Vaccine efficacy is calculated by comparing how often disease occurs in a vaccinated group versus an unvaccinated group during a clinical trial. The core formula is simple: take the disease rate in the vaccinated group, divide it by the disease rate in the unvaccinated group, and subtract the result from 1. A vaccine with 90% efficacy means vaccinated people got sick at one-tenth the rate of unvaccinated people. But this single number, clean as it looks on a headline, conceals layers of methodological choices that shape what it actually tells you about protection.
The Core Calculation
The formula works by measuring what epidemiologists call relative risk. You take the “attack rate” (basically, the fraction of people who got sick) in each group and compare them. If 10 out of 10,000 vaccinated participants got infected, the attack rate in the vaccinated group is 0.1%. If 100 out of 10,000 unvaccinated participants got infected, the attack rate in the unvaccinated group is 1%. Divide 0.1% by 1%, and you get 0.10. Subtract that from 1, and the vaccine efficacy is 0.90, or 90%.
When you see a confidence interval alongside a vaccine efficacy number, that range reflects statistical uncertainty around the estimate. Researchers have debated for decades which method produces the most reliable confidence intervals for vaccine efficacy. A simulation study found that several common approaches can have their coverage probability drift away from the target level, meaning the stated range may be slightly too narrow or too wide, particularly when the total number of confirmed cases in the trial is small.1PubMed Central. Confidence interval estimation for vaccine efficacy against COVID-19 For large Phase 3 trials with hundreds or thousands of endpoint cases, this matters less. For smaller trials, the choice of statistical method can shift the lower bound of the confidence interval enough to change whether a vaccine clears a regulatory threshold.
Relative Risk Reduction Versus Absolute Risk Reduction
The standard vaccine efficacy formula gives you a relative risk reduction. It tells you how much your risk drops compared to the unvaccinated group’s risk. But it does not tell you how large the unvaccinated group’s risk was to begin with, and that distinction matters enormously for understanding what a number like “95% efficacy” means in practice.
During COVID-19 vaccine trials, the headline relative risk reduction figures for the leading vaccines were around 95%. But because the absolute risk of getting symptomatic COVID-19 during the trial period was low in both groups, the absolute risk reduction was generally less than 1–2%.2PubMed Central. Efficacy and effectiveness of covid-19 vaccine – absolute vs. relative risk reduction That does not mean the vaccines were useless. It means most people in the control group also did not get sick during the relatively short trial window. When scaled across millions of people and longer time horizons, that small absolute difference prevents enormous numbers of infections. Still, reporting only the relative figure can make a treatment look more impressive than the raw numbers support, and reporting only the absolute figure can make it look trivially small. Both numbers together give the full picture.
Efficacy Versus Effectiveness
Efficacy and effectiveness are not interchangeable terms. Efficacy comes from randomized controlled trials, where participants are carefully selected, closely monitored, and randomly assigned to receive the vaccine or a placebo. Effectiveness comes from the real world, where people have varying health conditions, may not store the vaccine perfectly, and face a broader range of viral exposures. Mathematical models of vaccination often assume that trial-derived efficacy translates directly into real-world effectiveness, but in practice the two can diverge.3PubMed Central. Distinguishing vaccine efficacy and effectiveness
Real-world effectiveness tends to be somewhat lower than trial efficacy, because trial conditions are optimized and populations are often healthier. But effectiveness can sometimes appear higher if the vaccine also reduces transmission and creates indirect protection in the community. The gap between the two numbers is one reason public health authorities track vaccine performance continuously after rollout, rather than relying solely on trial results.
How Real-World Effectiveness Gets Measured
Once a vaccine is in widespread use, you cannot run a placebo-controlled trial anymore. Researchers instead turn to observational study designs. The most widely adopted approach in recent years is the test-negative design. In this setup, people who show up at a clinic with symptoms get tested for the pathogen in question. Those who test positive become the “cases,” and those who test negative serve as the comparison group. Researchers then look at how many in each group were vaccinated and calculate effectiveness from the odds of vaccination in each group.4PubMed. The test-negative design for estimating influenza vaccine effectiveness
This design was originally developed for influenza vaccines and has exploded in use. A systematic review identified 348 published test-negative design studies covering 12 different pathogens, with 90% of those studies published since 2011.5PubMed Central. The use of test-negative controls to monitor vaccine effectiveness: a systematic review of methodology The design’s appeal is that everyone in the study sought medical care for similar symptoms, which helps control for the tendency of people who feel sick to seek testing. It is not perfect, though. If asymptomatic infections are much less likely to be detected than symptomatic ones, and the vaccine is better at preventing symptoms than preventing infection altogether, the design can overestimate how well the vaccine blocks infection.6Clinical Infectious Diseases. Measuring Vaccine Efficacy Against Infection and Disease in Clinical Trials: Sources and Magnitude of Bias in Coronavirus Disease 2019 (COVID-19) Vaccine Efficacy Estimates That kind of nuance rarely makes the headline.
Researchers have been developing ways to improve test-negative studies further. One emerging approach uses “negative control” variables to detect hidden biases. For example, in a study of COVID-19 vaccine effectiveness in young children, hepatitis B vaccination status can serve as a control exposure, since the hepatitis B vaccine should have no effect on COVID-19 risk. If the analysis shows an apparent association between hepatitis B vaccination and COVID-19, that signals confounding that needs correcting.7The Journal of Infectious Diseases. Improved Methods for Vaccine Effectiveness Studies
The Healthy Vaccinee Problem
One of the trickiest biases in observational vaccine studies is the healthy vaccinee effect. People who get vaccinated tend, on average, to be healthier and more health-conscious than people who skip vaccination. That means a straightforward comparison between vaccinated and unvaccinated groups will make the vaccine look better than it actually is, because the vaccinated group was healthier to begin with.
A systematic review of influenza vaccine studies found that adjusting for confounders changed effectiveness estimates substantially. Accounting for confounding and healthy vaccinee bias increased apparent vaccine effectiveness against all-cause death by an average of 12 percentage points and against hospitalization by about 9 percentage points.8PubMed Central. Frequency and impact of confounding by indication and healthy vaccinee bias in observational studies assessing influenza vaccine effectiveness: a systematic review In other words, the raw numbers were exaggerating the vaccine’s effect by that margin before statistical corrections.
COVID-19 studies ran into the same issue. A national cohort study in Qatar found that vaccinated people had a 24% lower rate of non-COVID-19 death in the first six months after vaccination, with the gap especially pronounced early on. During the first six months, the vaccinated group’s death rate from causes completely unrelated to COVID was roughly a third of the unvaccinated group’s rate.9PubMed Central. Assessing healthy vaccinee effect in COVID-19 vaccine effectiveness studies: a national cohort study in Qatar Since the vaccine obviously does not prevent car accidents or cancer, that gap reflects a baseline difference in who chose to get vaccinated. After the first six months, the pattern actually reversed, with the vaccinated cohort showing a higher non-COVID death rate, possibly because the very frailest individuals had died in both groups and the remaining composition had shifted.
A separate analysis of over two million health records corroborated this pattern, finding that all-cause mortality was consistently and substantially lower in vaccinated groups regardless of whether a COVID-19 wave was occurring. The healthy vaccinee effect appeared to be the only plausible explanation.10PubMed. Does the healthy vaccinee bias rule them all? Association of COVID-19 vaccination status and all-cause mortality from an analysis of data from 2.2 million individual health records Any real-world vaccine effectiveness estimate that does not account for this baseline difference will be inflated.
How Protection Wanes Over Time
Vaccine efficacy is not a fixed number. It is a snapshot taken at a specific moment after vaccination, and for most vaccines, protection erodes as months pass. A large systematic review and meta-regression found that average vaccine efficacy or effectiveness against COVID-19 infection dropped by about 21 percentage points between the first month and the sixth month after full vaccination. Protection against symptomatic disease fell by roughly 25 points over the same period. Protection against severe disease held up better, declining by about 10 percentage points.11The Lancet. Effectiveness of COVID-19 vaccines against the, severity of infections over time: a systematic review and meta-regression
This pattern, where protection against infection fades fastest while protection against hospitalization and death declines more slowly, is not unique to COVID-19 vaccines. It reflects how immune memory works. Antibody levels drop relatively quickly after vaccination, reducing the ability to block infection at the mucosal surface. But memory B cells and T cells persist longer and can ramp up a response once infection takes hold, preventing the progression to severe disease.
Booster doses restore much of the lost protection. An Italian nationwide study found that booster doses reduced infections by about 65%, hospitalizations by roughly 69%, and deaths by 97% compared to the efficacy seen six or more months after the primary vaccination course.12PubMed Central. Primary COVID-19 vaccine cycle and booster doses efficacy: analysis of Italian nationwide vaccination campaign Among older adults, the protection from boosters was similarly dramatic, with roughly 75% lower risk of infection and over 80% lower risk of hospitalization compared to those who completed their primary course five or more months earlier.13PubMed Central. Efficacy of COVID-19 vaccine booster doses in older people
But booster protection also wanes. A test-negative study in England tracked bivalent COVID-19 boosters and found that their incremental effectiveness against hospitalization peaked at about 53% in the first two to four weeks, then dropped to roughly 36% after ten or more weeks.14The Lancet Infectious Diseases. Effectiveness of monovalent and bivalent COVID-19 booster vaccines against hospitalisation in England: a test-negative case-control study Statisticians have developed methods to estimate vaccine efficacy as a smooth function of time rather than a single number, producing curves that show protection rising, plateauing, and then declining.15American Journal of Epidemiology. Estimation of Vaccine Efficacy in the Presence of Waning: Application to Cholera Vaccines These time-varying estimates are more honest than a single headline number but harder to communicate to the public.
When the Virus Changes
A vaccine’s efficacy number is always measured against a specific version of the pathogen circulating at the time of the trial. When the pathogen mutates, the number can shift dramatically. The emergence of the Delta variant of SARS-CoV-2 provided a clear illustration. After a single dose of either the Pfizer or AstraZeneca vaccine, effectiveness against the Delta variant was about 31%, compared to roughly 49% against the earlier Alpha variant. Two doses of the Pfizer vaccine brought effectiveness against Delta up to about 88%, compared to about 94% against Alpha. For the AstraZeneca vaccine, two doses reached about 67% against Delta versus roughly 75% against Alpha.16PubMed Central. Effectiveness of Covid-19 Vaccines against the B.1.617.2 (Delta) Variant
These shifts are not unique to COVID-19. Influenza vaccine effectiveness varies from year to year depending on how well the vaccine strains match the circulating strains, which is why influenza vaccines are reformulated annually. For COVID-19, the move toward updated boosters targeting newer variants follows the same logic. The efficacy formula itself does not change, but the number it produces is only meaningful for the pathogen version tested.
Herd Immunity and Population-Level Math
Individual vaccine efficacy feeds directly into calculations of herd immunity, the coverage threshold at which enough people are immune to interrupt transmission and protect the unvaccinated. The basic relationship is straightforward: the more effective the vaccine and the less transmissible the pathogen, the lower the coverage needed. But both variables can work against you simultaneously.
A modeling study examined the vaccination coverage required for herd immunity against SARS-CoV-2 across a range of transmissibility values. With a basic reproduction number between 3 and 10 and vaccine effectiveness between 70% and 100%, the required coverage varied enormously. Higher transmissibility and lower effectiveness both pushed the threshold up, and factors like breakthrough infections and crowded settings made it even harder to reach.17PubMed Central. Percentages of Vaccination Coverage Required to Establish Herd Immunity against SARS-CoV-2
Another wrinkle: standard herd immunity calculations assume a homogeneous population where everyone mixes equally. Real populations are heterogeneous, with different age groups, contact patterns, and susceptibilities. When models account for this heterogeneity, the herd immunity threshold drops. One analysis using realistic mixing patterns and a vaccine efficacy of 95% showed that the herd immunity threshold fell to around 40% in a heterogeneous population, compared to 63% when the population was assumed to be uniform.18PubMed Central. Vaccination and herd immunity thresholds in heterogeneous populations The practical implication is that simple threshold calculations often overestimate how many people need to be vaccinated, though the precise adjustment depends on local contact patterns.
How Efficacy Numbers Get Misread
Even a perfectly calculated vaccine efficacy number can be misinterpreted when taken out of context. One of the most common errors during the COVID-19 pandemic was the base rate fallacy. As vaccination rates climbed above 80% or 90% in some populations, the majority of hospitalizations and deaths inevitably occurred among vaccinated people, simply because vaccinated people made up the vast majority of the population. Media and social media commentators pointed to this as evidence that vaccines were not working, ignoring the denominator entirely.19PubMed Central. Tracking vaccine effectiveness in an evolving pandemic, countering misleading hot takes and epidemiologic fallacies
To see why this reasoning is wrong, imagine a population of 1,000 people where 950 are vaccinated and 50 are not. If the vaccine has 80% efficacy against hospitalization, and the unvaccinated hospitalization rate is 2%, then 1 unvaccinated person (2% of 50) and about 3.8 vaccinated people (0.4% of 950) end up in the hospital. Nearly 80% of the hospitalized patients are vaccinated, yet the vaccine clearly works: your risk of hospitalization is five times lower if you got the shot. The raw count of vaccinated patients tells you nothing without knowing how many vaccinated people there were in total.
Conditional Effectiveness and Layered Outcomes
Vaccine effectiveness is often reported separately for different outcomes: infection, symptomatic disease, hospitalization, and death. These numbers are not independent. Each more severe outcome is a subset of the less severe one, which introduces a concept called conditional effectiveness. This measures how much the vaccine protects against a severe outcome given that the less severe outcome has already occurred.20PubMed Central. Estimating conditional vaccine effectiveness
For example, a vaccine might have 50% effectiveness against infection and 90% effectiveness against death. The conditional effectiveness against death given infection tells you how much the vaccine reduces the case fatality rate among those who got infected despite being vaccinated. This layered view is particularly useful for understanding what a vaccine does for you if you do get a breakthrough infection: even if the vaccine failed to prevent infection, it may still substantially reduce your chance of ending up in the hospital or dying.
Immune Correlates and the Future of Efficacy Measurement
Running massive randomized trials every time a vaccine is updated is expensive and slow. One of the most active areas of vaccine research is identifying immune correlates of protection: measurable markers in the blood, like antibody levels, that reliably predict whether someone is protected. If a specific antibody threshold can be validated as a correlate, then future vaccine variants could potentially be authorized based on whether they generate antibodies above that threshold, rather than requiring a full efficacy trial with disease endpoints.21PubMed Central. Four Statistical Frameworks for Assessing an Immune Correlate of Protection (Surrogate Endpoint) from a Randomized, Controlled, Vaccine Efficacy Trial
This approach has been used for decades with some vaccines, like those for hepatitis B, where an antibody level above a known threshold is considered protective. For respiratory viruses like influenza and SARS-CoV-2, establishing correlates has been harder because protection against infection is partial and depends on multiple arms of the immune system. Still, the COVID-19 pandemic accelerated work in this area considerably, and regulatory agencies have already used immunobridging data, rather than clinical endpoints, to authorize updated COVID-19 boosters. The efficacy formula has not changed, but the way it gets applied is evolving.