The outlier must attract questions

An outlier, like the record 9 mn vaccinations on 21 June, must be treated with skepticism
An outlier, like the record 9 mn vaccinations on 21 June, must be treated with skepticism
There’s a lesson that’s quickly learned in statistics and mathematics more generally: the outlier must be treated with scepticism.
For example, let’s say you’re monitoring patients’ reactions to a particular treatment. You’re trying to understand how long it is before they show no more symptoms of the disease. You find that for hundreds of patients, it’s consistently between one and two months— except for one woman, who is up and about in a day.
Question: In drawing conclusions about this, do you take that woman into account? Or do you treat her as an outlier? I think you would agree with the latter course. Meaning, assume that her miraculous recovery was just that, a miracle; that in general, the treatment takes a month or two to work. You will likely search for an explanation for the miracle; but no more than that.
This idea applies in all kinds of ways. If tennis Grand Slams are being won by Nadal, Djokovic and Federer over several years, but one year a certain Dilip D’Souza makes a run through the draw and wins Wimbledon, you should not assume he has broken the dominance of those three. If the daily count of deaths in India due to covid hover between 300 and 400 for many days, but one day there’s a spike of 2,000, you should not assume that spike will henceforth be the norm. (This actually happened: on 16 June 2020, India suddenly reported about 2,000 deaths, a number we would not see again till mid-April 2021).
Yes, we should ask questions about why D’Souza won that lone tournament or why the death count suddenly spiked. But that’s just the point: outliers must attract questions. Scepticism.
That’s the way to consider this week’s miracle that’s been all over the news: the day, Monday 21 June, when India vaccinated well over 8 million people; actually, closer to 9 million.
Let’s be clear to start— this was a stunning achievement. The logistics, the preparation, the materials required to administer so many doses— all deserve applause. Our battle against the virus is on such a huge scale that efforts like this one are not just welcome; they are necessary.
Yet let’s also be clear— it’s precisely because it was such a stunner that this is an outlier, that there are questions. Let me try to answer some, using data from the superb site covid19india.org.
Over the month before last Monday, India had been vaccinating about 3 million people a day. In fact, that has been true for a while now. We’ve seen rising and falling trends and outliers on a smaller scale— a dip to 260,000 on 28 March, a spike to nearly 5 million on 20 May. But that 3 million mark has held up fairly consistently since we first reached it in mid-March. (Remember we started vaccinations about the beginning of this year).
Given consistency like that over so many weeks, how did we suddenly leap to nearly 9 million on Monday? What does it mean for the future?
And when we ask such questions instead of— or at least in addition to—the applause, we start getting answers.
Consider Madhya Pradesh. Over the month before Monday, MP was averaging about 180,000 vaccinations a day. Again, there were occasional outliers, but that average held up. It holds up even though I included lower numbers from the four days immediately prior to Monday: 131,000 on 17 June, 19,000 on 18 June, 39,000 on 19 June, 1,900 (yes, 1,900) on 20 June. Though even those four may be exaggerated; using data from the Indian government’s own Cowin vaccination platform, the journalist Supriya Sharma reported even smaller figures, down to just 692 (!) doses on 20 June.
Whichever way you look at it, there was a significant slowdown in vaccinations in MP over those four days. Why? Those slowing numbers qualify as outliers too, and we could use an explanation, not that there is any forthcoming. But then 21 June rolled around, and MP vaccinated 1.7 million people that day: nearly 1,000 times as many as on 20 June, nearly 10 times its daily average through the previous month, nearly 20% of the figure for all of India that day. A slowdown, followed by a huge spike: it’s only natural to wonder why, to think that just maybe MP was stockpiling its doses for a few days, waiting for whatever reason for Monday. Subtract the numbers for those four days from the MP average, 180,000. We have 50,000, 160,000, 140,000 and 178,000, or a “backlog" of 528,000 vaccinations from just those days. That is, nearly a third of the 21 June spike in MP can be attributed to a possible four-day stockpile.
Consider Karnataka. That state was averaging about 250,000 vaccinations a day since late May. But on 20 June, it vaccinated only 90,000 people, a number not seen there for a month. And on 21 June, Karnataka followed MP’s spiking example and vaccinated 1.1 million, over four times its recent average, and more than a 10-fold leap from the day before.
Together, Karnataka and MP reeled off almost one-third of the nationwide 21 June spike. What’s common to those two states? Both are ruled by the Bharatiya Janata Party, the party that rules at the Centre. The six states that contributed the highest numbers on 21 June were, in order: MP (1.7 million), Karnataka (1.1 million), Uttar Pradesh (729,000), Bihar (559,000), Gujarat (511,000) and Haryana (501,000). That’s a total of 5.1 million vaccinations in these states, or 58% of the spike on 21 June. What’s common to these six states? All are ruled by the BJP or a political ally.
Take this a little further: put together, the population of these six states is about 530 million. That is, 39% of India’s population got 58% of the vaccinations administered on 21 June. It gives the 9 million mark some perspective, perhaps?
So one answer to the questions above is that BJP-ruled states had the vaccines to rack up the numbers on 21 June. Make of that what you will.
Of course, what would make the number remarkable is if it wasn’t a one-off, if it sustains. Can that happen? Well, in my column about the claim of 2 billion doses by December (bit.ly/3wRXSyw), you’ll find that by July, the Serum Institute of India must produce 100 million Covishield doses per month. By September, Bharat Biotech must produce 100 million Covaxin doses per month. No other vaccine is available in India in remotely comparable numbers, so let’s stick with these two.
Let’s say both have reached their 100 million/month targets already, instead of a month or three from now. That gives us a supply of about 6.7 million/day. How can we sustain that 9 million mark of 21 June?
Answer: We can’t. On 22 June, India’s vaccination count dropped to 5.9 million. Of those, Gujarat administered 437,000. Karnataka, 430,000. Bihar, 396,000. Haryana, 123,000. MP saw a 30-fold drop, to just 52,000, and UP was the only one of the six states to register an overnight increase, vaccinating 863,000.
You look at all this, and the real truth of the 21 June figure emerges: this was an outlier. But this was, in fact, a carefully-staged exercise to thump chests and claim a “world record". No more, no less.
Being so, it tells us nothing about how we will vaccinate our citizens.
This column draws on Supriya Sharma’s report in Scroll (bit.ly/35NQTeb) and V. Sridhar’s tweet thread (bit.ly/2SSu8D7)
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun
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