Binding assay
Measures antigen-specific binding under a defined assay procedure. A binding result does not by itself establish that the antibodies prevent infection.
Vaccine science · optional learning companion
Understand the immune response.
Keep the measurement in view.
A short, illustrated guide for biostatisticians: what changes after vaccination, what an assay measures, and what a study result can support.
Recognition, selection and memory
Vaccination introduces antigen, or instructions for producing it, in a context that can generate an adaptive response. In germinal centres, B cells undergo mutation and selection; some descendants become antibody-secreting plasma cells or memory B cells. Human vaccine studies have measured persistent germinal-centre responses and continued antibody maturation. Turner et al., 2021; Kim et al., 2022.
1 · Encounter
Antigen recognition and immune context shape which cells participate.
2 · Selection
Mutation and competition, including T-cell help, alter the responding B-cell population.
3 · Persistence
Plasma cells supply antibodies; memory cells can contribute to later responses.
Schematic, not a timeline or complete immune-system model. T-cell responses and other immune functions are not represented by an antibody concentration alone. Experiments supporting selection through T-cell help: Victora et al., 2010.
Binding and neutralization answer different questions
Neutralization assay
ID50 is commonly a reciprocal serum dilution producing 50% inhibition in that assay. For an antibody concentration IC50, a lower value instead denotes greater potency under comparable conditions.
Primary example measuring binding and neutralization separately: Pinto et al., 2020. Keep assay, antigen/variant, units and sample time attached to every result.
A correlate is contextual.
In the COVE trial, binding and neutralizing markers were associated with symptomatic COVID-19 risk, with important limitations on population, follow-up and circulating virus. That does not create a universal antibody threshold for individual protection. A descriptive threshold response is not automatically a validated correlate or surrogate. Gilbert et al., 2022.
Higher affinity means a lower KD
For a simple one-to-one equilibrium interaction, KD = koff/kon. Lower KD means tighter binding under comparable conditions; the association constant KA is its reciprocal. Avidity reflects combined multivalent binding and depends on the assay format. Serum titer is neither KD nor a direct measure of affinity.
Explore one-to-one occupancy
Synthetic values. Fixed free ligand concentration L = 10 nM. This toy excludes avidity, depletion and kinetics.
Selected KD: 10 nM.
Fraction occupied = L / (KD + L)
Read the direction correctly
At L = 10 nM, KD values of 1, 10 and 100 nM give approximately 90.9%, 50.0% and 9.1% occupancy.
These are calculations under the stated binding model. They are not probabilities of clinical protection, predicted vaccine efficacy, or outputs of the analysis module.
Primary affinity and avidity measurement example: Pinto et al., 2020.
Keep the population and pairing visible
| Readout | What it summarises | What to verify |
|---|---|---|
| Geometric mean | exp(mean(log positive values)). Use GMT for titers or GMC for concentrations as appropriate. | Assay units, population, visit, censoring rule and the number analysed. |
| Geometric mean fold rise | exp(mean(log(post/baseline))) for matched participants. | Paired baseline/post records, missing pairs and the declared baseline. |
| Threshold / fold response | A participant proportion meeting a specified rule. | Threshold, inequality, evaluable denominator, assay limits and unresolved results. |
| Solicited symptom summary | Participant occurrence and maximum recorded grade within a defined dose window. | Expected diaries, observation coverage, unknown grades and the grading convention. |
A t-based interval for a geometric mean is computed on logs and exponentiated. It describes uncertainty in the mean under its assumptions, not a reference interval containing a chosen percentage of participants. One observed value can give a point estimate but cannot supply an empirical standard error. R Student-t documentation.
Worked example: a missing pair changes the question
Two participants have baseline titers 10 and 100. Only the first has a post-baseline titer, 40. The paired GMFR is 40/10 = 4, from one pair, with no estimable t interval. Dividing the post GMT, 40, by the baseline GMT, √(10 × 100) ≈ 31.62, gives 1.26 and uses different participants. It does not estimate the paired fold rise. If both summaries use exactly the same pairs, their GMT ratio and the geometric mean of individual ratios agree.
The module guide gives the implemented endpoint rules. Thresholds and protocol definitions remain study decisions.
Symptoms are not a personal antibody test
Solicited local and systemic reactions are measured over specified periods after each dose. Their grading criteria depend on the symptom and protocol. Severity and seriousness are different concepts; a grade alone does not supply an SAE classification. FDA preventive-vaccine grading guidance.
Some studies find associations between systemic reactions and antibody levels. In a COVE/TeenCOVE analysis, strong antibody responses also occurred without reported reactions. Symptoms therefore cannot establish whether an individual is protected. Dose-to-dose patterns depend on the vaccine, population and prior exposure; a stronger second-dose reaction is not a universal rule. Siangphoe et al., 2023; Thomas et al., 2021.
A missing diary is not “no symptom.”
Preserve three states: observed absence, observed occurrence, and insufficient information. A zero-event count becomes interpretable only alongside the number observed and the completeness rule.
mRNA changes how antigen is supplied
In mRNA vaccination, delivered RNA is translated into antigen. Nucleoside chemistry can alter innate sensing and protein expression. Experimental results depend on the RNA, formulation and experimental system; describing a modification as one universal “immune precision knob” would overstate the mechanism. Karikó et al., 2005; Andries et al., 2015.
This module accepts study-defined assays and treatment labels. It does not assume an mRNA platform, a particular pathogen, a manufacturer, or a dosing regimen.
“Immunity as inference” can organise questions
Memory can be compared with information carried forward; clonal selection can be compared with updating; an immune response can be compared with action. These are analogies. Calling a cell state a “belief” does not measure a probability distribution or prove that the cell implements a specific Bayesian algorithm.
A statistical boundary
A Markov blanket B separates internal variables I and external variables E only when the proposed distribution satisfies conditional independence:
p(I, E | B) = p(I | B) p(E | B)
A membrane is an anatomical boundary. Equating it with B requires explicit variables, a model, a time scale and justified independence assumptions. Membrane crossing is not, by itself, evidence of a Markov blanket.
A testable interpretation needs more
A claim about active inference needs a specified generative model, observable quantities, competing explanations and predictions that could fail. The learning analogy does not change the module’s endpoint definitions or validate its clinical conclusions.
Theoretical source: Friston, 2013. This is a modelling paper, not a vaccine trial or an empirical validation of these immune-system mappings.
No active-inference, free-energy or Markov-blanket variable is estimated by the analysis module. The analogy is optional reading.
Three-minute check
Can the result support the claim?
Answers and explanations
- 1 nM. Lower KD indicates tighter binding under the stated model.
- The assay criterion was met. A protection claim needs evidence linking that measurement to a relevant clinical endpoint in the applicable setting.
- Unresolved. Missing observations do not establish absence. Review the expected diary coverage and denominator.
Sources and scope
Links beside each claim lead to primary research or official methods guidance. The reference ledger records what each source supports and its limits.
The immune-system illustrations and numbers here are original teaching schematics. They are not patient data or empirical vaccine predictions. This companion adapts an earlier “Immunity as Active Inference” teaching concept with corrected scientific distinctions and a separate, explicitly optional modelling section.