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One of the many problems with COVID is that while this is a story which depends enormously on data, the data we have to depend on is sometimes unreliable, and is often easy to misinterpret.

Take figures on the number of people dying of COVID. If you look at sheer numbers previously released by Public Health England, considerably more fully-vaccinated people have died of coronavirus than those who are unvaccinated.

Is this a sign that the vaccination programme isn't working?

Not necessarily - because there are three pieces of context that change the complexion of that picture.

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The first is that even leaving aside the vaccination programme, older people are considerably more likely to die of COVID.

So for a true picture of what's going on one should ideally age-adjust the deaths numbers so that they account for the life expectancy of those dying.

The second is that vaccination uptake has been very high among the elderly, so the total pool of fully vaccinated older people far outweighs the unvaccinated.

The third is that while the vaccines seem to be very effective at preventing hospitalisations and deaths (far more effective than preventing infection, by the way) they are not 100% effective.

The upshot of all of this is that even if the vaccines were working precisely as expected, you would expect a small fraction of people to die of COVID even having been fully dosed.

A small fraction of a big number is often still a big number, and this is why the sheer number of fully-vaccinated people who are dying is higher than the unvaccinated (a bigger fraction of a far smaller number).

All of which is a long-winded way of saying it is worth being cautious of the deaths figures when it comes to COVID.

The Office for National Statistics has attempted to adjust for at least some of these factors in its latest report into the number of those dying of COVID. This series age-adjusts the figures and looks at deaths as a proportion of those vaccinated, and finds a clear gap between fully vaccinated people and unvaccinated people.

The headline figures are certainly stark: since January there were 38,964 age-adjusted COVID deaths among unvaccinated people, compared with only 458 among those who are fully vaccinated.

However, these figures, note, cover a large period of the year when most people were not vaccinated, so it is probably more reliable to focus on the rates of deaths, adjusted for the number of people who were vaccinated at that stage.

These numbers show that in late February - the peak of the winter wave earlier this year - there were 56 deaths per 100,000 unvaccinated people.

The age-adjusted rate among fully vaccinated people at that point was 0.5 deaths per 100,000. As of early July, the age-adjusted death rate was 1.6 per 100,000 among the unvaccinated, and 0.2 per 100,000 among the fully vaccinated.

The lesson is that there is a clear mortality difference brought about by the vaccines.

However, it's worth being cautious with these data for a few reasons. First, they mostly reflect the previous variant, Alpha, which was dominant in the spring.

Second, as of July, the gap between unvaccinated and vaccinated had narrowed.

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Fully-vaccinated people still had a far lower age-adjusted mortality rate, but the gap is less dramatic than those headline figures might suggest.

Even so, for those looking for evidence that the vaccines are protecting against death, the numbers are encouraging.