While writing a newspaper article on the performance of various possible Covid-19 vaccines from different organizations, my wife, who is neither a statistician nor a vaccine expert, asked me what the 90% efficacy of a vaccine means. And suddenly I realized that such figures for potential test vaccines are never very clear to ordinary people unless their implications are clearly illustrated.
In fact, different pharmaceutical companies are now publishing success stories of their potential vaccines, and the efficacy rates of these vaccines are reported to be high – 70%, 90%, 95%, etc.
This is how we can understand the efficacy of the vaccine.
Phase III trial
Vaccines are generally approved based on the results of three stages of clinical trials. The trials are aimed at evaluating short-term safety, the ability to elicit an immune response, and efficacy. Short-term safety is generally judged in the early stages.
The phase III trial, which is often the most elaborate, investigates the efficacy of the vaccine being tested, usually compared to a placebo, which may be a similar-looking injection that has no medical effect. In a phase III trial, often thousands of people receive the vaccine or a placebo, and then these people are monitored for several months to see if the people who receive the vaccine are infected at a lower rate than the people who receive the placebo , on average. .
Therefore, the performance of the vaccinated group is compared with that of the unvaccinated group. Phase III is a large-scale efficacy evaluation and provides an opportunity to monitor some safety issues that cannot be done in earlier phases. ‘Vaccine efficacy’ is defined to measure whether or not the vaccine is capable of significantly preventing disease and, if so, to what extent.
The mathematical deduction of the efficacy of the protective vaccine was proposed by M Greenwood and GU Yule in a research article published in the Proceedings of the Royal Society of Medicine in 1915, where statistics for typhoid and cholera inoculations were entered and interpreted.
Hazard radius
Vaccine efficacy is expressed as a proportional reduction in the disease attack rate, AR, between the unvaccinated, ARU and vaccinated, ARV groups in the phase III trial.
ARV is just the proportion of individuals within the vaccinated group who became infected during the study period. Similarly, ARU is the proportion of infected within the unvaccinated group.
The ratio of ARV to ARU is called the risk ratio, RR. A lower RR value clearly indicates better potential vaccine performance. When both the vaccinated and the unvaccinated groups have more or less the same number of individuals, RR is the simple relationship between the number of infected in the vaccine group and that of the placebo group. And one less RR, expressed as a percentage, is called “Vaccine Efficacy”.
Clearly, the higher the efficacy value of the vaccine, the better the performance of the potential vaccine. Therefore, an efficacy of 90% (ie, a RR of 10%) means that the proportion of infection in the vaccinated group is approximately one-tenth the proportion of infection in the placebo group.
Vaccine efficacy
Well my wife is satisfied with the answer. And the reported efficacy values of potential vaccines are also quite high.
The Moderna trial involved 30,000 people, and more than 43,538 people have enrolled in the Pfizer / BioNTech vaccine trial; about half received the vaccine and the rest a “placebo” in each trial. Of the first 95 who developed Covid-19 symptoms in Moderna’s trial, only five were in the vaccine group and the remaining 90 were in the placebo group.
Therefore, the RR for the Moderna vaccine so far is 5/90 and the efficacy of the vaccine is (1-5/90), which is 94.44%. Similarly, of the 170 cases in the Pfizer trial, 162 were in the placebo group, while 8 were in the vaccine group. The efficacy of the Pfizer vaccine is (1-8/162), which is 95.06%.
The Oxford-AstraZeneca vaccine candidate appeared to be 90% and 62% effective for the two dose regimens that had 2,741 and 8,895 individuals in the two groups, respectively. The average efficacy was announced to be 70%, and the initial analysis was based on 131 symptomatic cases of Covid-19 that had appeared in the study participants. But we still don’t know how many cases were found in each group of participants in the vaccinated and placebo groups, and also the split between the two dose regimens.
Short-term data
But we must bear in mind that the efficacy of the vaccine is based only on short-term data. Both the Modera and Pfizer trials were found to be nearly 95% effective in protecting Covid-19 in the short term, although both trials are still underway and the final figures could change.
For example, if among the next 100 infections 98 are from the placebo group and 2 from the vaccine group, the efficacy of the Moderna vaccine would increase to [1 – (5+2)/(90+95)], that is, 96.28%. However, if the effect of the vaccine diminishes over time and 70 and 30 of the next 100 infections are from the placebo and vaccine groups, respectively, the overall efficacy would be [1 – (5+30)/(90+70)], that is, 78.13%. However, if the next 100 infections occur equally within the two groups, the resulting efficacy will be only 60.71%.
Therefore, we must bear in mind that the efficacy of the vaccine is only a statistical measure of the short-term performance of the vaccine. It cannot guarantee the durability of the vaccine beyond the experimentation period, which in these cases is only a few months.
How by 2020 ‘Guidance for industry’ from the US Food and Drug Administration. for ‘Development and licensing of vaccines to prevent COVID-19’, All participants in the phase III trial are expected to be monitored for at least 1 year. Phase III recruitment for the Moderna vaccine took place in April and May, and that for the Pfizer vaccine began in late July. Therefore, all of these are short-term effective.
There is widespread speculation that the SARS-CoV-2 antibodies, which would make you immune to Covid-19, might not last more than a few months. This is also supported by different peer-reviewed articles in various journals. Therefore, it is not yet very clear how long a vaccine would protect against the disease. Whatever the case, the efficacy of the vaccine could change dramatically if the individuals in the study are monitored for another few months, at least. Hope for the best.
Atanu Biswas is Professor of Statistics at the Indian Institute of Statistics, Kolkata.
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