杏吧原创

THERE IS a quote from Nate Silver about statistics which I think is very nice: 鈥淭he numbers have no way of speaking for themselves. We speak for them, we imbue them with meaning.鈥� You can鈥檛 just collect some data and it鈥檒l tell you the answer. There is an art to trying to extract information, knowledge and understanding from data, and even in choosing what data to collect. It鈥檚 something we鈥檝e all been dealing with over the past few months with covid-19: can we believe these numbers? What do they mean?

Now if this were a live audience, I鈥檇 be asking how many people have done stats courses. If people put their hand up, I鈥檇 ask how many people actually enjoyed them, and most of the hands would go down. That makes me upset. I love statistics, I think it鈥檚 great. But it has tended to be taught in the past as a series of formulae and tests and regression and things like that.

My book The Art of Statistics takes a very different approach. It spends a lot of time on problem solving, on things like: what are you trying to do? Is this data suitable for what you鈥檙e trying to answer? What can we conclude from it? It鈥檚 amazing how far you can get without ever doing any fancy statistical methods or using probability theory or the sample distribution of the sample mean and all this sort of stuff we all had to endure 鈥� and which I鈥檝e always taught, of course.

The key is what is called the 鈥渄ata cycle鈥�. You don鈥檛 start off with data, you start off with a problem. You plan how are you going to try to answer it. Is there any data, and what might we collect? Then you collect data and wrangle it and manage it and clean it up. Only then do you come to the analysis. That鈥檚 normally the only thing that is taught in stats courses, but it鈥檚 only a small part of the whole cycle.

It鈥檚 followed by the communication, drawing the appropriate conclusions, putting the message out. And there always you have to start again. Because as we鈥檙e going to see again and again, how you do an analysis just leads to more questions.

I find the data cycle an immensely powerful way to structure the use of data to solve problems. How many sexual partners have people had? Is it worth me taking statins? Who was the luckiest person on the Titanic? What鈥檚 the probability that the skeleton found in that Leicester car park really was Richard the Third? Why do old men have big ears? I mean, these really important questions for the future of humanity.

Many of these issues I鈥檝e actually been working on. An example I use in the book is that of the doctor Harold Shipman. He murdered at least 215 of his patients, and probably considerably more, over 24 years working in the Hyde suburb of Manchester. I worked on the Shipman inquiry as one of the statisticians who were asked to look at the data and answer various questions. The first question really was, what was happening?

So here鈥檚 a graphic that just shows the pattern of his murders: the red dots are women, the blue are men. The histograms at the top and on the left show the distribution of the years of the killings and the age of the victims. So just from this data alone, the ages and sex of the victims and the dates of their deaths, what can we conclude?

Is he mainly killing old people? Yes, but it looks like more near the end, some of his victims were much younger. And do you notice that gap of a year 鈥� did he go on holiday? No, up to then he had been working in a joint practice, and tt鈥檚 thought that he suspected that he was being suspected. After that, he set up his own single-handed practice, and after that there鈥檚 no sort of control over him. By the time he was arrested, he was murdering people at a huge rate, quite extraordinary. We don鈥檛 know why: he never spoke, and then committed suicide in prison.

So this data just generates more questions. What was Shipman doing? What system was he using? How was he killing people? The general practitioner Richard Baker went and looked at all the death certificates that Shipman had signed, and those his colleagues had as well. It was a massive data collection exercise, but the analysis was completely trivial. It hits you between the eyes. The times of day when his colleagues鈥� patients had died were spread pretty uniformly over 24 hours, but Shipman鈥檚 victims were dying around two or three in the afternoon. We think that is when he did home visits, visiting elderly people on their own and giving them a huge dose of morphine. They would die in front of him peacefully. It鈥檚 chilling.

Again, it generates more questions. All the families wanted to know, could he have been caught earlier? Now this is tricky. Those of you who have suffered statistics courses will know that to test a hypothesis, you have to set up a null hypothesis. A null hypothesis is boring: in this case, that there鈥檚 nothing wrong with Shipman at all. How soon could we have rejected that hypothesis 鈥� how soon could we have detected something strange was going on?

So you work out how many deaths you expected to occur over time with different sex and age groups if things were normal. You can compare that with the observed number, subtract the one from the other and you get excess mortality. The reality is a bit more complex and you actually use a slightly different statistical measure. But in Shipman鈥檚 case you can say that, based on female deaths alone, by 1985, after only about 40 deaths, we could have been very confident something was strange. Of course nobody did do that at the time; it was no one鈥檚 job to do that.

The other interesting thing is that when they tried this method out on 1000 other doctors around the country, they found a few who were even worse than Shipman. It turned out that these were enormously generous and responsible, kind, caring doctors, who were just living in places with a lot of elderly people and allowing them to die peacefully at home. That鈥檚 the difference between correlation and causation: we could conclude that these doctors are statistically odd, but not why. We have to be enormously cautious. That data does not speak for itself.

The covid mortality spike

So let鈥檚 look at coronavirus. We can look at the data for deaths in England and Wales, as in the diagram. The blue is the deaths happening with covid not mentioned on the death certificate, and the red is deaths with covid mentioned. The base line is the five-year average of deaths for the same period. We can see a massive spike starting at the end of March, but we can see that now, even allowing for continuing covid deaths, there are fewer deaths than normal. Is it just continuing the pattern of lower deaths that we observed early in the year, when we had a milder flu season than normal? Or is this the first sign of what鈥檚 called mortality displacement, in which deaths of frail elderly people that would have occurred later in the year have been brought forward?

And there are other fascinating patterns going on when you look closer. For example, we know that young men between 20 and 24 had lower mortality than usual over the lockdown period, at one point 30 per cent down, even including a few covid deaths. We don鈥檛 know the details, but we can probably guess it might have to do with fewer car accidents and maybe less going out getting drunk.

Displaced deaths

But let鈥檚 go deeper: let鈥檚 look at the place in which people are dying. Let鈥檚 look at care homes. There鈥檚 been a big spike in deaths in care homes, but with a lot of non-covid deaths. It鈥檚 thought many of these could be covid deaths, especially of elderly people with dementia, just not labelled as such on the death certificate. It鈥檚 very difficult to make a definite diagnosis in these cases, and doctors have been unwilling to put it on the certificate.

When we look at hospitals, we can see this big rise starting in the middle of March. This is when they emptied the hospitals and sent people back home without testing whether they had covid, or sent people back to care homes. It鈥檚 been strongly suggested that that was one of the causes of the rise in deaths in care homes, along with the staff moving between different institutions.

But there is also a dip in non-covid deaths in hospitals. There鈥檚 been a huge reduction in attendance in hospitals of people with heart symptoms, with strokes and so on. Where have these people been dying? Well, they鈥檝e been dying at home. It鈥檚 extraordinary. There has been an enormous number of extra deaths at home, some 15,000 over the period we鈥檙e looking at 鈥� and that鈥檚 still happening. As we speak, there鈥檚 still a deficit of non-covid deaths in hospital and an excess in the home.

Again, that just raises more questions. We don鈥檛 know the quality of these deaths. Most people would prefer to die at home; dying in hospital in this current crisis has not been a good thing. But maybe some of these people might have lived longer, had they gone to hospital. So this just raises more questions, as we go round and round that data cycle.

Coronavirus and age

Let鈥檚 look now not just at the death rates, but the chance of someone in the population catching covid-19 and then dying. I think this is almost the most staggering bit of analysis I鈥檝e ever done. In England and Wales, there is a completely exponentially increasing risk of catching it and dying from it for the different age groups. It increases by about 12 to 13 per cent for each year older you are, and so doubles for every five to six years. That means that someone who is 20 years older has got 10 times the risk: compared to a 25-year-old, a 45-year-old has ten times the risk, a 65-year-old 100 times, an 85-year- old 1000 times. Draw a straight line on the logarithmic scale representing exponentially increased risk and it just carries on across the age range all the way from essentially five to 95. I鈥檝e never seen anything like that, it is quite extraordinary.

For school kids, five- to 14-year-olds, of 7 million in England and Wales, just three have died 鈥� a 1 in 2.5 million risk. Meanwhile, 138 have died of other causes over the period of the epidemic. So this is both a staggeringly low risk, and very low compared to the normal risk. But for people over 90, more than 2 per cent, one in 50, have died with covid. That represents about a one-third increase over the normal risk they would have had over this period.

The media have not been great always in covering this. The 鈥渞isk of dying from coronavirus鈥� is a very misused phrase. I鈥檝e been talking about what鈥檚 called the population fatality rate, the chance of getting it and then dying. There鈥檚 another risk, which is if you get it, you die 鈥� the infection fatality rate. It鈥檚 very easy to mix those up.

That happened when the UK Office for National Statistics did a very good report on risks for ethnic minorities. That鈥檚 an incredibly important issue. All the risks that were discussed are the risks of catching it and dying, and that includes the increased risk of catching it that many ethnic minority communities clearly have, because of their jobs, or perhaps because of deprivation, overcrowding and poor working conditions. However, some reports had it that ethnic minorities were 90 per cent more likely to die if they became seriously ill with covid-19. That鈥檚 not true.

We鈥檝e done lots of experiments at the Winton Centre, and we find that people have got a complete misapprehension about covid risk. Many people say, if I catch it, it鈥檚 50/50 whether I die or not. People are very anxious. They really think if I get it, this is a very high-risk situation. It is for some people, but for most people, it isn鈥檛, even if you catch it.

You can look at the actuarial risk of dying in a given year. I produced a graph back in March, before we鈥檇 had almost any deaths in the UK at all, saying that the risks if you get the virus are very similar to the risks that are there anyway for dying in the subsequent year. That means that if you get the virus it roughly doubles your chance of dying this year. I鈥檇 still argue that that鈥檚 roughly true. But I originally expressed this by saying the risks from covid were about the same as dying this year, which was very bad communication, as some people interpreted it meaning the death rate from the virus didn鈥檛 add to normal risk.

For a statistician, this has been quite a stressful time. It鈥檚 been great, but it鈥檚 been hard work, and I鈥檝e got things wrong. But a lot of what we鈥檝e seen is what I call number theatre, a lot of numbers put out there to impress people. This is not trustworthy use of statistics. People delivering the statistics should be proper professionals who know what they鈥檙e talking about, and they should treat the public with respect.

Data literacy is a vital skill in modern life. This covid crisis that made this even clearer: not just in the ability to manipulate data, but also to critique the numbers we are told.

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