isolate herself or get to a hospital.
We will assume that our symptomatic healthcare worker is delayed on being isolated by a half of a day. We’ll also assume that most of the sick folks in West Africa are symptomatic for five days, which means that our healthcare worker incurs 10% the risk to those around here compared to West Africans who become infected (because a half a day out of five is 0.10). So on average, 0.2 people would become infected each time a healthcare worker is struck by symptoms while mingling with the public (2 people infected x 0.10 to account for the half-day exposure to others).
So, How Many Healthcare Workers Would We Need to Quarantine to Prevent Spreading Ebola to One Member of the Public?
Let’s take account of where we are after making all of these assumptions:
- Chance that a returning healthcare worker is infected with Ebola: 2%
- Chance an infected healthcare worker will become symptomatic in public: 1%
- Number of people who would become infected if the healthcare worker became symptomatic in public: 0.2
As we noted earlier, the NNQ is the reciprocal of the absolute risk reduction gotten from quarantine. The absolute reduction is the chance that the healthcare worker is infected times the chance that she will develop symptoms in public times the number of people who become infected if she develops such symptoms: 2% x 1% x 0.2, or 0.00004.
Thus, the number needed to quarantine to prevent one infection to the public is 25,000 (= 1 ÷ 0.00004). This means we would have to quarantine 25,000 healthcare workers to prevent one Ebola infection to the US public.
Of course, your estimates might be very different than mine.