How likely is someone who gets treated for Ebola in the United States to die of the disease?
About two-thirds of the 2,387 people who’d contracted the disease before this year’s outbreak died worldwide. The fatality rate of more than 14,000 people who have been infected with Ebola in West Africa this year is 71 percent. But eight of the nine people who have been treated for the disease in the U.S. have recovered and been released from the hospital. One person has died.
It’s not obvious, even to statisticians and public-health experts, how to combine all this information.
One option is to treat all the cases the same, and calculate a single mortality rate for the virus, wherever it’s being treated. That approach would leave the mortality rate estimate unchanged — nine people isn’t enough to move the needle.
But that would ignore that these people have something important in common: being treated in the U.S. So another option is to assume Ebola treatment in the U.S. is so different than in West Africa — because of greater resources, earlier detection and a much smaller caseload — that the nine U.S. cases should be handled separately. That would leave you with an estimate of just an 11 percent mortality rate for Ebola in the U.S.
That approach isn’t ideal, either, though. It discards all prior knowledge about the disease, and relies on a very small sample of cases.
“Most people would probably agree that the right way to do it is between those two extremes,” Andreas Handel, an assistant professor in epidemiology and biostatistics at the University of Georgia’s College of Public Health, said in an email. He added: “My guess is if you ask 10 Bayesians (or statisticians/experts in general) you’ll get about 10 different answers. There is no one right way of doing it.”
I didn’t ask 10 experts, but I did ask a handful. They agreed there were plenty of reasons to think mortality from Ebola would be lower in countries with better-funded health-care systems — as is true for many diseases. “Cholera is a really strong example,” said Elizabeth Halloran, professor of biostatistics at the University of Washington’s School of Public Health, in a telephone interview. “You shouldn’t die of cholera, if you have rehydration therapy.” Yet cholera kills 100,000 to 120,000 people each year — many of whom didn’t get effective rehydration therapy.
Bayesian statistics seemed like a promising option for estimating U.S. mortality, because it provides a framework for updating prior informed belief (mortality rate in prior outbreaks in the U.S. and elsewhere) with new information (the lower mortality rate in the U.S. in this outbreak).
“Bayes Theorem is a machine that tells you how to update what you knew before with what you know now,” said Lance A. Waller, professor of biostatistics at Emory University’s Rollins School of Public Health, in a telephone interview.
Tony O’Hagan, emeritus professor of statistics at the University of Sheffield in the U.K., sent along a rough sketch of how a Bayesian would approach the problem. O’Hagan, who has written about using Bayes in health-outcomes research, started with the assumption that the Ebola mortality rate in the U.S. would be 30 percent, about half that in Africa — peppered with a liberal amount of uncertainty because it was essentially an educated guess. Then once he factored in the eight recoveries in nine U.S. cases, his estimate was of a mortality rate of 17 percent.
Waller offered some ideas for how to refine the analysis. What we want is a model that takes into account the individual attributes of each case when estimating the likelihood of death. Those attributes include age and health of the patient, time from first symptoms to start of treatment, training of medical staff and treatments used. What factors led to lower mortality in the U.S., and which can be replicated in the West African countries with climbing caseloads?
Building such a model would require detailed data not just on the nine U.S. patients, but on as many Ebola patients worldwide as possible. That data isn’t always collected and compiled in a usable way, though — especially in an emergency treatment setting. “There’s your dream set of data, and then there’s the data you can get,” Waller said. “If the data you can get is not to the full extent of what you would like, then you have to fill in what is missing.”