Archive for vaccination

Reasons for Optimism

Posted in Biographical, Covid-19, Education with tags , , , , , , on July 6, 2021 by telescoper

After an interruption of almost two months because of a Cyberattack on the Health Service Executive’s computer system, daily updates of Ireland’s vaccination statistics have at last resumed, including via the Covid-19 app (which has been moribund since 11th May).

You might think it strange but I find the restoration of daily updates reassuring. I suppose it’s because I work in a quantitative discipline but I like having things expressed in figures, though I am of course aware of their uncertainties and other problems involved in interpreting them.

The latest figures above show that about 70% of the adult population has received at least one dose while about 50% have had two doses; the latter are regarded as “fully” vaccinated as are the smaller number who have received the one-shot Janssen vaccine produced by Johnson & Johnson. Although the Government missed by some margin its target of giving one dose to 82% of the adult population by the end of June, I find myself much more optimistic than in past few weeks about how things are going.

Two developments in particular have helped.

First the Government is set to purchase about a million doses of Pfizer/BioNTech from Romania. That would be enough to fully vaccinated about 10% of the population. These doses have become available because take-up in Romania is very poor and the shots would go to waste if not disposed of elsewhere. What’s bad news for Romania is, however, good news for Ireland.

The second change is that the Government has decided to allow the AstraZeneca and Janssen vaccines to be used on adults in the age range 18-34 and that vaccinations of this group are now being carried out by pharmacists. Previously these vaccines were only to be given to persons aged 50 and over. Indications are that there is some reluctance among the younger cohort, which is hardly surprising since it was only a few weeks ago that they were being told these vaccines were too risky, but I suspect this change will go a long way towards fully vaccinating the adult population, which may be possible by the end of August.

I regard the immunization of students next year’s intake to third level education institutions as a necessary condition for opening up campuses to something like “normal” teaching. Just a couple of months ago I didn’t think this would be possible, but now it might be. It’s still possible that there will be disruptions in supply but it’s looking reasonably good at the moment based on the arithmetic of how many doses are available.

The fly in the ointment is of course the so-called Delta Variant, which has already gained a foothold in Ireland and is set to cause case numbers to rise substantially. We will soon see whether this causes an increase in hospitalizations and deaths. The most vulnerable should be protected so the probability of a case turning into serious illness or death should be much lower, but we don’t know by how much. Unfortunately the statistics of Covid-19 are still not being reported publicly. Some people seem to think this means they’re not happening. It doesn’t. It just means the system for reporting them is not working. I expect the forthcoming announcement of the backlog will cause some alarm.

The Irish Government recently decided to pause the gradual reopening of the economy to allow vaccinations to proceed further. There is still a race between the Delta variant and the vaccination programme. The number of people vaccinated increases approximately linearly with time, while the number of Covid-19 cases grows exponentially in the growth phase of the pandemic. I think the pause was sensible.

Across the Irish Sea there is a different situation. The English Government has decided to abandon all attempts to control the spread of Covid-19 at precisely the point when the pandemic is in another exponential phase. The number of cases is now likely to increase dramatically. The number of resulting deaths may be fewer than in previous waves but won’t be zero. Perhaps more importantly, allowing a huge pool of virus to develop increases the chance of yet another variant evolving, perhaps one that can evade the defences afforded by vaccination even more effectively than the Delta variant. I shudder to think of the consequences if that does happen. Perhaps it already has.

A Vaccination Fallacy

Posted in Bad Statistics, Covid-19 with tags , , , , on June 27, 2021 by telescoper

I have been struck by the number of people upset by the latest analysis of SARS-Cov-2 “variants of concern” byPublic Health England. In particular it is in the report that over 40% of those dying from the so-called Delta Variant have had both vaccine jabs. I even saw some comments on social media from people saying that this proves that the vaccines are useless against this variant and as a consequence they weren’t going to bother getting their second jab.

This is dangerous nonsense and I think it stems – as much dangerous nonsense does – from a misunderstanding of basic probability which comes up in a number of situations, including the Prosecutor’s Fallacy. I’ll try to clarify it here with a bit of probability theory. The same logic as the following applies if you specify serious illness or mortality, but I’ll keep it simple by just talking about contracting Covid-19. When I write about probabilities you can think of these as proportions within the population so I’ll use the terms probability and proportion interchangeably in the following.

Denote by P[C|V] the conditional probability that a fully vaccinated person becomes ill from Covid-19. That is considerably smaller than P[C| not V] (by a factor of ten or so given the efficacy of the vaccines). Vaccines do not however deliver perfect immunity so P[C|V]≠0.

Let P[V|C] be the conditional probability of a person with Covid-19 having been fully vaccinated. Or, if you prefer, the proportion of people with Covid-19 who are fully vaccinated..

Now the first thing to point out is that these conditional probability are emphatically not equal. The probability of a female person being pregnant is not the same as the probability of a pregnant person being female.

We can find the relationship between P[C|V] and P[V|C] using the joint probability P[V,C]=P[V,C] of a person having been fully vaccinated and contracting Covid-19. This can be decomposed in two ways: P[V,C]=P[V]P[C|V]=P[C]P[V|C]=P[V,C], where P[V] is the proportion of people fully vaccinated and P[C] is the proportion of people who have contracted Covid-19. This gives P[V|C]=P[V]P[C|V]/P[C].

This result is nothing more than the famous Bayes Theorem.

Now P[C] is difficult to know exactly because of variable testing rates and other selection effects but is presumably quite small. The total number of positive tests since the pandemic began in the UK is about 5M which is less than 10% of the population. The proportion of the population fully vaccinated on the other hand is known to be about 50% in the UK. We can be pretty sure therefore that P[V]»P[C]. This in turn means that P[V|C]»P[C|V].

In words this means that there is nothing to be surprised about in the fact that the proportion of people being infected with Covid-19 is significantly larger than the probability of a vaccinated person catching Covid-19. It is expected that the majority of people catching Covid-19 in the current phase of the pandemic will have been fully vaccinated.

(As a commenter below points out, in the limit when everyone has been vaccinated 100% of the people who catch Covid-19 will have been vaccinated. The point is that the number of people getting ill and dying will be lower than in an unvaccinated population.)

The proportion of those dying of Covid-19 who have been fully vaccinated will also be high, a point also made here.

It’s difficult to be quantitatively accurate here because there are other factors involved in the risk of becoming ill with Covid-19, chiefly age. The reason this poses a problem is that in my countries vaccinations have been given preferentially to those deemed to be at high risk. Younger people are at relatively low risk of serious illness or death from Covid-19 whether or not they are vaccinated compared to older people, but the latter are also more likely to have been vaccinated. To factor this into the calculation above requires an additional piece of conditioning information. We could express this crudely in terms of a binary condition High Risk (H) or Low Risk (L) and construct P(V|L,H) etc but I don’t have the time or information to do this.

So please don’t be taken in by this fallacy. Vaccines do work. Get your second jab (or your first if you haven’t done it yet). It might save your life.

Normal services will be resumed as soon as possible…

Posted in Biographical, Covid-19 with tags , , , on May 16, 2021 by telescoper

After posting updates about Ireland’s Covid-19 situation every single day since the end of March 2020 – a total of 441 entries so far – I’ve been forced to pause. The reason is that a “significant ransomware attack” has crippled many of the computer systems of the Health Service Executive and while it is being dealt with, no data on Covid-19 (including vaccinations) are being published. As far as I understand it, testing and vaccination are going on as before, but we will have to wait until systems are restored before announcements will resume and backdated data is published.

When the dust settles on this I’m pretty sure the inevitable investigation will reveal that the HSE has been using outdated IT hardware and software that made it much easier for the cybercriminals than it should have been.  The disruption is of course extremely annoying but there is a real possibility that the cancellation of urgent medical procedures may lead to loss of life. I sincerely hope the perpetrators are caught and subjected to the full force of the law.

Meanwhile, out of interest, here is my latest summary plot (dated 14th May) which shows new cases steady at the (uncomfortably) high level of around 430 per day (7-day average) but deaths falling:

It is reasonable to infer that the combination of falling mortality figures and constant infection rates is attributable to the vaccination most people in the groups most at risk.

Last Monday (10th May) saw various relaxations of the current restrictions around Covid-19 and tomorrow there will be further loosening. In particular all remaining “non-essential” shops will open. This won’t make much difference to me personally as I shall be locked down marking examinations for at least the next fortnight.

I don’t think the cyber attack will affect the timing of my second vaccine dose, which is due in early June, but that remains to be seen.

On Vaccination in Ireland

Posted in Covid-19 with tags , , , on March 31, 2021 by telescoper

Following from my weekend post about issues with Covid19 vaccination, which seems to have ruffled a few feathers, I thought I’d just mention a couple of recent developments.

The first is that on Tuesday (yesterday) the Irish Government decided to change the way it vaccinates the rest of the population. The previous plan was rather complicated with a number of groups to be vaccinated in order of priority:

That plan has now been scrapped and after the current groups 1-3 are completed it will revert to a simpler scheme with priority determined only by age. As an oldie I will benefit from this, moving up several steps in the pecking order as a consequence of the decision.

Frontline workers such as teachers and Gardaí are dismayed by this decision. On the news just now various folk were trying to argue that the change is for health policy reasons, stating that the prime factor in risk for Covid-19 is age. Actually, it isn’t. The prime factor is exposure to the virus.

What I mean is that the probability of dying from Covid-19 if you haven’t been infected is zero: 100% of those suffering death or serious illness from Covid-19 have been in contact with the virus. Someone who is 60 years old but able to work effectively at home at far lower risk of exposure than a 35 year old schoolteacher.

The real reason for the change is that Ireland does not possess a system that can be used identify groups by occupation in an efficient way. Doing it by age is far simpler and would lead to a much more rapid rise in the fraction of the population immunized. Sometimes decisions have to be made for such practical reasons, but I do wish certain people were more honest.

The slow rollout of the vaccine in Ireland should have provided the Government to work out how to implement their original strategy. Obviously they decided that they couldn’t.

Anyway, for myself, I am pleased that it now looks quite likely that I’ll get at least one jab by May. Assuming the vaccine supply holds up, of course.

I thought I’d end with a thought following on from my earlier post. Some people will ask whether I would have the AstraZeneca vaccine given my views about the company’s behaviour and the lower efficacy of the vaccine as compared to others available.

I think there are two motivations for getting vaccinated. One is self-preservation. I want to protect myself as much as possible. If I had the choice of vaccine for this reason I would pick Moderna or Pfizer-BioNtech but would accept AZ if that was the only one available. As things stand, over 75% of doses administered in Ireland have been Pfizer-BioNtech,

The other motivation is to help reduce the transmission of the disease. For that even a low efficacy vaccine would play a part. If the only shot available offered just 50% protection I would still take it, as if everyone did so the population dynamics would still be significantly slowed.

It’s a similar thing with face masks, actually. Their role is only partly to protect the wearer. The other part is to protect everyone else.

So on both grounds, yes I would take the AZ vaccine if that was the only one on offer, but if I had the choice I would pick a better one. I feel the same way about the Johnson & Johnson vaccine, which will start to become available in Ireland very soon.

SARS-Cov-2 Vaccine strategy: One Jab or Two?

Posted in Covid-19 with tags , , , , , on January 13, 2021 by telescoper

I’ve been thinking quite a lot about the issue of the Coronavirus vaccination programmes currently underway and have had some interesting and informative exchanges on Twitter about it. This morning’s news that AstraZeneca has finally applied to the European Commission for permission to market its vaccine within the European Union reminded me of those discussions so I thought I’d post a question here. I genuinely don’t know the answer, incidentally, so there’s no agenda here!

As you probably know all SARS-COV-2 vaccines (Moderna, Pfizer/Biontech and AstraZeneca) require two doses, administered about three weeks apart, for maximum efficacy. It’s worth saying before going on that the scientists involved deserve high praise for developing these highly effective vaccines at a speed that has exceeded all expectations.

At the moment however supplies of these vaccines are fairly limited and it’s early days for immunization programmes so there are serious logistical problems to be solved before we get anywhere near full vaccination. I grabbed this from Twitter yesterday showing the state of play in various countries:

Note, incidentally, that Denmark is doing particularly well within the EU but France, Netherlands, Luxembourg and Belgium have started very slowly. Ireland is about mid-table.

At the top of the league is Israel, though  they are not offering vaccination to the Palestinian people whose lands they occupy. Israel has just reported that after 12 days the Pfizer/BioNTech vaccine has about 50% efficacy after one dose based on results from its own programme. That number is roughly consistent with initial estimates of from trials this vaccine but the statistics aren’t great and there is a considerable margin of error on these figures.

Now the question I am asking myself is that given the limited supply is it better at this stage to give as many people as possible one dose of the vaccine, or follow the manufacturers’ original plan and give two doses to half as many people? There are reports that the UK has been deferring the second dose beyond the recommended interval, where there is no data on its efficacy. Perhaps I’m being excessively cynical but it seems to me that the UK Government’s approach is more driven by public relations than by public health considerations.

I understand that there are difficult issues here, not least the ethical one of having people sign up for a specific two-dose vaccination only to find that’s not what they get. Another issue is the speed with which doses are being made available relative to the size of the population. Yet another issue is who you prioritize.

Above all, though, there is the question of what you mean by “better”. One criterion would be to save as many lives as possible. Another might be to slow the rate of infections as much as possible. Another might be to allow the economy to open up as early as possible. These are all different and would lead to different decisions, particularly with regard to who should get the vaccine. Saving lives obviously means protecting the vulnerable and the people who care for them (e.g. health workers). Economic considerations would however lead you to prioritize those on whom the economy depends most directly, which would include workers who can’t easily work from home (many of whom are in low-paid manual jobs).

The following poll is therefore going to be very unscientific, but I’m interested to find out what people think. In  order to keep it simple, lets suppose you have a batch of two million doses of a vaccine (say the Pfizer one) and the next batch is due in three months.

You have to decide between the following two options:

  1.  Give 1,000,000 people one dose now and another dose in three weeks’ time
  2.  Give 2,000,000 people one dose now and hope that it is effective for three months (or that additional supplies appear more quickly than anticipated).

Vote now!

A similar poll I did on Twitter a while ago can be found here: there are some quite interesting comments in the ensuing thread.

Comments are of course welcome through the Comments Box!

P.S. I’m quite low down the pecking order in Ireland so it’s unlikely I’ll get vaccinated before the summer.

Vaccination in Ireland

Posted in Covid-19 with tags , , , , , , , on December 5, 2020 by telescoper

A very interesting twitter thread from Dr Ronan Glynn (Ireland’s Deputy Chief Medical Officer) inspired me to write something in response to the very positive recent developments with regard to a SARS-CoV2 (Covid-19 vaccine). In Switzerland the regulator does not feel that there is enough data yet for approval to be granted yet, so I have some reservations about the fast-tracking of the process in the United Kingdom. Nevertheless there has to be a tradeoff between the risk of potential reactions or side-effects of a vaccination and the immediate danger to public health arising from Covid-19. As someone recently said to me on Twitter: “if you’re not going to fast-track during a global pandemic, when would you?”.

Here in Ireland it is likely that a vaccination programme will commence early in the New Year. To answer a question I posed a few weeks ago, priority will be given to front-line health care workers, especially those working in care homes, and the elderly. If all goes to plan there will be something like full vaccination of the population by September 2021.

I am not in a priority group so will have to wait a while for my jabs, but I will certainly take the vaccine as soon as it is available to me.

No doubt there are some people out there who for various reasons will refuse to be vaccinated. I doubt anything I say here will persuade them but it is I think valuable to look at the history of vaccination programmes in Ireland for various illnesses, which is what Dr Glynn’s thread does.

To give a few examples:

  • Smallpox. In 1863 vaccination against smallpox was made compulsory for all children born in Ireland. Deaths fell from 7,550 for the decade to 1880 to the last reported death from smallpox here in 1907. Smallpox was declared eradicated in 1979 – this one vaccine saved 100s of millions of lives globally.
  • Diptheria. Diphtheria was a very common cause of death among children until the 1940s – there were 318 deaths from it reported in Ireland  1938. With the introduction of a vaccine, the number of deaths fell year on year with 5 deaths in 1950; the last death notified from diphtheria was in 1967.
  • Poliomyelitis. In Ireland, polio infection (mainly affecting young children causing long term paralysis) became more common after 1920 with major epidemics during the 1940s & 1950s. A vaccine was introduced in 1957. The last reported case of polio here in Ireland 1984.
  • Measles. The number of cases of measles declined dramatically after introduction of measles vaccine in 1985, from 10,000 cases in 1985 to 201 cases in 1987.
  • Meningococcal Meningitis. In 1999, there were 536 cases of meningococcal meningitis in Ireland The meningitis C vaccine was introduced in 2000, with the meningitis B vaccine introduced in 2016. Cases of meningococcal meningitis have dropped more than 80% since these vaccines were introduced.

These are of course wonderful advances in public health, but none of them provided total relief immediately. It will be the same with Covid-19. The availability of a vaccine will not end the pandemic overnight, but at least it will enable us to plan for a phased return to normal.

 

While there is great cause for long-term optimism, there are still reasons to be anxious in the short term. There will be many months before a full vaccination programme is in place and in that time cases (and, sadly, deaths) could rise substantially. There is a real danger will think that it’s all over, that they can let down their guard and ignore social distancing.

Ireland is currently relaxing its Covid-19 restrictions for the Christmas period, but it is doing so from a level of over 260 new cases per day. The Coronavirus is currently circulating in the community at a far higher rate than it was in the summer and if it increases at a similar rate to August then we could be in for a huge surge. I fear that by the New Year we might be in real trouble again. It would be tragic if people lost their lives owing to complacency with safety so nearly in sight.

 

Covid Questions for Ireland

Posted in Covid-19, Maynooth with tags , , on November 15, 2020 by telescoper

I’ve just done my daily update of Covid-19 numbers here and thought I’d show the latest figure:

There are now 262 data points on these graphs. When I started doing the updates I thought it might carry on for two or three months -i t’s now been almost nine and there’s no end in sight.

As you can see the 7-day average of new cases has been falling steadily since entered the period of Level 5 restrictions that is now about half-way through. That, of course, is good news. The problem is that the rate of decrease is really quite slow. The number of new cases on each day for the last week (including today) were: 270, 270, 362, 395, 482, 456, and 378 (today). That is fairly flat, the steep downward trend of the previous week apparently faltering. As a rough guess I’d say that by the time we come out of the current period of restrictions (at the beginning of December) we’ll probably still be having over a hundred new cases per day.

I think that level is far too high for comfort, but the current government is probably going to find it difficult to resist the political pressure to exit the lockdown in time for Christmas. If that does happen, I can see another lockdown looming in January. My superiors at Maynooth University are talking about having on-campus teaching again next Semester, but I think that’s highly unlikely in the circumstances.

Things are even worse in Northern Ireland where the number of new cases announced today was 478. Daily cases have been running higher there than in the Republic for some time, despite the fact that the six counties of Northern Ireland have a population of just 1.9 million compared to the 4.9 million of the 26 counties  in the Republic.

That brings me to the issue of the Pfizer Covid-19 vaccine that everyone is getting excited about. Assuming that it passes the various tests needed for it to be approved, Ireland would get about 2 million doses from the stock procured by the European Union.  The population of Ireland is about 4.9 million, and each person would require two doses, which means that supply will only enable about 20% of the population to be vaccinated.

(Actually I don’t know whether the 2 million refers to people that can be vaccinated or individual doses, but even if it’s the former that still accounts for only 40% of the population.)

The question then is who should be prioritized? I think we’d all agree that all health care workers should be vaccinated ASAP but that’s only about 25,000 people (source). Who should get the other doses? Most people seem to be assuming that those at highest risk of mortality should be vaccinated, but there’s also a case to be argued that  it should it should be those groups within which the virus is most likely to spread that should get it, which is presumably the otherwise healthy population.

I don’t know the answer, but it will be interesting to see how this all develops. In any case as far as I can see it there’s very little prospect of high levels of population immunity being reached by this time next year. And that’s even if the vaccine is available soon, which is by no means clear will be the case. As a matter of fact I wouldn’t bet against me still having to do daily updates on Covid-19 statistics for most of next year.