Spectral Analysis Of In-Hospital Deaths
I utilise an engineering tool to investigate periodicity within in-hospital deaths over the period 2017/w1 – 2021/w36 using EPR data supplied by an undisclosed NHS Trust
I was certain I had introduced readers to the dark art of spectral analysis before now but a quick search through my archive of 288 articles says not. This doesn’t exactly surprise me for it’s a bit of an odd fish to be throwing about in the field of medical research, but I am hoping that by the end of this article you’ll be as enthralled as I am!
Preamble
Spectral analysis is a familiar tool to sound and electronics engineers who work with oscillating signals over time. The simplest explanation I can offer is that it is a mathematical technique that detects periodic frequencies that may be embedded within a complex waveform. ‘Periodic’ simply means regular, like a tuning fork that sounds a regular tone at the international concert pitch of A = 440Hz when struck. If we took a tuning fork into a loud and brash New Year party and recorded the mayhem on our smartphone then spectral analysis would reveal that pure tone hidden within all the chatter, clatter, thumping, popping, clapping, slurping and stomping.
Spectral analysis software usually churns out graphical output in the form of a Periodogram, but before we gawp at one of these let’s have a look at an equivalent frequency analysis plot for a standard A = 440Hz tuning fork that I recorded on my cheapo Android whilst Mrs Dee was typing at her workstation and spooning ice cream from a small bowl, and whilst a robin was tweeting in the cherry tree outside my office window. The resulting sound file was passed through Adobe Audition sound editing software and a few buttons pressed:
Ain’t that funky? Along the x-axis we’ve got frequency (Hz) and up the y-axis we’ve got the sound level in decibels (dB). That first big spike on the left is sitting at f = 439.68Hz, which is pretty darn close to the international reference of A = 440Hz for a knackered old fork of 40 years standing! The second whopper spike is sitting at f = 880Hz, this being the octave; and so on, and so forth in multiples of 440Hz all the way up to f = 3520Hz. These represent the harmonic series of the tuning fork and give it that characteristic woooooo sound.
Eagle-eyed readers will note some odd-looking spikes that are nothing to do with the fork. There’s one sitting at f = 140Hz and a cluster around f = 1000Hz - 1400Hz. The former is the frequency of the hum of my workstation CPU fan and the high frequency cluster are produced by the deep-throated robin outside my office window. You could say that we are sound-sleuthing!
From Forks To Deaths
With all that in mind let us now flip to thinking in terms of daily, weekly, monthly and annual in-hospital deaths. These are four different sampling rates over which counts can vary. Deaths per week is a rate of ‘vibration’ just like the cycles per second (Hertz) of the tuning fork. If we consider monthly deaths and these were strongly seasonal (e.g. influenza) then spectral analysis (a.k.a. frequency analysis) would show a dirty great spike at a frequency of f = 0.083. Why that weird number? Well, because there are 12 months in a year and 1 / 12 = 0.083. In geek speak the span of 12 months is the wavelength (a.k.a. period).
If we now consider weekly deaths and these were seasonal then spectral analysis would show a dirty great spike at a frequency of f = 0.0192 since 1 / 52 = 0.0192. Equally, if we consider daily deaths and we see a spectral spike at f = 0.143 then this would indicate a weekly cycle within the death tally since 1 / 7 = 0.143.
Please do bear in mind that a ‘cycle’ doesn’t just mean an upturn in deaths, for downturns can also be periodic just like the sides of a tuning fork waver in and out to produce the pressure wave we experience as sound.
Folk with backgrounds in physics will consider these regular perturbations to be resonances, and time series data of any flavour can exhibit resonances just as well as sound-waves or light-waves. With that all said and done I suggest we take a look at some periodograms of the in-hospital death data I have been analysing in earnest since May to see what resonances may exist.
But Why Even Bother?
Because - setting seasonality aside - death is supposed to be a random process occurring any time of day or night and on any day of the week, is it not? So what if we picked up an unexpected weekly periodicity, or perhaps quarterly? That would be mighty curious indeed and would smack of death to order, so we better go take a look…