Methodology for Estimating Excess Mortality #2
The pursuit for the most robust and reliable model continues... Polynomial fitting to the cumulative series.
In this article, I set out the fundamentals of my first attempt to produce the most robust and reliable model for estimating excess mortality:
Methodology for Estimating Excess Mortality
Introduction There are many different ways to estimate excess mortality which, in very simple terms, is the difference between expected deaths and actual deaths. As it happens, the process is not at all simple as both datasets are fraught with error.
After rather intense peer review, mainly centred around my concerns of not capturing convexity in the mortality distributions of the younger cohorts, potentially resulting in over-estimation of excess deaths, I have made a material change to the model.
Instead of starting with a linear fit of the periodic data to guide the choice of polynomial order fit to the cumulative data, I am working the other way round.
In all cases, I fit a 3-order polynomial to the cumulative series to capture all potential dynamics (exponentially increasing, linear - increasing, flat and decreasing, S-shape and exponentially decreasing). All of these shapes are possible due to the Gompertz-like nature of the mortality distribution from birth to old age.
I then reverse engineer the periodic baseline from the cumulative one and compare that to the actual periodic data. As usual, I do this for each single year of birth and then aggregate afterwards for convenience (Figure 1).
As it happens, the unintended and unexpected outcome of this change is actually to better capture the concavity in the older cohorts which dominate the aggregated series.
This also results in a substantial increase in the overall excess mortality (Figure 2) compared to my first methodology, albeit with the same inflection points which is reassuring.
However, this method also better captures the convexity in the younger cohorts, perhaps suggesting that my concerns of over-estimating those excess deaths were justified (also reassuring), and also reveals that the youngest age cohort is subject to registration delay just like the others.
A new bulletin will necessarily follow, using this new methodology.
Methodology #3 is in process, relying on Gompertz fit instead of polynomial which should be even more robust because polynomials, especially higher order ones, can have a habit of producing unreasonable projections due to amplification of anomalies in the underlying data.
I may or may not wait for longer term data for this revision.
It reads like poetry to me, all these stat terms and notions, none of which I understand. But I can read your language and infer from that your absolute desire to cut out bias and arrive at an outcome that is as close to the “truth” as possible. And I can “read” your graphs 😉 thanks for all that unrelenting work❤️
Mr. Smalley;
Could you provide information on current "All cause mortality" for Canada? Stats Can nolonger seems to provide this. And the "Excess Mortality" is confusing for lay people like myself.
The coarse data like ACM is perhaps less scientific, but certainly enough for ordinary people when we know what the Historical numbers were.
Thanks
Paul