💻 bioinformatics

A Bayesian modelling framework for inference of latent infection risk patterns from virus neutralisation assay titration data

This paper introduces a two-part Bayesian framework that infers latent infection risk patterns directly from raw virus neutralisation assay titration data by modeling antibody concentrations and propagating uncertainty into an age-structured serocatalytic mixture model, thereby overcoming the limitations of conventional dichotomous methods and revealing distinct infection dynamics for enteroviruses A71, D68, and coxsackievirus A6 in England.

Original authors: Alrefae, T. A., Pons-Salort, M., Donnelly, C. A., Lambert, B., Kamau, E.

Published 2026-09-22

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CC BY 4.0

Original authors: Alrefae, T. A., Pons-Salort, M., Donnelly, C. A., Lambert, B., Kamau, E.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

To understand how a virus spreads through a population, scientists often look for the invisible footprints it leaves behind. When a person is infected, their immune system produces proteins called antibodies to fight the invader. These antibodies can linger in the blood long after the infection has cleared, acting as a historical record of exposure. By testing blood samples from many people, researchers can map out who has been infected and when, revealing the hidden patterns of transmission that symptom-based reporting often misses. A common way to measure these antibodies is through a virus neutralisation assay, a laboratory test where blood serum is diluted step-by-step and mixed with a virus to see how much dilution is needed before the virus can still infect cells. Traditionally, scientists have reduced this complex, step-by-step data into a single number, a "titer," which simply marks the point where protection stops. This method, however, throws away a vast amount of information about the actual strength of the immune response and provides no way to measure the uncertainty of that single number.

A team of researchers has developed a new way to look at this data, one that treats the raw results not as a simple pass or fail, but as a continuous story of immune strength. Instead of discarding the details of the dilution steps, they built a statistical framework that reconstructs the actual concentration of antibodies in each person's blood, complete with a measure of how certain that estimate is. They then fed these reconstructed antibody levels into a model that tracks how infection risk changes as people age. This approach allowed them to infer the dynamics of three specific enteroviruses—EV-A71, EV-D68, and CVA6—which are known to cause severe respiratory illness and hand, foot, and mouth disease. By analyzing blood samples from nearly 1,600 people in England collected over three different years, the researchers uncovered a much clearer picture of how these viruses move through communities, revealing that the risk of infection and the duration of immunity vary significantly between these closely related viruses.

The researchers applied their new method to three distinct viruses to see how their immune footprints differed. For two of the viruses, EV-A71 and CVA6, the results confirmed a familiar pattern: infection is most common in early childhood. The model estimated that the proportion of people recently infected peaks at around 40 percent for CVA6 by age five and 32 percent for EV-A71 by age seven. After these early peaks, the rate of new infections drops sharply, and the proportion of the population that remains susceptible to these viruses stays high, with over half of adults aged 40 and older showing no signs of recent or past infection. This suggests that while these viruses circulate heavily among young children, they do not infect everyone, leaving a large portion of the adult population vulnerable to future outbreaks.

In stark contrast, the third virus, EV-D68, told a different story. The researchers found that exposure to this virus is far more widespread and persistent. Their model indicated that the proportion of people who have been infected with EV-D68 exceeds 50 percent by age 13 and continues to climb, reaching nearly 90 percent by age 65. Unlike the other two viruses, where antibody levels tend to fade over time, the model suggested that antibody concentrations for EV-D68 remain elevated throughout a person's life. This implies that people are likely being re-exposed to the virus repeatedly, or that the initial infection triggers a very long-lasting immune response. The force of infection for EV-D68 also appeared to decline much more gradually with age compared to the steep drop seen with the other two viruses, suggesting that transmission continues well into adulthood.

A key finding of this work is that the new method produces different results than the traditional way of analyzing the same data. When the researchers compared their estimates to previous studies that used the old, simplified method of categorizing people as simply "positive" or "negative" based on a fixed cutoff, they found that their new approach estimated lower rates of infection for young children. This difference arises because the new model can distinguish between someone who has a high level of antibodies from a recent infection and someone with a moderate level from an infection years ago. The traditional method, by forcing every positive sample into a single category, cannot make this distinction and often overestimates the number of very recent infections. Furthermore, the new framework provided a way to quantify the uncertainty in these estimates, something the old method could not do.

The researchers also tested whether their findings held up if they assumed that people could eventually lose all immunity and become susceptible again, a process known as seroreversion. For the viruses EV-A71 and CVA6, the data did not support the idea that immunity disappears completely; the models suggested that if it does happen, it takes several decades, with a half-life of immunity measured in the tens of years. For EV-D68, the data was so strong that the model essentially collapsed into a scenario where once infected, a person remains immune for life. While the study did not find evidence for rapid loss of immunity, the authors noted that their model assumes a specific shape for how infection risk changes with age, which might slightly limit the resolution of the data for the very youngest children.

Ultimately, this work demonstrates that the raw data from virus neutralisation assays contains a wealth of information that is often lost when scientists summarize it into a single number. By using a two-part statistical framework that first estimates the actual antibody concentration and then uses those estimates to model infection history, the researchers were able to infer the age-specific risk of infection without relying on arbitrary thresholds. This approach revealed that EV-D68 is likely more common and persistent in the population than previously thought, while EV-A71 and CVA6 leave large pockets of susceptible adults. These insights, derived directly from the raw laboratory measurements, offer a more nuanced view of how these viruses circulate and could help public health officials better understand the risks of future outbreaks and the potential need for vaccination strategies.

Technical Summary: A Bayesian Modelling Framework for Inference of Latent Infection Risk Patterns from Virus Neutralisation Assay Titration Data

Problem Statement
Serological assays, particularly Virus Neutralisation Assays (VNAs), are the standard for estimating cumulative pathogen incidence and monitoring population immunity. However, conventional analysis of VNA data relies on a century-old interpolation method (e.g., Reed-Muench) to determine an "endpoint titre." This approach discards significant information inherent in the raw dilution-series data, treats the assay as a deterministic process despite inherent experimental imperfections, and produces point estimates without measures of uncertainty. Furthermore, traditional epidemiological analyses often dichotomise these titres into binary seropositive/seronegative categories based on arbitrary thresholds, obscuring the continuous variation in antibody levels and limiting the resolution of quantitative analyses at the population level.

Methodology
The authors propose a two-part Bayesian framework that infers latent infection risk patterns directly from raw titration data without dichotomisation.

Stage 1: Mechanistic Probit Model for Antibody Concentration
The first stage models the VNA process as a dose-response experiment. Instead of interpolating a single endpoint, the authors model the probability of cell survival at a given serum dilution $d$ using a mechanistic probit function.
- Formulation: The model assumes a latent underlying neutralising antibody concentration ( $\phi$ ) for each individual. The probability of cell survival $\pi(d)$ is modeled as $\Phi(k_1(\log \phi - \log d))$ , where $\Phi$ is the standard normal cumulative distribution function and $k_1$ controls the steepness of the dose-response curve.
- Inference: Using a binomial sampling model for the replicate outcomes at each dilution step, the framework estimates the posterior distribution of the latent antibody concentration $\phi$ and the slope parameter $k_1$ . This stage quantifies uncertainty in the antibody concentration for each sample, propagating assay-level noise rather than collapsing it into a point estimate.
Stage 2: Age-Structured Serocatalytic Mixture Models
The second stage integrates the uncertainty from Stage 1 into an epidemiological model to infer infection dynamics.
- Integration: Rather than fitting jointly, the framework uses a "cut" inference approach. It integrates over the posterior draws of individual antibody concentrations ( $\phi$ ) generated in Stage 1 to evaluate the likelihood in the second stage.
- Model Structures: The authors employ serocatalytic models to describe the evolution of serostates with age:
  - SII Model (Susceptible, Recently Infected, Infected a while ago): Used for Enterovirus A71 (EV-A71) and Coxsackievirus A6 (CVA6). This model includes a waning rate ( $\psi$ ) allowing transition from a high-concentration state ( $I^{++}$ ) to a lower, persistent state ( $I^+$ ), but excludes complete seroreversion ( $I^+ \to S$ ).
  - SI Model (Susceptible, Infected): Used for Enterovirus D68 (EV-D68), assuming no waning ( $\psi=0$ ) and treating infection as an absorbing state, reflecting high lifetime seroprevalence.
- Likelihood: The likelihood for an individual is a mixture of log-normal distributions corresponding to different serostates, weighted by the age-dependent probability of occupying that state derived from the ODE system.

Key Contributions

Direct Inference from Raw Data: The framework bypasses the need for predetermined seropositivity thresholds, inferring infection rates and antibody concentrations directly from the raw well-level outcomes of the titration assay.
Uncertainty Propagation: It is the first approach to propagate assay-level uncertainty (from the dilution series) through to epidemiological parameter estimation (force of infection, waning rates), providing credible intervals for all estimates.
Mechanistic Link: It bridges the gap between assay-level statistical models (which estimate titres) and epidemiological models (which estimate transmission), allowing for joint inference on latent serostate membership, force of infection ( $\lambda$ ), and serological waning rates.
Nuanced Serodynamics: By modelling antibody concentrations as continuous latent variables, the framework distinguishes between recently infected individuals ( $I^{++}$ ) and those infected previously ( $I^+$ ), offering a more granular view of immunity landscapes than binary classification.

Results
The framework was applied to three cross-sectional serosurveys of the English population (2006, 2011, 2017) for EV-A71, EV-D68, and CVA6.

Antibody Concentrations: EV-D68 showed consistently higher and more persistent lifetime antibody concentrations compared to EV-A71 and CVA6. For EV-A71 and CVA6, concentrations peaked in childhood and declined, whereas EV-D68 concentrations remained elevated into adulthood.
Serostate Dynamics:
- EV-A71 & CVA6: The proportion of recently infected individuals ( $I^{++}$ ) peaked around 32% (age 7) for EV-A71 and 40% (age 5) for CVA6, declining with age. A significant portion of the adult population (approx. 50-60%) remained in the susceptible state ( $S$ ), indicating residual susceptibility.
- EV-D68: The proportion of previously infected individuals exceeded 50% by age 13 and approached 90% by age 65. The susceptible fraction in adults was low (<10%).
Force of Infection (FOI):
- For EV-A71 and CVA6, the FOI was high in early childhood and declined rapidly, approaching zero by age 10.
- For EV-D68, the FOI declined more gradually with age. The authors note that pooling data across survey years (2006–2017) may average over a changing transmission regime, particularly given the 2014 global EV-D68 outbreak.
Comparison to Previous Methods: Compared to previous analyses using binarised data ("Old" method), the new framework ("New" method) estimated lower forces of infection, particularly in the 1–10 year age group. The authors attribute this to the mixture model's ability to probabilistically assign intermediate antibody levels to serostates and the explicit modelling of waning, which allows the FOI to be estimated without forcing all age-related declines into the transmission rate.

Significance and Claims
The authors claim that their framework uncovers wide-ranging variation in antibody levels often obscured by conventional endpoint titre methods. By avoiding dichotomisation at fixed thresholds, the method provides a clearer picture of seroconversion dynamics and improves the estimation of virus transmission and population susceptibility. The approach is presented as a principled means to estimate cumulative incidence and track immunity dynamics directly from serological data. The authors note that while the method is demonstrated on enteroviruses, it is generalisable to any antibody titration-based system where SI or SII models are appropriate. They acknowledge limitations, including the assumption of age-dependent (rather than time-varying) FOI in the primary analysis and the exclusion of seroreversion in the primary models due to identifiability issues, though sensitivity analyses were conducted where possible.

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