How the efficacy measure is computed, bounded and defended in challenge studies — where sample sizes are small, attack rates sit near the boundary, and the case definition does more work than the model.
Prevented fraction is the proportion of disease in the vaccinated group avoided relative to controls. It is one minus the relative risk:
PF = 1 − (attack rate in vaccinates ÷ attack rate in controls)
A prevented fraction of 0.80 means eighty percent of the cases that would have occurred were prevented. It is the standard efficacy measure in veterinary biologics because it maps directly onto the label claim being sought — and because the challenge study design, with a deliberately infected control group, gives a clean denominator that field studies rarely do.
Challenge studies are small. Ten to twenty animals per group is typical, and attack rates commonly sit near zero in vaccinates and near one in controls — precisely the regime where normal approximations fail.
A Wald interval on a proportion near a boundary can extend past the logical limits of the parameter, and its actual coverage can be far from the nominal ninety-five percent. Reporting a prevented fraction of 0.85 with an interval whose lower bound is computed by normal approximation invites a reviewer to recompute it, and the recomputation will not agree.
Exact or score-based intervals maintain coverage at these sample sizes and produce bounds inside the admissible range. This is not a refinement — the lower bound is what supports the label claim, so the method used to construct it is the method that determines whether the claim holds.
Prevented fraction is computed from a binary classification of each animal. Everything therefore depends on the threshold separating a case from a non-case.
A lenient definition — any clinical sign, any positive isolation — raises the control attack rate and usually raises apparent efficacy. A strict one, requiring multiple concurrent criteria, lowers both arms and can make an effective vaccine look weak if the challenge model does not reliably produce severe disease.
This is why the case definition must be pre-specified with the clinical or laboratory criteria fully stated, including how borderline and missing observations are handled. It is not recoverable after the fact, and a regulator will ask how it was set — a question with only one good answer, which is that it was set before anyone saw the data.
If no controls become infected, the study has failed as an efficacy trial regardless of what happened in the vaccinated group. Prevented fraction is undefined when the control attack rate is zero, and no analytic manoeuvre recovers it.
This is the reason challenge study protocols carry a validity criterion: a minimum attack rate in controls, pre-specified, below which the study is declared invalid rather than analyzed. A study that misses that threshold and is reported anyway produces a number that looks like efficacy and is not.
Saying so is uncomfortable and occasionally expensive. It is also the only defensible position, and the alternative fails at the point where it matters most.
Prevented fraction can be adjusted for covariates through a regression model on the binary outcome. At challenge-study sample sizes, it often should not be.
With ten to twenty animals per group there is very little information with which to estimate a covariate effect, and an adjusted estimate can be less reliable than the unadjusted one while appearing more sophisticated. Where a covariate is genuinely expected to matter — sex, housing block, litter — the better answer is usually to handle it in the design, through blocking or stratified randomization, rather than to correct for it afterwards.
Where adjustment is warranted, as in a longer-duration safety or stability study with repeated measures on the same animals, mixed models with the animal as a random effect are the appropriate structure — and there the covariate information genuinely exists.
MRP Group has served as statistician to a veterinary biologics manufacturer across efficacy, assay validation and safety studies: prevented-fraction efficacy analysis for a Salmonella Typhimurium vaccine; assay validation for recombinant adenovirus and rabies glycoprotein detection, assessed through precision, accuracy and ruggedness; and a 120-day master seed safety study for a combined bursal disease, infectious laryngotracheitis and Marek's disease vaccine, analyzed with mixed models including a gender covariate.
Client named on request.
The proportion of disease in the vaccinated group avoided relative to controls — one minus the relative risk. PF = 1 − (vaccinate attack rate ÷ control attack rate). It is the standard efficacy measure in veterinary biologics because it maps onto the label claim.
Because challenge studies are small and attack rates sit near the boundaries, where Wald intervals lose coverage and can exceed the parameter's logical range. The lower bound supports the label claim, so the construction method determines whether the claim holds.
More than any modeling choice. Prevented fraction is computed from a binary classification of each animal, so the threshold that separates a case from a non-case determines the attack rates in both arms and therefore the estimate. A lenient definition raises the control attack rate and usually raises apparent efficacy; a strict one lowers both. The definition must be pre-specified with the clinical or laboratory criteria fully stated, because it is not recoverable after the fact and a regulator will ask how it was set.
The study has failed as an efficacy trial. Prevented fraction is undefined with a zero control attack rate. This is what the pre-specified validity criterion is for: declare the study invalid rather than analyze it.
Usually not at challenge-study sample sizes — there is too little information to estimate covariate effects reliably, and adjustment can make the estimate worse while looking better. Handle expected covariates in the design through blocking or stratified randomization instead.
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