Calculating the break line

Fluctuating daily coronavirus figures make it hard to keep track of the underlying trend. In the last week alone the number of cases per day has ranged from 5,600 to 8,800. It’s hard not to be alarmed by the kind of sudden leap we saw on Saturday, when the 8,868 reported cases represented the second highest level this year. But Saturday’s increase was consistent with the trend of the last few weeks and less dramatic in percentage terms than Wednesday or Thursday, when the number of cases was 25% higher than a week earlier.

Reported infection numbers follow a weekly cycle, with a low point on Tuesday, a rapid rebound on Wednesday and a peak on Friday or Saturday. A more useful measure than day-to-day shifts is to compare numbers against the previous week, work out the percentage increase and then calculate the average over the last seven days. This weekly average has been gradually declining since March 17, when it reached 25.6%, and on Sunday fell to 15.2%. An upward ripple in midweek following the high figures on Wednesday and Thursday was balanced by an exceptionally low increase of 2.6% on Friday.

The third wave has behaved differently from the first two, when a rapid rise of 45% or more for a few weeks prompted a hard lockdown, which in turn triggered an equally swift decline. We are still living with the legacy of the catastrophic misjudgments in September and October, when the weekly average showed an increase of between 35% and 70% for 42 straight days until October 19 – five days after the government belatedly imposed a partial lockdown. In February and March we have seen a slower but longer upturn, with the weekly average increase peaking at just over 25%. This suggests the lockdown, though less effective, has made a significant difference, but the more virulent strains of the virus that originated in the UK and South Africa have been harder to contain.

Where did it all go wrong? Here, basically: September 8 to October 19, 2020 …
… when 60% weekly increases were not exceptional and the ‘answer’ was to shut the bars an hour early.

Any increase in infections during a lockdown is a bad development, but the first shift in the right direction is a slowdown in the growth rate. This is where the break line is useful. Because cases fluctuate so much from day to day, a small or moderate increase in midweek may actually be a positive sign, while a small decline at the start of the week can mask the fact that the underlying trend is upwards. The break line is the mark at which the increase in cases is unchanged from the previous day. If the headline figure is above the break line, the rise in cases is accelerating; if it comes in lower, it’s an indication that growth is slowing down. It doesn’t mean things are getting better, but it does mean they’re not getting any worse. We can only speak of an improvement once the numbers start declining week on week, at which point the break line arguably becomes redundant.

Calculating a rolling seven-day average is pretty straightforward. Every day you take out the number from seven days ago and replace it with today’s figure. The break line represents what the number of infections would be if the weekly percentage change from seven days ago were replicated, leaving the average unchanged and the growth rate static. That makes it possible to calculate the break line for the next seven days. Some break lines represent bigger week-on-week increases than others: on Wednesday and Thursday next week, for example, the break line is 9,750, which would rightly be seen as cause for serious concern. But if the actual increases on those days are smaller, the break line for the following week will reflect this declining trend. The purpose of the break line is purely to show whether the growth rate is accelerating or slowing down, regardless of any desired or predetermined target level. So for the upcoming 7 days we have:

Monday (29/3): 7200
Tuesday (30/3): 6350
Wednesday (31/3): 9750
Thursday (1/4): 9750
Friday (2/4): 7800
Saturday (3/4): 10250
Sunday (4/4): 8000

One small complicating factor is that every day a number of cases – anything between 30 and 100 – are deducted from the total as ‘corrections’. These cases are included in the daily headline figure but not in the overall numbers, which I fix by subtracting them from the daily figure after the numbers have been published. That means the percentage increase is always inflated, sometimes by as much as 1%, while the weekly average is distorted by a smaller amount – typically 0.1% to 0.2%. To reflect this, and the fact that calculating the break line is an imprecise exercise anyway, I round the break line figure up by between 30 and 80, to the nearest 50.

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