Compute VE from a vaccine trial 2×2 table — attack rate, relative risk, confidence interval (Katz method), ARR, NNV, and statistical tests. All calculations run in your browser.
Enter the number of cases and total participants in each group, then press Calculate.
VE is a relative measure. This table helps you read the size of the relative risk reduction — always read it together with its confidence interval.
| VE range | Statistical meaning |
|---|---|
| ≥ 90% | A very large relative risk reduction. |
| 70% – <90% | A large relative risk reduction. |
| 50% – <70% | A moderate relative risk reduction. |
| 30% – <50% | A small relative risk reduction. |
| 0% – <30% | A very small reduction — check whether the confidence interval includes 0%. |
| < 0% (negative) | Relative risk in the vaccine group is higher in these data. This pattern usually signals confounding, non-comparable groups, or random variation in a small sample — it calls for investigating the study design, not a causal conclusion. |
Note: the cutoffs above are descriptive for reading the number, not regulatory approval criteria. Regulators assess the lower bound of the confidence interval, not the point estimate (see FAQ).
Recomputed with this calculator from the published case counts and at-risk populations. Confidence intervals are computed with the Katz (log-RR) method; the original publications used slightly different methods, so interval bounds may shift slightly.
Both terms use the same statistical formula — what differs is the data source:
| Efikasi (efficacy) | Efektivitas (effectiveness) | |
|---|---|---|
| Data source | Randomized controlled trial | Observational studies in the general population |
| Conditions | Ideal and controlled: selected participants, dosing schedule followed, strict follow-up | Real world: imperfect coverage, behavior variation, different pathogen variants |
| Comparison group | Placebo / randomized control | Unvaccinated population (statistically adjusted) |
| Association measure | Usually direct relative risk | Often the odds ratio from case–control studies |
This calculator computes the same statistics for both contexts; the case–control (OR) mode is provided for observational data. The "efficacy" or "effectiveness" label is determined by the source data's study design, not by the formula.
Standard formulas from the vaccine epidemiology literature (cited in the footnotes).
z values: 1.645 (90%), 1.960 (95%), 2.576 (99%). The log-RR method requires at least 1 case in each group; when a = 0, the VE point estimate = 100% is still reported but its interval cannot be computed. When c = 0, RR is undefined.
Formula sources: Kirkwood & Sterne, Medical Statistics (SE log-RR); Manfrin & Joshi 2021, J Anal Pharm Res 10(2):93–96 (CER/EER/RR/ARR/NNT/VE framework + 95% & 90% examples); Medicina 2021, 57:199 (ARR CI, NNV, VE CI = 1 − RR CI); NCSS PASS documentation for unpaired case–control VE design.
VE is a measure of how much the relative risk of disease is reduced in the vaccinated group compared with the unvaccinated (or placebo) group, computed from clinical trial data. VE 90% means disease risk in the vaccine group is 90% lower in relative terms — not that 90 out of 100 people are absolutely protected.
Compute the attack rate for each group: ARV = vaccine cases / vaccine total, ARU = control cases / control total. Relative risk RR = ARV / ARU, then VE = (1 − RR) × 100%. Example: 10 cases among 1,000 vaccinated participants (ARV = 1%) and 90 cases among 1,000 control participants (ARU = 9%) gives RR = 0.111 and VE = 88.89%.
Efficacy refers to randomized controlled trial results under ideal conditions and selected participants, while effectiveness refers to real-world performance in the general population with imperfect coverage and potentially different pathogen variants. The statistical formula is the same; what differs is the source data's study design.
Negative VE occurs when the attack rate in the vaccine group is higher than in the control group (RR greater than 1) in those data. This pattern can signal differences in characteristics between groups (confounding), non-comparable study design, or random variation in a small sample — not evidence of a causal relationship. Check the confidence interval and the study design before interpreting.
VE is a relative measure, while ARR = ARU − ARV is the absolute risk difference in percentage points. They answer different questions: VE 95% for a disease striking 1 in 10,000 people means an ARR of only about 0.0095 percentage points. NNV = 1/ARR states how many people need to be vaccinated to prevent one case.
NNV = 1/ARR, rounded up to the next individual. If ARR = 8% (0.08), then NNV = 13: on average 13 people need to be vaccinated to prevent one case in a population like the study's. NNV depends heavily on how common the disease is — a rare disease yields a large NNV even with high VE.
A 95% confidence interval is the range of VE values consistent with the data at 95% confidence. A narrow range means a more precise estimate, usually from a large sample. If the interval includes 0%, the difference between groups is not necessarily statistically real at that confidence level.
Trial protocols generally require the lower bound of the confidence interval to sit above a certain threshold, e.g. 30% or 50%. VE 90% with a 20% lower bound has weaker data support than VE 60% with a 45% lower bound — the latter is supported by stronger data even though its point estimate is smaller, because the lower bound states the efficacy the data can sustain.
Yes. VE estimates can differ across follow-up periods because immune responses change over time, pathogen variants change, or population behavior changes. VE is an estimate for a specific study period and population, not a universal constant that holds forever.
In case–control studies, participants are selected based on disease status rather than vaccination status, so RR cannot be computed directly. VE is then estimated as (1 − OR) × 100% with OR = (a·d)/(b·c). For rare diseases, the OR approximates the RR, so both approaches give similar results.
No. VE 95% means the relative risk is 95% lower than in the control group. If 1% of the control group falls ill, then about 0.05% of the vaccine group falls ill. The size of absolute protection always depends on the disease's baseline risk, expressed by ARR and NNV.
No. This calculator is an educational tool for understanding vaccine trial statistics from aggregate data. Health decisions are individual and consider many factors beyond the VE figure. Discuss with a healthcare professional.
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