## Monday 24 January 2022

### Computing years of lost life: why actuaries really need to be able to do counterfactual reasoning

Hugh Osmond recently put out this interesting twitter thread:

Although the average age of death in the UK is around 82, if a person reaches 82 then on average (i.e. without knowing any details of the particular person) the person can expect to live about another 8 years. We know the average age of a person dying from Covid is also 82, so it seems reasonable to assume that a typical person dying from Covid loses 8 life years. But, as Hugh points out, this reasoning is flawed. Hugh provides what is essentially an informal argument. In what follows we provide a formal explanation.

The question we are trying to answer is:

Knowing that an individual (let’s say it’s a man called Fred) has died from Covid at the age of 82, how much longer would Fred have lived if he had not got Covid?

This is a classic ‘counterfactual’ question. We want to know what would happen to Fred in an alternative world if something that happened in the real world (namely, getting Covid) was changed. And we want to take account of everything we can learn about Fred that will be unchanged in the counterfactual world from what happened in the real world.

Crucially, because we know that Fred died of Covid, we learn from the real world that (compared to the average 82 year-old) Fred is much more likely to also have had some critical pre-existing illness. And this knowledge must be retained in the counterfactual world.

As very well explained by Judea Pearl, answering counterfactual questions requires a causal model and an inference method that are beyond what can be achieved with traditional statistical methods.  In what follows we use illustrative and simplified assumptions to explain this counterfactual reasoning.

First, we need a causal model of the ‘real world’. Such a basic causal model is shown in Figure 1.

Figure 1 Basic causal model (for 82 year-olds)

This tells us that whether a person suffers a Covid death depends not just on whether the person becomes infected, but also on many other factors including whether the person has a pre-existing critical illness. Similarly, a person’s life expectancy depends on the same factors (among others).

When we assign prior probabilities to the nodes ‘Covid infection’ and ‘Pre-existing critical illness’, and conditional probabilities to the nodes ‘Covid death’ and ‘life expectancy’, then the causal model becomes a Bayesian network for which we can perform Bayesian inference.

In what follows we use the following assumed prior and conditional probabilities:

•  Covid infection: 1%
•  Pre-existing critical illness: 10%
• Covid death given Covid infection is false = 0%
•  Covid death given Covid infection and Pre-existing critical illness = 10%
•   Covid death given Covid infection and no Pre-existing critical illness = 0.1%
• The full set of conditional probabilities for life expectancy is given in Table 1

Table 1 Conditional probability table for 'life expectancy'

Changing any of these probability assumptions (within reason) does not change the thrust of the argument (readers are free to try out the model and make their own changes using their favourite Bayesian network software**).

With these assumptions we get the prior marginal probabilities shown in Figure 2.

Figure 2 Prior marginal probabilities

So, in the real world the median life expectancy of an average 82-year-old is 8 years.

But, if we know that an individual dies from Covid then, while obviously this means that ‘Covid infection’ must be true,  through Bayesian inference we also get the revised probability for ‘pre-existing critical illness’ shown in Figures 3.

Figure 3 Revised probabilities are observing Covid death

We can now use this new information about the probability this individual has pre-existing critical illness in a counterfactual world where he is not infected with Covid. The counterfactual model required for this is shown in Figure 4.

Figure 4 Counterfactual world

The ‘Covid infection’ and ‘life expectancy’ nodes in the counterfactual world are simply copies of the same named nodes from the real world model. They have exactly the same prior and conditional probability tables respectively. When we enter ‘Covid infection’ is false in the counterfactual world, we get the revised probability distribution for life expectancy. This individual has a median of 2 years life expectancy, rather than the 8 years.

The inference performed in this counterfactual model is not possible using the original model alone.

For more information on Bayesian networks and counterfactual reasoning see our book and short videos.

**The model used here can be downloaded and run in the free trial version of AgenaRisk (we declare an interest - Directors of the company that owns the software).

29 Jan update:  Here is a 5 minute video explanation on the above with an even simpler model (that can be downloaded by right clicking)

## Thursday 13 January 2022

### Debunking the hypothesis that the "healthy vaccinee" effect explains anomalies in ONS mortality data

In our previous report led by Martin Neil, we showed that ONS England data from November did NOT support vaccine efficacy claims once we adjust for obvious anomalies in the ONS data. Some, including the ONS themselves in their December report, imply that our conclusions were wrong because the anomalies we identified are caused by the so-called "healthy vaccinee" effect.

We examined the new ONS data and found NO evidence to support this claim. We have therefore produced a new and significantly revised report with our updated analysis.

The healthy vaccinee effect is the hypothesis that people closer to death are too ill to be vaccinated and so become concentrated in a shrinking unvaccinated population, thus increasing the group’s mortality rate.  This hypothesis to explain their anomalous data is stated on Page 5 of the ONS report:

Page 5: “The all-cause ASMRs for the year-to-date were lower in the first three weeks after a vaccine dose than in subsequent weeks after that dose. This could be because of a “healthy vaccinee effect” where people who are ill (either due to COVID-19 or another relevant illness) are likely to delay vaccination. Therefore, the people who have been recently vaccinated are, in the short term, in better health than the general population.”

However, this not only contradicts NHS guidance report ("Joint Committee on Vaccination and Immunisation: advice on priority groups for COVID-19 vaccination", Page 3), which states:

but is also contradicted by ONS on page 8 of their own report:

Page 8: "…the vaccination roll-out was also prioritised by health status of individuals, with the extremely clinically vulnerable and those with underlying health conditions being vaccinated earlier…

If the ONS hypothesis was correct then we would see:

a) The percentage of the unvaccinated in poor health rise as vaccine rollout progresses

b) A steady non-Covid mortality rate among the unhealthy (because they are dying at same rate as they always have done).

To support their claim the ONS released the percentage of 70-79 age group with "very poor" health in each vaccination category. Oddly, the vaccinated population contains a higher percentage of those in very poor health and this increases over time. Surprisingly the unvaccinated population has the LOWEST concentration of the unhealthy and the percentage declines over time:

In this unhealthy sub-population we found the non-Covid mortality rate for the unvaccinated is HIGHER than for the vaccinated. Both rates should be equivalent Again, we see unnatural spikes in non-Covid mortality just after vaccine roll out as seen before in whole population:

Therefore, those in poorest health were NOT more likely to remain unvaccinated. Also, there is a rise in non-Covid mortality, coincidental with vaccine rollout that is not only seen in the population as a whole but is also seen in those with the poorest health.

We conclude that the "healthy vaccine effect" cannot explain the anomalies we discovered in the ONS data and believe it is up to advocates for this hypothesis to now prove their case using the released data.

Full report:

Full url: https://www.researchgate.net/publication/357778435_Official_mortality_data_for_England_suggest_systematic_miscategorisation_of_vaccine_status_and_uncertain_effectiveness_of_Covid-19_vaccination

## Monday 3 January 2022

### No fancy statistics: a simple plot of vaccination rate against Covid death rate for all countries in the world

Using the "Our Word in Data" website we have extracted the latest snapshot for each country of total vaccinations per hundred people and total 'covid deaths' per million. The full data by country - in order of vaccinations - is listed at the bottom of this page (all numbers rounded to 0 decimal places).

We use inverted commas for 'covid deaths' because (as readers of this blog will know) this is a very vague metric and we have no confidence that it is accurate or consistently collected for any country in the world. If the data were accurate, and if the vaccines worked as claimed, then what we should see when we plot the vaccinations against deaths is something like this:

i.e. the more vaccinations in a country the fewer deaths.

Obviously there are multiple confounding factors (other than inconsistent reporting) that can impact on the relationship (timing when covid first hit, average population age, population density, geographial location, access to healthcare, etc) not to mention all the missing factors previously discussed**. Ideally the deaths should also be restricted to post-vaccination roll out (difficult to do that using the Our World in Data spreadsheet). But it is still surprising that the following is the actual plot:

All pretty random*** but note the high number of low vaccination, low covid death countries (mainly in Africa) as shown in this map:

But what it really shows more than anything is how poor all the 'official' covid data are (look at the laughable China data) and, because of the universally poor data, how little evidence there is of either the severity of Covid or the effectiveness of any covid interventions.

**As we have been saying since March 2020 all of the 'official' Covid data are essentially useless because they do not provide us with the necessary information to take account of all of the causal explanations for what is observed:

 Country total vaccinations per hundred total deaths per million Gibraltar 322 2968 Cuba 268 735 Chile 230 2035 United Arab Emirates 224 216 Iceland 209 108 Denmark 209 560 Isle of Man 208 784 Malta 208 922 South Korea 202 111 Uruguay 200 1771 China 197 3 Cayman Islands 196 165 Faeroe Islands 196 285 United Kingdom 195 2181 Ireland 194 1186 Portugal 191 1864 Belgium 186 2434 Seychelles 185 1324 Bahrain 185 797 Spain 184 1909 Italy 184 2278 France 183 1830 Austria 182 1520 Bermuda 182 1707 Canada 181 798 Israel 180 887 Cambodia 180 178 Brunei 179 222 Germany 178 1336 Norway 178 239 Qatar 178 211 Malaysia 176 961 Singapore 175 149 Finland 175 282 Sweden 173 1507 Cyprus 172 698 Argentina 168 2569 Greece 167 2005 Australia 165 88 Luxembourg 165 1429 Liechtenstein 165 1804 Mongolia 161 619 Kuwait 160 570 Mauritius 160 188 New Zealand 160 10 San Marino 159 2793 Japan 158 146 Switzerland 158 1397 Sri Lanka 158 698 Hungary 156 3934 Netherlands 155 1193 Brazil 155 2894 Turkey 155 968 Lithuania 154 2752 United States 153 2476 Aruba 153 1689 Ecuador 153 1881 Vietnam 151 322 Costa Rica 151 1429 Andorra 150 1719 Bhutan 148 4 Peru 148 6071 Thailand 147 309 El Salvador 147 585 Taiwan 146 36 Maldives 145 482 Saudi Arabia 144 251 Czechia 144 3374 Turks and Caicos Islands 144 586 Fiji 140 772 Slovenia 140 2693 Greenland 138 18 Iran 137 1545 Latvia 137 2443 Morocco 135 397 Panama 135 1696 Anguilla 134 264 Curacao 132 1147 Hong Kong 132 28 Dominican Republic 129 388 Monaco 126 835 Colombia 126 2533 Poland 124 2581 New Caledonia 123 971 Antigua and Barbuda 123 1195 Serbia 120 1840 British Virgin Islands 118 1282 French Polynesia 116 2251 Nicaragua 116 32 Croatia 116 3072 Oman 116 787 Uzbekistan 115 44 Estonia 115 1458 Mexico 114 2299 Slovakia 112 3046 Azerbaijan 111 818 Wallis and Futuna 108 631 Belize 105 1462 Venezuela 105 183 India 104 346 Barbados 104 904 Saint Kitts and Nevis 102 523 Cape Verde 102 625 Tunisia 102 2141 Indonesia 101 521 Montenegro 101 3844 Russia 101 2080 Trinidad and Tobago 100 2054 Rwanda 99 102 Philippines 98 463 Guyana 97 1318 Honduras 95 1037 Paraguay 95 2301 Kosovo 94 1678 Kazakhstan 92 959 Botswana 92 1020 Timor 89 91 North Macedonia 84 3752 Romania 83 3072 Suriname 83 2009 Bolivia 82 1661 Belarus 82 570 Albania 81 1116 Jordan 80 1205 Bangladesh 80 169 Laos 79 19 Bahamas 76 1796 Nepal 74 390 Pakistan 70 128 Grenada 69 1770 Ukraine 65 2354 Lebanon 65 1350 Tajikistan 64 13 Palestine 63 932 Georgia 63 3457 Guatemala 62 883 Sao Tome and Principe 62 255 Montserrat 61 201 Comoros 59 170 Myanmar 58 350 Saint Lucia 57 1600 Saint Vincent and the Grenadines 55 728 Armenia 55 2676 Bulgaria 54 4492 Egypt 51 207 Vanuatu 49 3 Zimbabwe 48 332 Bosnia and Herzegovina 48 3590 South Africa 46 1515 Mozambique 46 62 Moldova 44 2556 Jamaica 41 833 Libya 39 819 Iraq 34 586 Angola 34 52 Eswatini 34 1102 Kyrgyzstan 34 423 Lesotho 32 308 Equatorial Guinea 31 121 Namibia 29 1398 Algeria 28 139 Togo 28 29 Gabon 25 125 Ghana 24 40 Congo 23 63 Guinea 21 29 Uganda 21 69 Guinea-Bissau 21 74 Djibouti 20 189 Kenya 18 98 Cote d'Ivoire 18 26 Liberia 17 55 Central African Republic 16 21 Benin 14 13 Senegal 13 110 Afghanistan 13 183 Sudan 12 72 Sierra Leone 11 15 Gambia 11 138 Syria 10 156 Ethiopia 9 59 Somalia 9 81 Zambia 9 197 Malawi 9 120 Nigeria 7 14 Papua New Guinea 6 65 Mali 5 32 Burkina Faso 5 15 Tanzania 4 12 Niger 4 10 Cameroon 4 67 Madagascar 3 34 Yemen 3 64 South Sudan 2 12 Chad 2 11 Haiti 2 66 Burundi 0 3 Mozambique 0 22

***For those who place value in correlation coefficients for such relationships (we don't) there is a significant positive correlation of 0.31 between number of vaccines and number of deaths