Outside my field, I’ve found that people generally respond to mathematical analysis in one of two ways. The first is with suspicion. This is understandable: if something is opaque and unfamiliar, our instinct can be to not trust it. As a result, the analysis will probably be ignored. The second kind of response is at the other extreme. Rather than ignore results, people may have too much faith in them. Opaque and difficult is seen as a good thing. I’ve often heard people suggest that a piece of maths is brilliant because nobody can understand it. In their view, complicated means clever. According to statistician George Box, it’s not just observers who can be seduced by mathematical analysis. ‘Statisticians, like artists, have the bad habit of falling in love with their models,’ he supposedly once said.[72]
We also need to think about the data we put into our analysis. Unlike scientific experiments, outbreaks are rarely designed: data can be messy and missing. In retrospect, we may be able to plot neat graphs with cases rising and falling, but in the middle of an outbreak we rarely have this sort of information. In December 2017, for example, our team worked with MSF to analyse an outbreak of diphtheria in refugee camps in Cox’s Bazar, Bangladesh. We received a new dataset each day. Because it took time for new cases to be reported, there were fewer recent cases in each of these datasets: if someone fell ill on a Monday, they generally wouldn’t show up in the data until Wednesday or Thursday. The epidemic was still going, but these delays made it look like it was almost over.[73]
Diphtheria outbreak in Cox’s Bazar Bangladesh, 2017–18. Each line shows the number of new cases on a given day, as reported in the database as it appeared on 9 December, 19 December and 8 January.
Data: Finger et al., 2019
Although outbreak data can be unreliable, it doesn’t mean it’s unusable. Imperfect data isn’t necessarily a problem if we know how it’s imperfect, and can adjust accordingly. For example, suppose your watch is an hour slow. If you aren’t aware of this, it will probably cause you problems. But if you know about the delay, you can make a mental adjustment and still be on time. Likewise, if we know the delay in reporting during an outbreak, we can adjust how we interpret the outbreak curve. Such ‘nowcasting’, which aims to understand the situation as it currently stands, is often necessary before forecasts can be made.
Our ability to nowcast will depend on the length of the delay and the quality of data available. Many infectious disease outbreaks last weeks or months, but other outbreaks can occur on much longer timescales. Take the so-called opioid epidemic in the US, in which a rising number of people are addicted to prescription painkillers, as well as illegal drugs like heroin. Drug overdoses are now the leading cause of death for Americans under the age of 55. As a result of these additional deaths, average life expectancy in the US declined three years running between 2015 and 2018. The last time that happened was the Second World War. Despite some aspects of the crisis being specific to the US, it isn’t the only area at risk; opioid use has also been on the rise in places like the UK, Australia and Canada.[74]
Unfortunately, it’s hard to track drug overdoses because it takes especially long to certify deaths as drug-related. Preliminary estimates for US overdose deaths in 2018 weren’t released until July 2019.[75] Although some local-level data is available sooner, it can take a long time to build up a national picture of the crisis. ‘We’re always looking backwards,’ said Rosalie Liccardo Pacula, a senior economist at the RAND Corporation, which specialises in public policy research. ‘We aren’t very good at being able to see what’s happening immediately.’[76]
The US opioid crisis has received substantial attention in the twenty-first century, but Hawre Jalal and colleagues at the University of Pittsburgh suggest that the problem goes back much further. When they looked at data between 1979 and 2016, they found that the number of overdose deaths in the US grew exponentially during this period, with the death rate doubling every ten years.[77] Even when they looked at the state rather than national level, they found the same growth pattern in many areas. The consistency of the growth pattern was surprising given how much drug use has changed over the decades. ‘This historical pattern of predictable growth for at least 38 years suggests that the current opioid epidemic may be a more recent manifestation of an ongoing longer-term process,’ the researchers noted. ‘This process may continue along this path for several more years into the future.’ [78]
Yet drug overdose deaths only show part of the picture. They don’t tell us about the events that led up to this point; a person’s initial misuse of drugs may have started years earlier. This time lag happens in most types of outbreak. When people come into contact with an infection, there is usually a delay between being exposed and observing the effects of that exposure. For example, during that 1976 Ebola outbreak in Yambuku, people who were exposed to the virus often took a few days to become ill. For infections that were fatal, there was then another week or so between the illness appearing and death. Depending on whether we look at illnesses or deaths, we get two slightly different impressions of the outbreak. If we focus on newly ill Ebola cases, we’d say that the Yambuku outbreak peaked after six weeks; based on deaths, we’d put the peak a week later.
1976 Ebola outbreak in Yambuku
Data: Camacho et al., 2014
Both datasets are useful, but they’re not measuring quite the same thing. The tally of new Ebola cases tells us what is
