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Pfizer and BioNTech just released the interim results of their COVID-19 vaccine trial.
Although it is not the only vaccine in the later stages of testing, the trial’s large size and careful design, not to mention the promising results, have sparked understandable excitement around the world.
As we approach the long-awaited launch of the COVID-19 vaccine, it is worth seeing how statisticians help clinicians establish the safety of vaccines.
How effective is the vaccine?
It is not easy to find out how effective a vaccine is. First, researchers need to know if the simple act of injecting someone can help. The trials involved large numbers of people, half of whom received a vaccine and the other half a placebo.
The participants should then be exposed to the infection with the expectation that most of those in the control group will become ill, but the vaccine protects at least some of the treated group.
In some cases, as in the case of HIV or Ebola, even giving a placebo can be ethically controversial, as they have such a high mortality rate.
For coronavirus, researchers must rely on natural infection because no study, as of yet, intentionally exposes participants to the coronavirus. As a result, the efficacy estimate is based on a relatively small number of people who contracted COVID-19 from contact with other infected people.
The efficacy of the vaccine reflects a proportion of the number of people who became ill in the vaccinated group and in the unvaccinated group. The Pfizer / BioNTech trial involved nearly 44,000 participants, and 21,999 received the vaccine.
Researchers use statistical analysis to set milestones where they can be increasingly confident that the vaccine works, or not, as cases progress.
If the numbers are small, it would not be clear if the difference in results between the placebo group and the treated group is real or is simply the result of chance.
Statisticians use so-called “power analysis” to find out how many cases to look at. For the Pfizer and BioNTech vaccines, the target was 164 cases when the final estimate of efficacy can be made, but this was based on the assumption that the vaccine is only 60 percent effective.
This was based on the efficacy of the seasonal influenza vaccine. However, given that the figures exceeded expectations, the company decided to publish the results in one of the intermediate analysis points.
Ninety-four cases were reported, and the division of approximately 86 cases in the placebo group and eight cases among the vaccinated showed 90 percent efficacy. This level of protection against infection is remarkable.
Although the study is based on a relatively small number of cases, the statistical analysis allows researchers to extrapolate what might happen when the vaccine is deployed.
The trial included different ages, as well as people from different ethnic minority groups, but more studies would be needed to assess how the most vulnerable groups are protected.
The ultimate efficacy is likely to be lower, as delivering the treatment is difficult for many logistical reasons, including the requirement that mRNA-based vaccines, of which the Pfizer vaccine is one, be stored at very low temperatures.
In the real world, the vaccine may not be stored at the correct temperature and therefore spoil.
How safe is the vaccine?
If the vaccine is to be applied widely, the medical community and the public must be assured of its safety.
The Pfizer vaccine was administered to 21,999 people. Some people reported a reaction similar to the one that occurred after vaccination against seasonal flu, but so far no serious side effects have been reported. But how can we be sure that this will hold if treatment is extended to millions of people?
Statisticians came up with the “rule of three.” The rule tells us that if 21,999 participants were treated with no side effects, then with 95% confidence the probability of a vaccine side effect is expected to be less than three (hence the name) divided by 21,999 and less. one in 10,000.
The chance of these side effects is probably even lower, but the researchers will be willing to expand the trials to confirm this.
Safety is as important as efficacy. If you take a one in 10,000 chance and extrapolate it to the 300 million people scheduled for vaccination in the US alone, the number of people with side effects could go up to 30,000.
Clearly, doctors need to make sure they are not causing harm, but also any serious side effects attributable to the vaccine would damage reputations and significantly affect adoption.
How to use the vaccine so that it is effective and safe?
Medical authorities are now devising ways to implement vaccination in national programs, but the details on how to do this depend on several factors.
The UK government has ordered 40 million doses of the Pfizer vaccine, which, with a two-dose treatment, would vaccinate 20 million people, that is, all people over 55 years of age. However, deployment will not be quick as production and delivery will take time.
The strategy also depends on what the vaccination program is supposed to accomplish. Childhood vaccines, such as measles, are given to newborns to maintain herd immunity. In this case, only a relatively small proportion of the population needs to be vaccinated. With the rapid spread of COVID-19 and high levels of infection, the proportion should be much higher.
Predictions for the level of immunity required to achieve herd immunity depend on our estimate of the basic reproductive number of COVID-19, R. In the absence of control measures, R is estimated to be around 3 and therefore at least 67 percent of the public needs to be completely immune only for the epidemic to stop growing.
Higher values would be necessary if the goal is to eradicate the virus.
This level can hardly be reached with an efficacy of 60 percent, even if the entire population is vaccinated. The value of R = 3 assumes a return to behavior prior to the pandemic. If we maintain a certain level of restrictions and use masks, R could be lower and the group immunity easier to achieve.
On the bright side, our simple models may be too pessimistic about herd immunity levels. Also, if perhaps up to 20 percent of the public have already had COVID-19, the required level of vaccination could be much easier to achieve.
Alternatively, vaccination can be applied to those segments of society that are at high risk of infection (healthcare and nursing home workers) or at high risk of death (vulnerable, nursing home residents). This is the recommended strategy in the UK.
Are we there yet?
The results of the Pfizer vaccine trial are very promising. But the road to eradicating the coronavirus is likely to be long and difficult.
In addition to establishing the potential of the vaccine to protect against the virus, we also need to know if it provides long-lasting immunity or if it should be given repeatedly, for example, as with tetanus or seasonal flu vaccines.
But policymakers and researchers must also balance the requirement to stop the pandemic with fears of the side effects and indecision resulting from the vaccine.
While these concerns are easy to dismiss, they must be taken seriously for vaccination to be successful. 
Adam Kleczkowski, professor of mathematics and statistics, University of Strathclyde.
This article is republished from The Conversation under a Creative Commons license. Read the original article.
