Stats Chat

There are lots of questions about the current pandemic that need expertise in microbiology or international freight logistics or sociology or whatever, but there’s the occasional one that is basically statistical.  In particular,  lots of people would like to know how bad COVID-19 actually is: what’s your (or your kid, or your grandmother’s)  chance of needing hospital treatment or dying?  This post will try to explain why we don’t know the answer, and aren’t going to know the answer for a while, although there are some questions that sound similar where we do know the answer or will know fairly soon.

The mortality rate (case fatality rate) for a disease is the number of people who die from it divided by the number of people who catch it.  For the initial outbreak in China we have a reasonably good idea of the number of people who died (at least if you trust the PRC statistics), and the rest have recovered. We don’t know how many people were infected; the health system had more urgent things to do than testing apparently healthy people. The same is likely true for some of the smaller outbreaks in other Asian countries.  In the rest of the world we don’t even know the numerator of the rate, because most of the people who have been sick are still sick and we have to wait to see how many recover and how many die.

To some extent the mathematical epidemic models can work around this problem.  If people with few or no symptoms are still infectious,  they’ll contribute to the growth of the epidemic, and the number can be estimated from the shape of the epidemic curve.  That doesn’t work perfectly, but it works to some extent.  However, if people with few or no symptoms are less infectious, they’ll tend to be missed. People who have no symptoms and who don’t pass the virus on are invisible to the models, at least until there are enough people like that to get herd immunity working.  This post on Andrew Gelman’s blog looks at two fairly sophisticated modelling attempts, which don’t agree all that closely.

In the long run, it will be possible to get a reliable estimate of the number of people who have been infected, because they will end up with antibodies to the virus, and someone will develop a test for the antibodies and apply it to a suitable population sample.  That sort of data goes into the mortality rate estimates for flu: the mortality rate among people who develop classic, serious, flu symptoms is quite high, but there are a lot of people who are infected without ever knowing it — as much as 10% of the population — so the mortality rate among everyone infected is very low. In the same way, the retrospective mortality rate of COVID-19 will likely be lower (by some unknown factor) than the current ratio.

We do have reasonably good information on what happens to people who get sick enough to need medical attention, and  we know how that number grows with good or not so good control efforts. That’s the number that matters if you get sick. But we don’t know as much as we’d like about the structure of the epidemic and how many people will eventually get seriously ill, because we haven’t been able to find and count the subset of basically healthy cases.

Team Ratings for Round 7

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 40 matches played, 25 of which were correctly predicted, a success rate of 62.5%.
Here are the predictions for last week’s games.

Predictions for Round 7

Here are the predictions for Round 7. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 14

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 78 matches played, 52 of which were correctly predicted, a success rate of 66.7%.
Here are the predictions for last week’s games.

Predictions for Round 14

Here are the predictions for Round 14. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 14

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 89 matches played, 69 of which were correctly predicted, a success rate of 77.5%.
Here are the predictions for last week’s games.

Predictions for Round 14

Here are the predictions for Round 14. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 1

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Predictions for Round 1

Here are the predictions for Round 1. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

From the Herald (and from the front page in the squashed-trees edition)

I’m not disputing the basic message that people being stabbed is bad and we’d like less of it.  And it’s good that numbers are being given, but there’s at least three issues with those numbers.  On top of the familiar “quote a total over four years because it’s bigger”.

The first is that the numbers don’t refer exclusively to “Aucklanders”.  As the story says

But a spokeswoman noted it was a regional 24/7 trauma centre for patients around Auckland and Northland, meaning many of the most serious trauma cases were directed to Auckland Hospital.

And secondly, the definition of ‘stabbing injury’ varies by DHB: Auckland DHB was reporting only stab wounds from assaults and self-harm, but

Counties Manukau chief executive Fepulea’i Margie Apa said the DHB’s figures included all stabbing injuries from any cause, “not only those from violence”.

Are there many cases of accidental stabbings? Well, we regularly get told about carving-knife accidents at Christmas, and about ‘avocado hand’, so there are some, but it’s hard to guess how many.  If you were doing this seriously, you’d come up with a list of relevant ICD-10 categories and ask the DHBs for numbers in those categories, but that takes medical knowledge and might risk a ‘too hard’ refusal from the DHB.

The third issue is going from 1750 in four years to “at least one every day”.  On average, there were about 1.2 events per day.  At that rate it would be really surprising (and newsworthy) if there was at least one every day. You’d expect them to clump more than that.

The simplest mathematical model for counts of events is the Poisson process, which has no ‘built-in’ clumping: it describes a world where there are no high-risk days (hot, humid Saturday nights? Bad sports results?), and where all stabbings are independent (no multiple-stabbing fights or robberies).  Even under the Poisson model, you would expect about 30% of days to have no stabbings.   In the real world, you’d expect more days with two or more stabbings and more days with zero.

Getting less clumpiness than a Poisson model takes some sort of conspiracy.  The best-known NZ example is two-dimensional (space) rather than one-dimensional (time), as in this photo by Flickr user Alexander Kesselaar

Glow worms in a cave spread out more evenly than a Poisson process would predict, because they keep away from each other. Stabbings probably don’t

Team Ratings for Round 6

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 33 matches played, 19 of which were correctly predicted, a success rate of 57.6%.
Here are the predictions for last week’s games.

Predictions for Round 6

Here are the predictions for Round 6. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 13

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 72 matches played, 47 of which were correctly predicted, a success rate of 65.3%.
Here are the predictions for last week’s games.

Predictions for Round 13

Here are the predictions for Round 13. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 11 Postponed Match

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 88 matches played, 69 of which were correctly predicted, a success rate of 78.4%.
Here are the predictions for last week’s games.

Predictions for Round 11 Postponed Match

Here are the predictions for Round 11 Postponed Match. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

I wasn’t going to post about this, but I’ve seen two good Kiwi journalists retweet versions of this today already and I’m having a sense of humour failure about it.

A US public relations company did a phone survey. They don’t describe the methodology very clearly (a bad sign), but suppose we assume for the sake of argument that it was competent.  They don’t given the exact question they asked (also a bad sign), but their conclusion was

• 38% of beer-drinking Americans would not buy Corona under any circumstances now

Ten years ago, I lived in the US and would have counted as a ‘beer-drinking American’ for phone survey purposes.  I would probably have answered ‘Never’ to a question on whether I would buy Corona.  Strictly speaking, that might have been an exaggeration (and let me point you to one of the great 1980s Australian beer ads as a possible counterexample), but as far as I recall I didn’t ever buy Corona.

Lots of ‘beer-drinking Americans’ don’t buy Corona because they don’t like the flavour or because it’s advertised for a different social group, or whatever. It wouldn’t be surprising if that came to 38% who always preferred Bud or Molson or Coors or Mirror Pond Pale Ale or PBR.

The survey also asked people who usually drank Corona (clearly a minority of the respondents) whether they would still drink it. 4% said no. Unless your survey is exceptionally well conducted, that’s down at the level of alien abductions and lizard people.

The CNN story also referred to a YouGov survey that said the ‘intent to buy Corona’ was at the lowest level in two years. Here’s the graph

Intent to buy Corona is down about one percentage point from Christmas and maybe two-tenths of a percentage point from October.

While I’m on the topic, I’d like to point out the Infodemic blog. It goes into great detail (with animated gifs and so on) on simple ways to fact-check claims about coronavirus — or anything else.   It’s the same sort of techniques that I use in writing StatsChat, but Mike Caulfield explains them patiently and carefully and I just try to show how I use them.