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:

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).

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.

Figure 2

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.

Figure 3

Figure 4

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.