There is no 'seemingly' about it. That's precisely what your data show - cases peaked before lockdown.
As I said, and as you have conceded in response to Mikeey's comment, it was a plateau, not a 'peak'
Right - in that case, your data is skewed and we can deduce that cases peaked 3 days earlier than your graph shows.
It's not 'skewed', it is what it is intended to be, namely "the mean of the most recent 7 days" - which, as I suggested is probably the most appropriate sort of average for a purpose like this.
Any form of averaging over days obviously 'distorts' the data to some extent, and it doesn't really matter which one is used, since one cannot 'please all of the people all of the time', and anyone who knows what they are looking at can 'adjust' the dates by 3-4 days if they would prefer the other type of MA - but some sort of smoothing of the day-to-day variation is really needed.
However, I personally think that the way I've done it is probably the less potentially confusing ... imagine a (different) situation in which was expecting some fairly large change to show itself on the day after some intervention. If one useda 7-day average centred on the day of the intervention, then one's data would show 'the effects of the intervention' as starting to be seen 3 days
before the intervention - which would be a little odd.
This adds a further skew to the data, also meaning that cases peaked another few days more before lockdown since test reports always lag specimen days by varying amounts (about 3 days, give or take, depends on weekends), and is sometimes quite lumpy.
I've explained why I routinely use 'reported date' for cases but, as you say, if one uses specimen dates (which one can only do retrospectively), it will move the curves about 3 days 'to the left'.
You must also not use reported date for deaths, since these have an even bigger skew, sometimes up to 2 weeks.
My death figures are PHE (or equivalent for other UK countries) "28day Deaths", not ONS ones. Whilst obviously imperfect, there is no significant lag, the figures attempting to relate to the actual number of qualifying deaths in the most recent 24-hour period. We know that these figures are pitifully low at weekends and bank holidays, but they 'catch up' on the day after the weekend/holiday, so the 7-day averaging takes care of that. Similarly, the hospital admissions figures are allegedly 'real-time' (most recent 24 hours) ones.
I leave it to you to decide whether or not it is pedantry. I merely presented a graph I already had to illustrate what I've been saying about the November lockdown.
However, pedantic or not, as I suggested previously, you do seem to have shot your argument fairly well in the foot ... if one does as you would like (use specimen date for 'cases' and used a 7-day average centred on the displayed date, then what one gets is:
This shows 'cases' rising until about a week after the onset of the lockdown, whereupon the fall starts, which is precisely what one would expect if the fall was the result of the lockdown. You comment that:
... and then introducing another assumption that it would take 'well over a week' for an effect to be shown
... and maybe I should have said "at least about a week", but that
IS what we expect. The average interval from exposure to onset of symptoms is around 5-6 days, and it usually takes a day or two after onset of symptoms or a test to be arranged, undertaken and a result obtained - so, if a lockdown does have an effect on new case numbers, one would not expect to see it until a week or so after the start of that lockdown. Furthermore, although you wrote:
I also mistrust the small secondary peak in the case data - the data is real enough, but it's not reflected in the death count which is most reliable proxy for cases. We would expect them to track, and this is an anomaly ...
... both the peak and the subsequent trough of the deaths curve above occur 3-4 weeks after the corresponding peak and trough of the 'cases' curve, which is what one would expect, isn't it?
... and you are one trying to demonstrate not only correlation but causation. It may be there, but you'll need to do some more accurate analysis.
As I'm sure you are aware, it's never possible to conclude causation from correlation by any sort of analysis of observed data, no matter how 'accurate' that analysis, and that it
not what I am 'trying to do'.
I'm rapidly coming to regret that I did, but I presented the graph of the November lockdown simply to illustrate graphically what I (and I would imagine the vast majority of others) already 'knew' (on the basis of common sense and knowledge of how viruses are transmitted) - and I don't really understand why you don't also 'know' it (i.e. why you are sceptical).
We surely both know that the virus is transmitted by contact or proximity between people (or, less commonly by contact with an object that has been exposed to an infected person)? If we know that, it surely is inevitable that if we introduce measures which reduce that inter-personal contact/proximity, then that will have the effect of reducing the amount of transmission, hence the number of new cases (and all that follows therefrom). One surely doesn't need any mathematics, or even data, to understand that?
You recently started talking, by implication, about 'strategies', and not all strategies require control/reduction of the number of new (or prevalent) 'cases' (quite the converse for some strategies). Some of these strategies therefore do not require NPIs (whether 'full lockdowns' or whatever), but if one
does introduce NPIs then (without the need for any maths to support the fact), one
will inevitably get a reduction in new cases.
This all seems so obvious to me that I struggle to know how to sensibly quiz you further about your viewpoint! If you are truly unconvinced that lockdowns reduce cases, what mechanism/mode of transmission do you envisage would cause the number of new cases arising during a lockdown to be the same as had been the number prior to the lockdown?
Kind Regards, John