The Imperial College Study: Part 3B

[Links to the full series]

Part 1
Part 2
Part 3A
Part 3B

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1. How were the CFR and IFR calculated for the Imperial College study?

Since the Imperial College study is a microsimulation, it was simulating a whole population and hence needed to use an IFR, not a CFR. It got an IFR from this study: https://www.medrxiv.org/conte…/10.1101/2020.03.09.20033357v1

Let's look at how this study came up with their numbers:

The report estimated the CFR and IFR based on three different datasets and using multiple techniques in order to validate the results. They looked at data from mainland China (70,000+ cases as of February 11th, then cross checked with latest results as of March 3rd), data from the Diamond Princess cases, and data from cases being tracked outside China (about 2000 cases as of February 25th).

My description of their techniques is going to be very much an oversimplification because I find it hard to describe the statistical techniques employed in a short space. Here's my understanding of some of the key features of the technique used for the mainland China data:

1. They broke the population into 10 year age bands and assumed that covid-19 would attack each age band equally.
2. They took the actual age demographics of the infected areas and projected how many people should get sick in each age band.
3. The looked at how many people were diagnosed as sick in each age band. For the younger age bands, this was fewer than projected given an equal attack rate. This gave them an age-band-specific underreporting amount.
4. Most of the fatalities were in Wuhan, but Wuhan had a much higher fatality per reported case than mainland China. They assumed this was due to hospital overcrowding causing milder cases to get turned away, so they added in a further factor representing hospital overloading to scale down the Wuhan numbers to be in line with the rest of the Chinese numbers.
5. For each age-band, they then identified which CFR that--given the onset-to-death times which were observed--would have produced the observed total cumulative deaths as of the most recent data, given the underreporting factors that they identified.
6. They then aggregated these age-band specific CFRs into a population-wide CFR, which turned out to be 1.38%. Note, though, that this number is specific to the Chinese age demographics.

To estimate an IFR from this CFR, they used data from people repatriated out of China back to their homelands. All of these people were tested, and it was discovered that there were about as many asymptomatic people who tested positive as there were symptomatic people who tested positive. This led to the final IFR for the Chinese outbreak being estimated at 0.66%. I should note here, though, that the data sample size here was particularly small: a total of 6 asymptomatic people who tested positive from those flights.

To validate their IFR using the Diamond Princess data, they took a timeline of onset-of-symptoms for the 705 diagnosed passengers on the cruise. Then applying their age-specific onset-to-death results on the actual ages of the diagnosed passengers, they projected that by March 5th, between 3 and 14 people should have died if their IFR was correct. Since 7 passengers had died by that date, the Diamond Princess case was judged to be consistent with their results.

To separately estimate a CFR from all of cases outside China, they used two different methods, neither of which I have looked into enough to understand. At the time this study was done, this was a pretty small sample size (1334 cases out of 2000+ met their inclusion standards). Also, they didn't have individual-level onset-of-symptom or recovery data for a lot of those cases. For these two reasons, the CFR estimates cover a wide range, from 0.4% to 7.2%, with 1.2% being the best fit to the data. This basically validated the reasonableness of the 1.38% result from mainland China.

2. That's a lot of information. What's the bottom line for the Imperial College study again?

What the Imperial College study took from all of the above is that the Covid-19 IFR is about 0.66% for Chinese demographics. They also took the age-specific IFR from the study and applied it to the older Great Britain demographics to get an IFR that they used for their simulations of 0.9%. They also used the onset-to-death time periods and the percentage of hospitalizations from that study (which I didn't get into here but was another thing calculated from the same data).