More on trends
Last week I wrote this on trends in hospitalisations in England for Covid-19. That was using data that is released daily by the National Health Service here.
There were at least two points to the exercise — one was to see whether trends were exponential, and the other was to see whether an automatic trend selection algorithm may help with detecting when trends are beginning to change.
We hope that trends are beginning to change, because that may well indicate that policy measures are taking effect. If the log of a time series has a split trend, where the more recent part of the trend is flatter, then that suggests that the daily percentage growth rate is less — good news. If that continues to happen, then it suggests that the data are no longer growing exponentially — a log trend is no longer appropriate.
To illustrate, here’s cases as reported by the government, by specimen date, with a log trend:
Since August 17, cases have been growing at about 5% a day, and are now over 10,000 daily. While that is worrying, it’s worth noting that cases, back when mass testing wasn’t in place, in March, were growing at a rate well over 20% a day.
The same is true when it comes to hospitalisations, when we piece together the two data sources the NHS provides:
Growth in March was 12%, and if you take the green line to be a reasonable estimate of the trend (I do have some doubts from eye-balling), then it’s been just shy of 5% since mid-August. I think eye-balling that potentially suggests that the trend remained negative until the end of August before turning positive then — a few weeks after cases had done.
Since posting last week, I’ve been updating daily, and tweeting the graphs, in case you want the daily update (hope that trends turn, or morbid fascination, you choose). Here is today’s, the October 5 update. First for all of England:
In the last few days, the trend has wavered between being solid upward, to having this kink around September 14. This is an algorithm finding a trend that is consistent with a procedure trying to find what is “best”, statistically. What is “best” statistically differs from person to person, and so this isn’t the gospel. But it suggests that some of the measures at a national level may have had some impact on slowing hospitalisations in mid-September.
Around the regions there is, of course, rich variation. The charts are all below:
The North West, which has had stricter restrictions in place longer than anywhere else, remains on a grisly 6.6% trend that it’s been on since August 16. While it begs the question what effect have the restrictions had, it also begs the question of how bad might it have been without any restrictions?
Both the North West and North East appear to be adding 100 Covid-19 hospitalisations a day now, and if that continues to grow at 5–6%, we will surely start to hit capacity constraints soon.
The England trend of a seemingly slightly flattening rate of growth is perhaps driven by London and the Midlands, which both plausibly have plateaued in the last ten days or so.
