group <- c("Vaccinated", "Unvaccinated")
cases <- c(5, 25)
population <- c(500, 500)
risk <- cases / population
barplot(
risk,
names.arg = group,
col = c("steelblue", "tomato"),
main = "Risk of Infection by Vaccination Status"
)
Outbreak Context
An outbreak of measles, a highly contagious viral disease, occurred in a semi-urban community with mixed vaccination coverage. Measles is one of the most transmissible infectious diseases, with a basic reproduction number (R₀) often estimated between 12 and 18.
Public health teams initiated an outbreak investigation to:
identify confirmed and suspected cases
determine vaccination status
assess transmission patterns
estimate the real-world effectiveness of the vaccine
For an overview of measles epidemiology, see: https://www.who.int/news-room/fact-sheets/detail/measles
Understanding Vaccine Effectiveness
Vaccine effectiveness (VE) refers to how well a vaccine performs in real-world conditions, outside controlled clinical trials.
Unlike vaccine efficacy, effectiveness reflects:
population diversity
variation in exposure
real-world healthcare access
behavioural factors
👉 Learn more: https://www.who.int/news-room/feature-stories/detail/vaccine-efficacy-effectiveness-and-protection
Why This Matters in Public Health
Estimating vaccine effectiveness is essential for:
evaluating vaccination programmes
identifying vulnerable populations
informing outbreak response
guiding policy decisions
For further reading: https://pmc.ncbi.nlm.nih.gov/articles/PMC6734418/
Key Concept
Important
Vaccine effectiveness measures the reduction in disease risk among vaccinated individuals compared to unvaccinated individuals in real-world conditions.
Observed Data
The following table summarises the number of cases and non-cases among vaccinated and unvaccinated individuals during the outbreak.
| Group | Cases (a, c) | Non-cases (b, d) |
|---|---|---|
| Vaccinated | 4 | 96 |
| Unvaccinated | 20 | 80 |
Formula for Vaccine Effectiveness
Vaccine effectiveness is calculated as:
VE = (1 − Relative Risk) × 100
Step-by-Step Calculation
Show calculation
Calculate risk in the vaccinated group: 5 / 500 = 0.01
Calculate risk in the unvaccinated group: 25 / 500 = 0.05
Relative Risk = 0.01 / 0.05 = 0.2
VE = (1 − 0.2) × 100 = 80%
Pause and Reflect
TipSelf-check
Why might vaccine effectiveness differ between populations?
Show suggested answer
Differences in exposure, population structure, healthcare access, and underlying health conditions can influence estimates.
Plotly Data visualistion
Distribution Explorer: Health-Related Measures — open in a new window
Youtube
Panopto
R Code Demos R Code and Output
R Code Only
group <- c("Vaccinated", "Unvaccinated")
cases <- c(5, 25)
population <- c(500, 500)
risk <- cases / population
barplot(
risk,
names.arg = group,
col = c("steelblue", "tomato"),
main = "Risk of Infection by Vaccination Status"
)R Output Only
Interactive R Code
R Code Table example
Interpreting the Results
An 80% vaccine effectiveness means vaccinated individuals have substantially lower risk compared to unvaccinated individuals.
The calculation assumes both groups are comparable and equally exposed.
Confounding factors such as age, immunity, or healthcare access may influence results.
Epidemic Curve
Outbreak Report
Download Dataset
Quiz
Based on the outbreak data, what does a vaccine effectiveness of 80% mean in practice?
Show answer
Answer: Vaccinated individuals have an 80% lower risk of infection than unvaccinated individuals
Explanation:
Vaccine effectiveness compares the risk of disease in vaccinated and unvaccinated groups under real-world conditions. An 80% VE means the vaccinated group experienced substantially lower risk, not that infection risk was eliminated entirely.
Key Takeaway
Tip
Vaccination significantly reduces the likelihood of infection and severe disease, even if it does not eliminate risk entirely.
Binomial Theorem equation
\[(x + a)^{n} = \sum_{k = 0}^{n}{\binom{n}{k}x^{k}a^{n - k}}\]
Latex Equations Approach
Display equation example
\[ P(X=x)=\binom{n}{x}p^x(1-p)^{n-x} \]
Further Reading
WHO Measles Fact Sheet : https://www.who.int/news-room/fact-sheets/detail/measles Vaccine Effectiveness Overview : https://www.who.int/news-room/feature-stories/detail/vaccine-efficacy-effectiveness-and-protection Measles Vaccine Impact Study : https://pmc.ncbi.nlm.nih.gov/articles/PMC6734418/