Covid-19 Vaccines – Comparison of Effectiveness, with Confidence Intervals
With Covid-19 vaccines now becoming a reality, the question of their efficacy has come up. Curiously, I haven’t seen much reference to confidence interval comparisons, so here’s my version. I have just used a fairly standard calculation for confidence intervals for proportions (95% CI, exact binomial calculation in Excel). Below is a graph of the results of those calculations.
There are a few points about this graph to be aware of:
· The important thing to look at is the difference in Covid cases between the people who received the vaccine and those who received the placebo, for each type of vaccine.
· However, the size of the gap can be misleading. For example, the Oxford .5/1 vaccine (my shorthand for the half-dose followed by full-dose treatment) has the largest absolute improvement in their risk of getting Covid-19 (0.22% in the treatment group vs 2.18% in the placebo group, an absolute improvement of 1.96 percentage points). However, the the best relative improvement was for those who took the Pfizer vaccine (0.04% vs .75%, which meant that those people were about 20 times as safe as the placebo group).
· It is interesting that the Oxford placebo group had the highest incidence of Covid-19, much higher than the placebo groups for the other vaccines. Presumably, that vaccine must have been tested in regions that had much more severe outbreaks than the others, or the time for the trial was much longer.
· Note also that the confidence intervals were different for the various vaccines. That is a reflection of the sample sizes, mostly.
· It is also interesting to note that the percentage of the placebo groups that developed Covid-19 was in the 0.6% to 2.2% range, with an average of about 1.3%. Given that the period of the studies was generally about half a year, this would indicate that something like 2.5% of the underlying populations developed Covid per year, assuming that the placebo groups were an accurate random draw of the underlying populations. Though, in fact, I believe these test groups tended to be younger and heavier than the populations from which they were drawn.
There are a number of other measures that can be used in these situations, such as relative risks and odds ratios. A common one is the odds ratio, which is shown for each vaccine in the graph below, based upon the numbers given in the vaccine studies. I used standard confidence interval calculations here as well (95% C.I. standard calculation). Note that the confidence intevals around the means are not necessarily symmetrical. That’s a function of sample sizes and range restriction (most of the odds ratios are fairly close to 0, so there is more room for uncertainty on the upside than the downside).
As the name implies, the odds ratio gives the odds (or probability) of getting Covid if you received the shot, compared to if you didn’t. For example, the people who got the Pfizer shot were only about 3% as likely to get Covid as the people who received a placebo, in that study.
So based on these results, all of the vaccines give good results, assuming the Oxford half-dose/full-dose results hold up as more numbers come in. It still has rather large confidence intervals (i.e. there is a lot of uncertainty in the numbers).
There are some other factors that come into play:
· Availability – who can meet the demand in the shortest time frame.
· Distribution – the Pfizer vaccine has some challenges in its requirements for handling, notably its need for very cold storage temperatures. Moderna also requires fairly cold temperatures, while the others just need routine refrigeration.
· Price – who can provide it at the best price.
· Politics – will this break along geopolitical lines, such that Sputnik, for example, gets little take-up in the west, but lots in the non-western nations.
· New vaccines – when will the Chinese vaccine come out and will they sell it to the rest of the world.
· Side effects – will there be many adverse effects and how much will this vary between the vaccines.
It will also prove to be interesting, once vaccines have been given to the most vulnerable groups (people in nursing homes, health care workers, the advanced aged). It is quite likely that death rates will fall enormously once those groups are vaccinated (likely by 80% to 90%). At that point, people’s Covid fatigue will become very pronounced, and the willingness to go along with public health measures may greatly dissipate. The possible political difficulties of that situation are rather obvious.
Sources:
Covid-19 Vaccines
· Pfizer: Safety and Efficacy of the BNT162b2 mRNA, New England Journal of Medicine
· Moderna: FDA Briefing Document Moderna COVID-19 Vaccine
· Sputnik: The Arrival of Sputnik V, The Lancet
· Oxford: Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK, The Lancet
Some earlier Covid-19 blogs:
https://dodecahedronbooks.blogspot.com/2020/09/covid-19-continues-to-travel-around.html
https://dodecahedronbooks.blogspot.com/2020/07/has-covid-19-become-less-deadly.html
https://dodecahedronbooks.blogspot.com/2020/07/july-2020-update-covid-19-death-rates.html
https://dodecahedronbooks.blogspot.com/2020/05/covid-19-death-rates-correlate-highly.html
https://dodecahedronbooks.blogspot.com/2020/06/covid-19-impact-on-employment-no-impact.html
https://dodecahedronbooks.blogspot.com/2020/04/is-there-model-that-can-predict-when-to.html
https://dodecahedronbooks.blogspot.com/2020/03/estimating-fatality-rate-of-coronavirus.html
=====================================================
And, here’s a more pleasant travel story than anticipating the worldwide journey of a virus.
A Drive Across Newfoundland
U.S.: https://www.amazon.com/dp/B07NMR9WM8
U.K.: https://www.amazon.co.uk/dp/B07NMR9WM8
Germany: https://www.amazon.de/dp/B07NMR9WM8
Japan: https://www.amazon.co.jp/dp/B07NMR9WM8
Canada: https://www.amazon.ca/dp/B07NMR9WM8
Australia: https://www.amazon.com.au/dp/B07NMR9WM8
India: https://www.amazon.in/dp/B07NMR9WM8
Newfoundland, Canada’s most easterly province, is a region that is both fascinating in its unique culture and amazing in its vistas of stark beauty. The weather is often wild, with coastal regions known for steep cliffs and crashing waves (though tranquil beaches exist too). The inland areas are primarily Precambrian shield, dominated by forests, rivers, rock formations, and abundant wildlife. The province also features some of the Earth’s most remarkable geology, notably The Tablelands, where the mantle rocks of the Earth’s interior have been exposed at the surface, permitting one to explore an almost alien landscape, an opportunity available on only a few scattered regions of the planet.
The city of St. John’s is one of Canada’s most unique urban
areas, with a population that maintains many old traditions and cultural
aspects of the British Isles. That’s true of the rest of the province, as well,
where the people are friendly and inclined to chat amiably with visitors. Plus,
they talk with amusing accents and party hard, so what’s not to like?
This account focusses on a two-week road trip in October 2007, from St. John’s
in the southeast, to L’Anse aux Meadows in the far northwest, the only known
Viking settlement in North America. It also features a day hike visit to The
Tablelands, a remarkable and majestic geological feature. Even those who don’t
normally consider themselves very interested in geology will find themselves
awe-struck by these other-worldly landscapes.
A Ride on the Kettle Valley Rail Trail: A Biking Journal Kindle Edition
by Dale Olausen(Author), Helena Puumala(Editor)
The Kettle Valley Rail Trail is one of the longest and most scenic biking and hiking trails in Canada. It covers a good stretch of the south-central interior of British Columbia, about 600 kilometers of scenic countryside. British Columbia is one of the most beautiful areas of Canada, which is itself a beautiful country, ideal for those who appreciate natural splendour and achievable adventure in the great outdoors.
The trail passes through a great variety of geographical and geological regions, from mountains to valleys, along scenic lakes and rivers, to dry near-desert condition grasslands. It often features towering canyons, spanned by a combination of high trestle bridges and long tunnels, as it passes through wild, unpopulated country. At other times, it remains quite low, in populated valleys, alongside spectacular water features such as beautiful Lake Okanagan, an area that is home to hundreds of vineyards, as well as other civilized comforts.
The trail is a nice test of one’s physical fitness, as well as one’s wits and adaptability, as much of it does travel through true wilderness. The views are spectacular, the wildlife is plentiful and the people are friendly. What more could one ask for?
What follows is a journal of two summers of adventure, biking most of the trail in the late 1990s. It is about 33,000 words in length (2 to 3 hours reading), and contains numerous photographs of the trail. There are also sections containing a brief history of the trail, geology, flora and fauna, and associated information.
After reading this account, you should have a good sense of whether the trail is right for you. If you do decide to ride the trail, it will be an experience you will never forget.
Amazon U.S.: https://www.amazon.com/dp/B01GBG8JE0
Amazon U.K.: https://www.amazon.co.uk/dp/B01GBG8JE0
Amazon Germany: https://www.amazon.de/dp/B01GBG8JE0
Amazon Canada: https://www.amazon.ca/dp/B01GBG8JE0
Amazon Australia: https://www.amazon.com.au/dp/B01GBG8JE0
On the Road with Bronco Billy
Amazon U.S.: http://www.amazon.com/gp/product/B00X2IRHSK
Amazon U.K.: http://www.amazon.co.uk/gp/product/B00X2IRHSK
Amazon Germany: http://www.amazon.de/gp/product/B00X2IRHSK
Amazon Canada: http://www.amazon.ca/gp/product/B00X2IRHSK
No comments:
Post a Comment