The Office for National Statistics (ONS) have released the latest data from their COVID-19 Infection Survey, looking at the characteristics of people more likely to be infected with the Omicron variant compared with the Delta variant.
Dr James Doidge, Senior Statistician, Intensive Care National Audit & Research Centre (ICNARC); and Honorary Associate Professor, London School of Hygiene and Tropical Medicine, said:
“This is an obtuse and unintuitive way of analysing data that significantly limits the conclusions that we can draw from it. The key thing to note is that the entire analysis is among those who test positive (for any variant). Among positive cases, the more doses of a covid-19 vaccine that you have, the more likely it is that the infection will be Omicron (technically, Omicron-compatible) rather than Delta, and similar with prior infection. This indicates that the risk of breakthrough infection or reinfection is increased with Omicron compared with Delta. But how much are they increased? It is impossible to tell because the baseline risk with Delta is not shown and anybody not infected at all is excluded. It would be a misinterpretation to look at Table 1b and assume this means that risk of infection increases with more vaccine doses or with prior infection – that is not what the data are showing.”
Prof Kevin McConway, Emeritus Professor of Applied Statistics, The Open University, said:
“It’s good to see these new results from the ONS Coronavirus Infection Survey (CIS). CIS estimates are based on PCR tests carried out in a representative sample of the UK community population aged 2 and over, ‘community’ meaning that it doesn’t cover people living in communal or institutional places such as care homes or prisons, but the community population makes up the overwhelming majority of the total population. Most of the figures that have appeared so far on Omicron-variant infections in the UK have been based on the results of tests carried out through the testing services whose primary purpose is to detect infected people, to advise them to self-isolate, or to trace their contacts, or to manage them appropriately in hospital. Those results can be subject to biases if the numbers or types of people that present themselves for testing change, as they have been doing recently, but the results from the CIS will not be subject to those biases.
“That said, these new results do need to be interpreted with considerable care, for several reasons. Perhaps the most important reason for caution is that they are based on only a fortnight’s data from the CIS, from 29 November to 12 December, which is all that’s available so far since there were first enough Omicron cases available for statistical analysis. The number of people included in the analysis is not particularly high, as these things go – in all it is based on data from 1,701 positive tests, and of those, only 115 gave PCR results compatible with the Omicron variant (while, for this analysis, the remaining 1,586 are taken to be probably compatible with Delta). So there’s inevitably a lot of statistical uncertainty. Also, because these results are from close to the start of the Omicron wave, we just can’t be at all certain that the findings will continue to apply in the same way as time goes on and Omicron cases (presumably) continue to rise and move further through our communities.
“You might perhaps be wondering why there were only 1,701 tests for analysis, when the CIS tests something like 100,000 people each week. The reason is that the data for these analyses are only from people who tested positive for the virus during that period, so there are no comparisons with people who did not test positive. The results here look at how the chance of having an infection compatible with being Omicron rather than Delta varies according to various personal characteristics, in people who test positive. So they say nothing at all about how the chances of testing positive for Omicron or for Delta are varying over time in the community population as a whole, or how the Omicron and Delta infection chances compare in the population as a whole. Nothing in this data release says anything about how fast Omicron infections are growing in the country. Doubtless there will be CIS results relevant to that sort of question later, but this release doesn’t give them.
“I should also point out that, for reasons that I consider sensible and appropriate, these results are not based on all the positive tests from the CIS during the fortnight in question. The results are not based on sequencing the full virus genome from the positive swab tests, but instead on what some have called a lucky feature of the mutations in the Omicron variant. The PCR tests used for the CIS look for fragments of viral material from three different genes, called (for short) S, N and OR. The mutations in Omicron mean that the S gene has changed enough so that the PCR tests cannot detect it – so a test result that finds OR and N but not S is compatible with an Omicron infection. However, one of the reasons the tests look for three genes and not just one is that, if the amount of virus in the sample is small, the test might fail to detect a gene even though it is present in very small amounts. This means that it is not appropriate to use the absence of an S gene in a positive result as an indicator of Omicron, if the amount of virus is low (as indicated by the Ct value being 30 or more – high Ct values indicate low viral load). Therefore the analysis is based only on so-called ‘strong positive’ test results where the Ct value is less than 30. And, because failure to detect the S gene could possibly happen in a few cases where the variant is Delta rather than Omicron, ONS are careful to refer to “infections compatible with the Omicron variant” rather than simply “infections with the Omicron variant”.
“Given all those provisos and explanations, what were the findings? I think they are summarised pretty well in qualitative terms in the ONS statement. For example, ONS say, “there is some evidence to suggest that people who test positive for COVID-19 and report being from ethnic minorities are more likely to test positive with infections compatible with the Omicron variant compared with those who identify themselves as White.” What this doesn’t say is how much more likely an infection is to be compatible with Omicron in people who test strongly positive and report that they come from an ethnic minority, compared to the chance of the infection being compatible with Omicron in people who test strongly positive and report that their ethnicity is White. Some estimates of the quantitative differences are given in the data file that comes with this ONS statement, and I’ll say more about that under “Further information” below, but it’s really important to understand that these results don’t say anything directly about the chance the a person from an ethnic minority, in the community population, will test positive (or that a person with White ethnicity will test positive).
“But the upshot is that, in my view, at this stage there’s inevitably so much statistical uncertainty in the figures that looking at these numerical details isn’t really very helpful in my view. In any case, some of the most striking characteristics in this report, such as differences between regions and nations and between urban and rural residence, are likely to change quite quickly as Omicron becomes dominant across the country because of its very high infectivity.
“What is less likely to change, in terms of what we know so far, is that the chance of a strong positive test result being due to Omicron in someone who has previously been infected is a lot higher than the chance of a strong positive test result being due to Omicron in someone who had no previous infection. Again, though, these data tell us nothing at all about what the chance of a reinfection (with Omicron or with Delta) is for someone in the population as a whole, because these results are based only on data for people who tested positive and say nothing about infection chances in the population as a whole.
“The same goes for the results on vaccination. These results indicate that, for people who test positive after three vaccine doses, the chance that their infection was Omicron rather than Delta is a lot higher than for people who test positive after not being vaccinated at all. But they say nothing about what the chance of testing positive (from either variant) actually is, for fully vaccinated or unvaccinated people. You just can’t make that comparison at all using these data, because they do not report how many people in the overall sample did not test positive. We already know that two vaccine doses plus a booster provides good protection against infection with Delta, and the evidence so far (from other sources) is that two doses plus a booster also provides reasonable protection against Omicron, but not so good as against Delta. ONS point out in their statement that “individuals who had received at least one dose of a COVID-19 vaccine continued to be less likely to test positive for COVID-19, regardless of variant”, and personally I have no doubt that that is true, but this ONS data release doesn’t give us the actual numbers to support that. No doubt they will appear later.
“Just to see how the numbers work, and how (on the basis of the small amount of data so far) the detailed numbers don’t tell us anything very definite, I’ll say a bit more about those numbers classified by ethnicity. The data sheet tells us that 1,658 people who reported they had White ethnicity produced a strong positive test result in the fortnight in question, and of those, 92 give a result compatible with an Omicron infection. So about 5.5% of the people who tested positive and said their ethnicity was White tested positive – that’s about 1 in 18. There were many fewer people who tested positive and reported being from an ethnic minority – only 224 of them, of whom 10 had a test result compatible with Omicron. (The overall number is smaller than for White positive cases simply because there are many more people of White ethnicity in the UK than of ethnic minorities.) So for the strong positive tests from people from ethnic minorities, about 15%, or about 1 in 7, were compatible with Omicron. Looks like a big difference. But just comparing 1 in 18 with 1 in 7 is rather misleading. Both of those numbers are subject to statistical uncertainty, and rather a lot of it for the much smaller number of ethnic minority positive results. And, further, just comparing those numbers doesn’t pick out the difference that is specifically related to ethnicity, because there are differences (on average) between people of White ethnicity and ethnic minorities in terms of the regions where they live, their average age, the level of deprivation where they live, and more, and all of those things may also affect the chance that an infection is Omicron.
“The ONS statisticians fit a statistical model that allows for these differences in other demographics, and basically compares what would happen in a set of people of White ethnicity and another set, who have the same demographic characteristics as the White group except that they have different ethnicity. This produces what’s called an odds ratio, and that says that the odds of having an infection compatible with Omicron, in the set from ethnic minorities, would be 1.75 times as large as in the comparable set of people with White ethnicity. It’s slightly awkward that this compares odds, rather than proportions, but there are technical reasons why it makes sense to do that, and one can work through the calculations in terms of proportions instead. So, if our set of people of White ethnicity who have tested strongly positive is demographically like those in the data, so that 1 in 18 have an infection compatible with Omicron, those calculations show that the proportion of a set people from ethnic minorities who test strongly positive, and demographically just like the White people apart from their ethnicity, who have an infection compatible with Omicron would be somewhere between about 1 in 7 and about 1 in 18, with a central estimate of about 1 in 11. So the proportion of the ethnic minority set of people (who tested strongly positive), who have an Omicron infection is indeed estimated as probably being higher than for the White people testing strongly positive, but it could be very much higher (about 1 in 7 compared to 1 in 18 for the White group), or it could be about the same (1 in 18 in both groups). Most of the margins of statistical error for other characteristics are similarly very wide, which is why I feel that at this stage, it’s not really worth getting too preoccupied with the numerical details. Better information will emerge pretty soon.”
All our previous output on this subject can be seen at this weblink:
Prof Kevin McConway: “I am a Trustee of the SMC and a member of its Advisory Committee. I am also a member of the Public Data Advisory Group, which provides expert advice to the Cabinet Office on aspects of public understanding of data during the pandemic. My quote above is in my capacity as an independent professional statistician.”
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