Opinion

Numbers behind different COVID-19 vaccines

Published

5 years ago

2021/08/18

By M. C. M. Iqbal

The vaccines against COVID-19, available today, are based on different strategies and come with different numbers to indicate their performance. Many of us wish to know if one vaccine is better than the other. Two concepts underlying the performance of the vaccines are efficacy and effectiveness. The Pfizer-BioNTech vaccine has an efficacy of 95 percent, the Moderna Vaccine is 94.5 percent and the Russian made Sputnik vaccine is over 90 percent. Does this mean some vaccines are better than the other? The short answer is no. All the approved vaccines are equally good. So, let us look at what these numbers mean.

These numbers refer to statistical calculations to interpret the results of vaccination trials conducted by the manufacturers of vaccines, following a prescribed format. The method of calculation was developed over 100 years ago by two statisticians, who published their results in the Proceedings of the Royal Society of Medicine in 1915. They, Major Greenwood (Major is his first name and not a military title) and Udny Yule, were tasked with interpreting the results of immunization of British soldiers against typhoid and cholera, who were fighting in different regions of Europe and Asia favourable to the development of cholera epidemics. In a paper stretching over 82 pages, the authors developed the theoretical and mathematical background for calculating the efficacy of vaccines.

This article seeks to explain to the lay reader what these numbers imply and to bring out the differences between efficacy and effectiveness of a vaccine.

Efficacy and effectiveness

At first sight these two terms appear to be synonyms. However, in the world of vaccines and medicine, these two terms are not the same. Efficacy of a vaccine is how it performs under ideal and controlled conditions in a clinical trial (see below). During clinical trials, the outcome of vaccination is compared between a group of vaccinated people and another group given an inactive form of the vaccine (called a placebo). The effectiveness of a vaccine is how the vaccine performs in the real world – that is after the vaccine is approved by the regulatory agencies and you and I are vaccinated.

The efficacy of a vaccine is measured by the manufacturers under ideal conditions in a clinical trial where criteria are specified for selecting and excluding volunteers. These criteria are usually age groups, gender, ethnicity, geographical location and socio-economic standing. If the criteria are specific, then the effects of the vaccine or drug would not be applicable across the population. For example, if the COVID-19 vaccines are not tested on children below 18 years, then the approved vaccine cannot be used on children.

The effectiveness of a drug or vaccine is a measure of how well the drug or vaccine performs in real life, in a diverse population: Fitness geeks and couch potatoes, housewives and nurses, and farmers and office workers. Effectiveness is of relevance to the medical community and healthcare authorities who are treating the patients. Thus, studies on effectiveness would look at to what extent the vaccine is beneficial to the patient to prevent infection.

One may ask, why not simply look at the effectiveness of the vaccine? This is because if the participants in an initial trial of the vaccine are not carefully controlled, then it is difficult to interpret the outcome of the trial. We have many characteristics, which can potentially interfere with the outcome of a trial testing a vaccine. The person volunteering for the trial could be young or old, pregnant or not, a marathon runner or an average person and smoker or non-smoker. Thus, the volunteers selected for the trials are very similar within their groups with many criteria to exclude persons who could confuse the results (for example, an unhealthy person with other diseases would be excluded).

Efficacy of a vaccine asks the question ‘Does the vaccine work under ideal conditions?’ On the other hand, a study on the effectiveness of the same vaccine asks the question ‘Does vaccination work in the real world?’

Clinical trials

Under normal circumstances, vaccines take many years of research and testing to be approved. The COVID-19 pandemic was unprecedented, and pharmaceutical companies embarked on a race against time to produce safe and effective vaccines. The genome of this coronavirus, which was discovered by Chinese scientists, in January 2020, was a major contribution to the development of the vaccines. At the moment there are 94 vaccines being tested on humans in clinical trials, 32 of which have reached the final stage of Phase 3 testing.

To obtain approval for a vaccine, the vaccine manufacturers go through a prescribed process to ensure that the vaccine is safe. All the countries have a national drug approval agency, who should approve the use of a drug or vaccine in that country. The Food and Drug Administration (FDA) in the United States is an important regulatory agency, which has stringent criteria to approve medicines and drugs. In Sri Lanka, it is the National Medicines Regulatory Authority. COVID-19 vaccines are also assessed and approved by the WHO.

Initially, the vaccine is tested on cells in the laboratory and then given to animals, usually mice or monkeys. After this, if the mice or monkeys are happy, human volunteers are recruited to conduct the clinical trials, which is done in three phases. In the first phase, the vaccine is tested on a small group of people to determine the safety, dosage and ability to stimulate our immune system. If this is confirmed, the vaccine then moves into the Phase 2 stage where the safety of the vaccine is tested on hundreds of people who are split into different groups. Once these trials are successful, the vaccine moves to the final Phase 3 trials. Here thousands of people are recruited as volunteers. For the Pfizer-BioNTech vaccine there were over 40,000 volunteers, above the age of 16, from different countries. This trial is more comprehensive, with the volunteers belonging to different age groups, physical fitness, ethnicities and geographical locations. The volunteers are divided into two groups. One group gets the real vaccine while the other group gets a fake vaccine or placebo (the syringe has just water). The volunteers would not know if he/she is getting the vaccine or a placebo and neither do the nurses and doctors giving the vaccine. This is called a double-blind clinical trial. Thus, no one knows, except those conducting the trial, who was vaccinated with what.

After some time, the volunteers, who fell sick with the coronavirus, are PCR tested to confirm if they are COVID-19 positive. The scientists will be on the lookout for any side effects of the vaccine; if they find any cause for concern the trial can be stopped temporarily to conduct investigations and remedy the problem. If the scientists are not satisfied, the trial would be abandoned. Once the results are in, the calculations are done, and all the details are submitted to the regulating authorities. The regulators would ask the manufacturers more questions and once they are satisfied, approval is given to manufacture and market the vaccine. To accelerate the process, such as now during the COVID-19 crises, Phase 1 and 2 may be combined and run in parallel.

Calculating efficacy

The calculations involved are quite simple once the data is collected. Let us assume that 50,000 volunteers were recruited for the vaccination trial. Half were given the vaccine and the other half a placebo. Let us assume that of the 25,000 who received the vaccine, 10 persons were infected, and of the other 25,000 who received the placebo, 200 were infected. Although the numbers of people infected are small, those in the placebo group are 20 times larger (see Table). The researchers are concerned with the relative risk between the groups. This is called the efficacy of the vaccine.

The risk of infection is calculated as follows.

What is the difference in the risk of infection between the vaccinated group and those who got the placebo? From the table this is, 0.80 percent – 0.04 percent = 0.76 percent.

Thus, the vaccine reduced the risk of infection by 0.76 percent, which looks quite small. This is what would happen if we are vaccinated. To understand this in terms of the risk of infection, if none were vaccinated, we look at the ratio of the Reduction in Infection (0.76 percent) to the Risk of infection (0.80 percent – those who got the fake vaccine). This is the Vaccine Efficacy (VE).

VE percent = Reduction in infection ÷ Risk of infection = 0.76 ÷ 0.80 = 95 percent

If this is still confusing, let us see what it means in a population of 100,000 persons who are vaccinated with a vaccine of 95 percent efficacy, and exposed to the virus. From the table above, the risk of infection for the vaccinated population is 0.04 percent, which translates to 40 persons (0.04 percent x 100,000). That is, we can expect that 40 persons would fall ill with an infection by the coronavirus and the rest of the vaccinated people may not develop an infection at all or develop an asymptomatic infection (you are infected but do not show symptoms) or get a mild disease.

(This example of calculating Vaccine Efficacy is adapted from an article by Dashiell Young-Saver in the New York Times of December 13, 2020, where the above calculation is explained in detail for students.)

What does efficacy mean?

The efficacy of a vaccine refers to two aspects. The first is how many of us are protected by the vaccine if we are exposed to the virus; this is given by the percentage. The vaccine also refers to different disease conditions it is capable of preventing. This could be causing an infection, mild disease, severe disease, hospitalisation, or death. This information can be found if one looks carefully at the statements issued by the vaccine manufacturer and regulatory agencies. For example, the statement by Pfizer-BioNTech states: Pfizer-BioNTech COVID-19 vaccine, BNT162b2, was 91.3 percent effective against COVID-19 (symptomatic cases of COVID-19), measured seven days through up to six months after the second dose. The vaccine was 100 percent effective against severe disease as defined by the US centres for Disease Control and Prevention (CDC), and 95.3 percent effective against severe disease as defined by the US FDA.

The efficacy of a vaccine (VE) is the relative reduction of being infected, if we are vaccinated, compared to the placebo or unvaccinated group. If the vaccine is perfect, then the risk of being infected is totally eliminated, so that VE = 1 or it is 100 percent. On the other hand, if there is no difference in the number of people infected between the two groups, the vaccine has no efficacy, or it is zero. Even with a perfect vaccine, our capacity to acquire an infection is determined by our age, health and immunity status.

In short, efficacy is a statistical measurement based on clinical trials of the vaccine’s ability to prevent infection. The volunteers taking part in the trials are not a perfect sample or representative of the real world (for example, children and sick people do not take part). Is there a lower limit for the efficacy of a vaccine to be accepted? Under the present circumstances, the FDA said it would consider granting emergency approval if the vaccines showed even 50 percent efficacy; the vaccines that have received approval now show an efficacy of over 90 percent.

Effectiveness

The effectiveness of the vaccine tells us how well the vaccine is performing among the population, in the real world, to prevent infection. The effectiveness of the vaccine depends on the impact it makes on society. After vaccination our immune system is primed to combat the coronavirus, reducing the multiplication of the virus in our body. This will gradually slow down the spread of the virus as more and more people are vaccinated. In other words, it is important that most if not all the people are vaccinated to have a large impact on the spread of the virus in society. Good examples are the smallpox vaccine, which completely eliminated the smallpox virus, and the polio vaccine, which has almost wiped out the polio virus except for a few small pockets in Pakistan, Afghanistan and Africa. Thus, the effectiveness of a vaccine looks at the medical and societal importance of the outcome.

Here is the above in a nutshell. The percentage numbers given with a vaccine refers to its efficacy – its ability to prevent an infection developing into a serious condition, determined under controlled clinical trials. Vaccines do not prevent infection – they prevent the infection from developing into a severe disease. Once we are vaccinated, our immune system is activated. If we are infected by the coronavirus, the virus has a small window of time to multiply, before it is eliminated by our immune system. This means we can release virus particles from our body, but much less than if we were not vaccinated. The message is we should get vaccinated with the first available vaccine and still wear our masks when going outside, even if we are vaccinated. The chances of ending up in a hospital is low and the chances of ending up in the ICU is very low. There is always a chance.

‘Tis impossible to be sure of anything but Death and Taxes (Christopher Bullock, 1716).

(M.C.M. Iqbal is Associate Research professor, Plant and Environmental Science, National Institute of Fundamental Studies, Hanthane Road, Kandy, and can be reached at iqbal.mo@nifs.ac.lk)

References

Zimmer, C. New York Times Nov. 20, 2020. Two companies say their vaccines are 95 percent effective. What does that mean?

Haelle,T. Association of Health Care Journalists. October 22, 2020. Know the nuances of vaccine efficacy when covering Covid-19 trials. https://healthjournalism.org/blog/2020/10/know-the-nuances-of-vaccine-efficacy-when-covering-covid-19-vaccine-trials/

Greenwood, M., & Yule, G. U. (1915). The Statistics of Anti-typhoid and Anti-cholera Inoculations, and the Interpretation of such Statistics in general. Proceedings of the Royal Society of Medicine, 8 (Sect Epidemiol State Med), 113–194.

Food and Drug Administration, US Department of Health and Human Services. https://www.fda.gov/media/139638/download

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Opinion

A tariff deal with the US? Make haste slowly

Published

13 hours ago

2026/09/24

Sahan Weerasooriya

by Gomi Senadhira

Sri Lanka’s former ambassador to the United States Mahinda Samarasinghe is back in Sri Lanka lobbying for speedier finalisation of a new tariff deal with the United States. According to news reports, delivering the keynote address at the Sri Lanka Institute of Directors’ Annual Meeting last week, he stated, “I have recommended very strongly to the government that we need to conclude the agreement so that we can lock in the very favourable tariff rate that Sri Lanka has got up to now“.

I do not understand why the former ambassador is urging the government to expedite the finalisation of a new tariff deal or what is “the very favourable tariff rate” he refers to in his speech. However, given the ongoing terrible tariff turbulence in the United States and the fragile economic situation in Sri Lanka, I believe, this is not the right time to rush into finalising any trade agreement with the United States. I am also of the opinion that at this juncture Sri Lanka should maintain strategic patience and explore all available options.

Lessons from the countries that rushed for trade deals

To better comprehend this, let’s look at experiences of the countries that rushed to conclude tariff deals with the United States after President Donald Trump declared his “reciprocal tariffs” under the International Emergency Economic Powers Act (IEEPA) in April 2025. As Samarasinghe stated in his keynote, “The bottom line on all these negotiations was that every country that finally agreed to sign the agreement had to give either complete duty-free access for American exports into those markets, or near complete duty-free access.” In exchange for these tariff concessions and other market access commitments these countries managed to get the newly introduced country specific “reciprocal tariffs” reduced.

However, in February 2026, the Supreme Court of the United States (SCOTUS) struck down these “reciprocal tariffs” under the IEEPA. With that, the market access gains these countries received in exchange for complete duty-free access for American exports into their markets evaporated under U.S. domestic law. By moving too fast to conclude bilateral tariff agreements with the United States these countries are now bound to strict obligations whereas the benefits they bargained from the U.S. administration are not worth the paper those were written on.

Sri Lanka’s experience

In April 2025, President Trump declared his “reciprocal tariffs” and labelled Sri Lanka as the worst offender, imposing one of the highest additional duties at 44%. Since then, Ambassador Samarasinghe and other negotiators have managed to negotiate this down to 20%. I do not know what the deal was through which Sri Lanka managed to reduce the 44% tariff to 20% or what we gave in return for this “concession.” However, what we received in return has absolutely no value after the decision by the SCOTUS.

Current state of US tariffs

After the decision by SCOTUS, the U.S. administration introduced a temporary 10% additional tariff on all countries for 150 days. At the end of that period, this 10% tariff was replaced by a new “forced labor tariff ” of 10% to 12.5% on all trading partners under Section 301 of U.S. trade law. Twenty-five U.S. states and several small businesses have already filed lawsuits against these tariffs in U.S. courts. This new “forced labour tariff ” on Sri Lanka was first fixed at 12.5%. Later, after President Anura Kumara Dissanayake issued a gazette notice prohibiting the importation of goods produced using forced labour, it was reduced to 10%. That means Sri Lanka has already made a substantial commitment to receive this “tariff concession,” and I presume our negotiators understand the implications of this commitment.

Make haste slowly

After President Trump imposed 44% “reciprocal tariffs” on Sri Lanka, through an article published in The Island on 25th April 2026 (), I urged the government to engage immediately with the US administration on these tariffs. However, I also emphasised that the best way to move forward was to make haste slowly.

Two millennia ago, Augustus Caesar, the first emperor of Rome, frequently used the phrase, “make haste slowly”, because he detested rashness and haste in his military commanders. It was the recurring guiding maxim that he emphasised throughout his 40-year imperial rule. After 2000 years, this classical oxymoron remains a definitive golden rule for professional trade negotiators. More importantly it is the exact blueprint required when navigating turbulence in trade negotiations with the Trump administration.

The endgame – The most dangerous moment in trade negotiation

Samarasinghe has also stated the agreement is 90% complete. Any experienced trade negotiator should know that the final 10% contains high-stakes provisions and is the most dangerous moment in a trade negotiation. A single misplaced comma or ambiguous product description in a tariff schedule can cost millions through unintended loopholes. Rushing this last stretch to secure a deal can permanently expose Sri Lanka to sudden shifts in American trade policy, heavy compliance costs, or strict enforcement under Section 301 regarding supply-chain labour standards. Hence, this is the time for strategic patience.

(The writer can be reached at senadhiragomi@gmail.com)

Opinion

Buddhist law and constitutional amendments

Published

13 hours ago

2026/09/24

Sahan Weerasooriya

Upon reading the article titled “Prof. Pieris says Buddha Dhamma recognized as source of law under Constitution” (Island, September 12, 2026), the classical Sinhala idiom “Yanne Koheda? Malle Pol” immediately comes to mind. The expression, translating literally to answering “I have coconuts in my bag” when asked “Where are you going?”, underscores a complete disconnect in logic. Because it is uncertain whether the article accurately represents the professor’s precise words, the following critique addresses the contents of the report rather than the speaker himself.

The central premise of the report concerns a statement delivered by the Chief Justice regarding a petition filed against the 22nd Amendment to the Constitution. According to the report, the Chief Justice’s observation that the determination would be made strictly on the basis of established law rather than Buddhist teachings was characterised as a “cavalier dismissal” of the Buddha Dhamma. This assertion carries a host of unexamined assumptions. Had the writer specified precisely which tenets of the Buddha Dhamma were violated, a direct legal or philosophical evaluation could take place. However, no specific Buddhist tenet or law was identified as having been transgressed, and for good reason: no such statutory legal framework exists within the Buddha’s teachings.

To understand the flaw in this argument, one must examine the constitutional context alongside the canonical meaning of the terms involved. Article 9 of the 1978 Constitution of Sri Lanka mandates that the Republic shall give Buddhism the foremost place and that it shall be the duty of the State to protect and foster the Buddha Sasana, while guaranteeing the fundamental rights of all religions under Articles 10 and 14(1)(e).

While “Buddhism” and “Buddha Dhamma” are frequently used as interchangeable terms in casual dialogue, they represent distinct concepts. “Buddhism” is an umbrella term coined by 19th-century Western scholars to classify the global institutionalised religion, incorporating its diverse sects, cultural traditions, rituals, and socio-political histories. Conversely, Sasana is the ancient term designating the structural framework established by the Buddha to preserve and transmit his teachings, comprising the monastic order (Sangha) and its supporting institutions.

In classical Theravada commentarial literature, the Sasana operates as a functional three-tiered structure. It encompasses Pariyatti Sasana, the preservation and study of sacred texts; Paṭipatti Sasana, the practical execution of the doctrine through ethical conduct and meditation; and Paṭivedha Sasana, the direct experiential realization of ultimate truth, or enlightenment. This structural breakdown raises fundamental questions about state capacity. While a state can readily support Pariyatti Sasana through academic institutions, textual preservation, and educational funding, it cannot legislate or enforce Paṭipatti or Paṭivedha. Practical engagement and spiritual realisation are inherently internal, first-person experiences. Expecting the state to codify or guarantee enlightenment is a conceptual impossibility.

Furthermore, the Buddha Dhamma refers specifically to the unconditioned truths of existence and the teachings imparted to realize them, including the Four Noble Truths, the Eightfold Path, and Dependent Origination. As the late Venerable Professor Kotagama Wachissara Thera observed, there is no rigid ideologue or “ism” in the core Dhamma. The teachings do not constitute a system of divine commandments or a legal statute enforced through reward and punishment. Rather, Buddhist ethics function as self-directed guidelines for psychological clarity and moral inquiry. Even the Vinaya Pitaka, which contains explicit rules of conduct, functions as an internal monastic code rather than a civil or criminal law intended for the laity.

Throughout the Pali Canon, guidance regarding governance focuses on the moral character of leadership and the social duties of statecraft rather than rigid legal codification. In discourses such as the Cakkavatti Sihanada Sutta (DN 26), the Buddha observes that social instability and crime cannot be eliminated solely through punitive measures, emphasising instead that states must provide economic opportunities, fair wages, and resource distribution to maintain societal balance. Crucially, in the Maha Parinibbana Sutta (DN 16), the Buddha explicitly highlights the importance of respecting established laws and traditions rather than enacting arbitrary regulations.

The natural laws articulated in the Dhamma, such as the law of cause and effect or the three characteristics of existence, govern all phenomena universally, regardless of legal statutes or personal belief. They are not human laws to be applied or suspended by a court of law. Therefore, characterizing the Chief Justice’s adherence to constitutional jurisprudence over religious doctrine as a “cavalier dismissal” lacks logical and textual foundation. Framing the judiciary’s adherence to legal precedent as an attack on the Dhamma distracts from fundamental constitutional principles and risks misguiding the public for political ends.

Geewananda
Gunawardana,
Ph.D.

Opinion

Elementary, Dr. Watson!

Published

2 days ago

2026/09/23

Sahan Weerasooriya

by Usvatte

My friend, Sena Thoradeniya, has summoned up energy to raise two questions about my observations in your newspaper on 14 September, 2026. They both referred to comments I made about President Dissanayake and Prime Minister Amarasuriya.

I observed that President Dissanayake, having graduated in physics at Kelaniya, would be familiar with elementary calculus: differentiation and integration. It is a misapprehension to believe that one needs any knowledge of theoretical physics to be familiar with elementary calculus. Nor is it necessary that one needs to have published research for the same purpose. Those were the first lessons in calculus that our Mathematics Master and Principal, Mr. D. A. Devendra taught five of us in the first term 1952 at Hikkaduva Central School. Of the five, two still live and recall those lessons vividly. Dissanayake would surely have learnt them at his school in Anuradhapura. At Kelaniya his teachers probably included Dr. H. Somadasa, two years my junior at Hikkaduva, with a Ph.D. in number theory at Aberytswyth, Wales and Professor (physics) Charles Dahanayke, a renowned teacher of physics and my neighbour in Colombo. Dissanayake is unlikely to have been admitted to Physics at Kelaniya unless he had scored well in mathematics and physics with other subjects. Those elements of calculus have been learnt by millions of young men (and later women) since Isaac Newton and Gottfried Leibnitz. That Dissanayake from a school in Anuradhapura scored high enough to gain admission to Kelaniya to study physics is commendation enough for his intellectual capacity.

All of us know, some personally, the barriers to learning in places like Anuradhapura and Kuliyapitiya, compared to the facilities in Colombo, Galle. Jaffna and Kandy. I used that information to press the point that he was, in learning, entirely different from his predecessors and present competitors. One does not need to research in theoretical physics to know something as simple as the first lesson in calculus. Dirac made his momentous discovery sometime in the 1930s and by 1950 it must have been solidly in the teaching material in schools and universities. Dissanayake graduated in 1995 and, at least, must have heard of Dirac and the ‘God Particle’.

Paul Dirac was a legendary figure among graduate students when I was at Cambridge. He had written the shortest Fellowship and Ph.D. theses. He had had an interesting relationship with his father who was a French speaking Swiss and had insisted that he speaks French at table. Amrtya Sen, who was in 1965 a young Fellow of Trinity College and a teacher in the Economics and Politics Faculty at that time, had also written very short theses and not several volumes as many do.

I read about Higgs Boson in a wonderful book Inward Bound written by physicist Abraham Pais and, in The Science Times (Tuesdays) edited by Gina Kolata of the New York Times, and occasionally in Nature and other popular writings.

I was on the editorial board of Samskrti for some time. Amaradasa Virasinghe and Gananath Obeysekera had started that literary review in 1953 when I was in school and many of us read it avidly. Together with Susil Sirivardana, we decided to expand the scope of the journal to include social studies and science, which effort Sena knew well. The probable readership had increased manifold. In order to help prospective writers to pick up themes to write on, we held a popular lecture, one Saturday a month. I invited Dr. Harini Amarasuriya, then teaching at the Open University, Nawala, to speak to us on the scope and nature of sociology. She made a short fine introduction. That is where I learnt of August Compte. She was invited to a Seminar in Britain on the sociology of education, where I had strayed into from 1971. I did not read her paper, although she had promised to let me have it. I had good reason to respect her scholarship. It would be shocking had she not read Le`vy-Strauss. Many besides anthropologists read Le`vy-Strauss.

Sena stressed the obvious when he said that in public speeches made by these two politicians, there was no evidence of their expertise in physics and sociology. It would have been completely out of place to speak about elementary particles to a crowd in Beruvala or Anuradhapura. But one’s education, in subtle ways, informs the material and the ways that the material is presented in public speeches. Simply listen to Members of Parliament speak and you can guess roughly the level of education each had achieved: grade 2 in primary school or Quondam Professor of Law at Oxford.

I am sorry that Sena identified ‘an exaggerated parade of claims and sheer implausible boasts’ in what I wrote. It is entirely plausible, indeed certain, that an undergraduate in the Department of Physics in any university would be familiar with differentiation and integration.

An unprejudiced reading of my text will demonstrate that it contained no such claims and boasts. Mine was a pretty simple statement of the nature of differences between the present lot in government and the lots that were in power earlier. I related those differences to help understand the line up for and against the 22^nd Amendment to the Constitution. and not to build false images of any politician, man or woman. I am too old to set out, even in the formidable company of Sena, on the ‘long march’ to Mao.