Periodicity in cardiac admissions to A&E+
Additional slides for paid subscribers
I have been wondering what post to make to kick off the paywall series and my mind keeps wandering back to the strange, wave-like behaviour of cardiac admissions to A&E that we observed in previous posts. This ebb and flow wasn’t seasonal (more cases during winter) and seemed to have a periodic structure. I decided to utilise the CDS daily dataset spanning the period 1st November 2017 – 18th September 2021, this giving us 1,722 data points to play with. Counts of daily admissions were derived for those under 45 years of age and those aged 45 years and older in keeping with previous analyses; these two time series were run through a statistical technique called spectral analysis.
Spectral analysis is a method for determining if there are cyclical patterns in time-based data. For example, there is a strong weekly pattern to all elective surgery and we expect this to have a frequency of λ = 0.1429 within a daily time series. In case folk are wondering how on earth we arrive at this weird number (frequency is denoted by the Greek letter lambda) simply divide 1 by 7 on your trusty hand-held calculator. A frequency of λ = 0.1429 thus denotes a recurring 7-day cycle. If there was a 2-weekly cycle to surgical intake then the frequency would be 1 / 14 = 0.0714. With this in mind let is now consider two spectral plots called periodograms, one for the daily intake of cardiac cases <45y and the other for the daily intake of cardiac cases >=45y.
Figure 1: The first thing to note here is that great big red spike at a frequency just above zero. Its frequency is λ≈ 0.00115, which tells us there is a very long periodic component represented by an 868 day cycle or thereabouts. This equates to 124 weeks or around 28.5 months or around 2.4 years and means there is a long term trend in admissions for cardiac cases <45y. Of interest is the spike sitting at λ≈ 0.1429 – a figure we have just met! This represents a 7-day cycle for such admissions. There are a few small spikes beyond this that represent high-order harmonics of 2 – 3 days, almost as if good day-bad day flip-flops along.
Of interest here is the strong weekly component and it’s worth us asking why we see such a pattern in what are supposed to be emergency admissions occurring at any time. I can only think that some form of administrative function is being superimposed. The longer term trend of ~2.4 years is also interesting for this is not far off the 2.6 year harmonic of the solar sunspot cycle. This may sound wacko but there is a decent body of research linking solar cycles to cardiac conditions – something I may touch on at a later date.
Figure 2: In this slide for those aged 45 years and older we see the same low frequency spike of 2.4 years that may connect the ebb and flow of these cases to the solar cycle (or not!). We also observe the 7-day cycle at λ≈ 0.1429. What is different is that whopping great spike at λ≈ 0.2857 which represents a 3.5 day cycle, being exactly half of the 7-day cycle and thus a harmonic. This would suggest a strong weekly administration function, almost as if an interlocking week A – week B pattern. Why this is so we can only speculate but one thing is for sure and that is emergency admissions of cardiac cases are not flowing in a random manner over time and I find this most curious.
Hi John - what exactly is the CDS daily dataset?