Quantics can support you through the complete
vaccine development pathway.

Vaccine Bioassay Pathway

Correlates of Protection Experience

Quantics has been involved with the development, optimization and validation of a wide range of vaccine related bioassays for a number of UK, US and European customers. We have particular experience in supporting Correlation of Protection  and Passive Transfer analysis for complex  biodefence and biodefence vaccine programs including:

  • Bacillus anthracis (Vaccines and MAbs)
  • Yersinia pestis
  • Botulinum
  • Ricin

The Figure illustrates the steps in the estimation of vaccine efficacy.

Step 1: model the antibody levels associated with protection in animals. Typically a logistic regression model.

Step 2: measure the distribution of antibody levels in a group of subjects vaccinated according to the planned regime.

Step 3: From the animal prediction curve, predict the probability of protection at various human antibody levels.

Read more in our paper – Estimating vaccine efficacy using animal efficacy data

Read our Paper Here

Minimizing Laboratory Work

Quantics’ biomathematical experience can maximize the information obtained from expensive laboratory work. Quantics is a keen supporter of “3R” principles and our biomathematical expertise can significantly reduce the animals / replicates  / experiments required. For example, in a challenge or LD 50 assay, animal requirements can be reduced  by >40% in some instances simply by using mathematically efficient time-to-event analysis rather than the standard analysis of outcome at a certain timepoint.

Maximizing Information

  • Time-to-event analysis is fully accepted by regulators.
  • In use for batch release of licensed products.
  • Particularly beneficial and cost effective for BSL category 3-4 work.
  • Reduces cost of study dramatically.

The figure shows the precision of the estimate of relative potency obtained with the traditional (probit or logit) method in blue, and that obtained with time-to-event analysis (survival analysis) in red. The animation shows what happens as the number of animals per assay is reduced from 16 with survival analysis. You will see that when the number of animals per assay reaches 6, the precision of the survival analysis matches that of the traditional analysis using 16 animals.

So survival analysis can increase the assay precision, or reduce the number of animals required (or a mixture of both).


Saving Time, Money & Mice


A number of our clients have taken survival analysis for their studies.

Client A: This client reduced the number of animals from 16 to 12 per group and improved the precision of the RP estimate.

Client B:  This client was able to improve the precision of the RP estimate by a factor of approximately 2.

Client C: This client was able to improve the pass rate for their FDA-required test of parallelism (similarity) of the test samples versus the reference standard.  With a probit model the failure rate was 25%; with the survival model parallelism failures were reduced to 5%.

The Client C example illustrates a further benefit of using survival analysis: more precise estimates of the slope of the dose-response are obtained, impacting equivalence tests for parallelism.

Correlates of Protection Explained

This text below is a short extract of the paper Estimating vaccine efficacy using animal efficacy data written by Quantics staff Ann Yellowlees and Richard Perry.

European Journal of Pharmacology 759, 2015 https://www.sciencedirect.com/science/article/abs/pii/S0014299915002502?via%3Dihub

Vaccine efficacy is defined as the percentage reduction in the incidence of a disease among people who have received a vaccine compared to the incidence in unvaccinated people.

Ideally vaccine efficacy is measured directly in a randomised controlled trial with a vaccine challenge. When this is not possible, an indirect method has to be used.

The FDA document Product development under the animal rule[1] provides some guidance for the evaluation of vaccine efficacy in the absence of human clinical efficacy data by using “an appropriate immune marker”, otherwise known as a “protective correlate”. A protective correlate is a measurable marker that is statistically related to a clinical endpoint and is reasonably likely to predict the clinical endpoint.

[1] https://www.fda.gov/regulatory-information/search-fda-guidance-documents/product-development-under-animal-rule

During vaccine development the relationship between the protective correlate marker and the clinical endpoint in animals is modelled using data from animal studies. The relationship can then be bridged to humans by the assumption that the marker is also predictive of the clinical endpoint in humans.

Deriving the vaccine efficacy

Deriving the vaccine efficacy requires two separate sets of data:

  1. The animal study data relating the level of protective correlate to disease protection
  2. The levels of the protective correlate in humans which are achieved by the proposed vaccination regimen, assessed in a healthy volunteer clinical trial.

These are combined in a 3-step process:

Vaccine development: Correlates of Protection

Step 1: model the antibody levels associated with protection in animals. Typically a logistic regression model.

Step 2: measure the distribution of antibody levels in a group of subjects vaccinated according to the planned regime.

Step 3: From the animal prediction curve, predict the probability of protection at various human antibody levels.

The vaccine efficacy (percentage reduction in the incidence of a disease) is estimated using Bayes’ Theorem (Bayes T. and Price R., 1763) to combine the probability of protection (given the antibody level is x) with the likelihood of the antibody level being x.

Precision of the estimate of protection

In order to be useful, the estimate of the probability of protection needs to be sufficiently precise, typically measured by the 95% confidence interval.  If the confidence interval is too wide, the estimate of the protection may not be regarded as clinically convincing.  Calculating the confidence interval is mathematically complex.

Optimising the balance between animal and human data

During early vaccine development the initial experiments to create the animal antibody vs protection curve may not result in the mean animal antibody level being around the values ultimately seen in humans, leading to imprecise estimates of vaccine efficacy.

The estimate of the vaccine efficacy can be optimised either by conducting further animal experiments to improve the primary model fit, and by adding further information on human antibody levels.

Simulation can provide a guide to the increase in precision gained by the various options

The balance can be examined using simulation of adding data in both ways. For more detail on simulation techniques see blog:  using simulation in bioassay to reduce the need for laboratory work.

vaccine development: Correlates of Protection and immunity

The left panel illustrates adding more animal data at ED50, ED80 and ED95 to improve the primary model fit, and the right panel of this illustrates the alternative of adding more human data.


In situations where it is not possible to test a vaccine directly in humans, the indirect method using correlates of protection can be used. Early experiments use standard designs as there is usually no information about the primary model or human antibody levels.

The paper that this blog is based on shows that simulation can be used after initial data is obtained to provide some guidance on how to design further experiments. Such further experiments may be required so the resulting estimates of efficacy are adequately precise to support conclusions about the vaccine and the proposed regimen, or are adequately powered to detect differences between vaccine candidates.