Assessing immune correlates of vaccine protection

Putting causal methods under a microscope

Nima Hejazi

nhejazi@hsph.harvard.edu

Harvard Biostatistics

June 24, 2026

Immune correlates of protection (CoPs)

Vaccine efficacy RCTs are primarily used to quantify the (protective) effects of investigational vaccines on infectious diseases: COVID-19, HIV, malaria.

Immune correlates analyses (Plotkin and Gilbert, 2012) of vaccine RCTs aim to

• identify and/or validate possible surrogate endpoints (Prentice, 1989)
• improve understanding of the protective mechanism of a vaccine

If an immune marker reliably predicts vaccine efficacy (VE), it may serve as a primary endpoint in future trials—accelerating approval of vaccines in new populations or of next-generation products.

Correlates of risk are associative; correlates of protection (CoPs) are causal.

Measuring correlates: sampling complications

• Assaying immune responses on many thousands of participants is expensive and also statistically unnecessary
• Common to use a case-cohort design (Prentice, 1986), a version of two-phase sampling (Breslow et al., 2003) in vaccine trials (Follmann, 2006):
  • Phase 1: baseline covariates, treatment, outcome on everyone
  • Phase 2: immune response on a random subcohort plus all cases

Setting up the problem

The ideal data unit \(X = (L, A, S, Y)\) consists of the following variables:

• \(L\): baseline covariates (sex, age, behavioral/clinical risk)
• \(A\): randomized assignment to vaccine versus placebo
• \(S\): candidate immune response profile (e.g., neutralizing antibody titer)
• \(Y\): clinical endpoint (e.g., COVID-19 by 100 days after start of follow-up)

Instead of \(X\), we see the observed data unit \(O = (L, A, R S, Y, R)\), where

• \(R\) is the phase-two sampling indicator (inclusion in phase-two sample)
• \(R S\) is the immune response observed only for those in the subcohort or cases

Defining vaccine efficacy estimands

• Estimands for vaccine efficacy (VE) aim to quantify the impact of vaccination, \(A = 1\), on the endpoint of interest, \(Y = 1\).
• VE is generally presented as \(1 - \text{RR}\), where the risk ratio (RR) contrasts the risk in vaccine recipients to that in non-recipients.
• VE estimands have been designed and proposed also to assess the impact of vaccination through candidate immune correlates of protection.
• Two examples (Gilbert et al., 2024) introduced by the COVID-19 Prevention Network’s (CoVPN) biostatistics response team include
  • Controlled vaccine efficacy (CVE), based on the controlled direct effect (Gilbert et al., 2023)
  • Stochastic-interventional vaccine efficacy (SVE), based on modified treatment policies (Hejazi et al., 2021, 2023)

Controlled vaccine efficacy (CVE)

• For a hypothetical value \(s \in \mathcal{S}\), the controlled direct effect (CDE) quantifies the effect of \(A\) on \(Y\) while fixing \(S = s\), a static intervention.
• The hypothetical value \(S = s\) must be chosen carefully—to be scientifically informative and to avoid positivity violations.

• For two hypothetical values \(s_0, s_1 \in \mathcal{S}\), Controlled Vaccine Efficacy (CVE) is \[ \text{CVE}(\cancel{s_0}, s_1) = 1 - \frac{\E[\Pr(Y=1 \mid S=s_1, A=1, L=l)]} {\E[\Pr(Y=1 \mid \cancel{S=s_0}, A=0, L=l)]} \, , \] contrasting risk for vaccine receipt and \(S = s_1\) vs. placebo, where \(s_0 = 0\) is a plausible assumption in pathogen-naive populations (Gilbert et al., 2024).
• Answers: “What would VE be if the immune response were fixed at a given level?”

A more flexible approach

Modified treatment policies instead shift the immune response each unit would naturally have had (Dı́az and van der Laan, 2012; Haneuse and Rotnitzky, 2013): \[ d(s,l; \delta) = \begin{cases} s + \delta, & s+\delta < u(l) \\ s, & \text{otherwise} \end{cases} \]

An MTP shifts the natural (pre-intervention) distribution (red) to a new, modified (post-intervention) distribution (blue).

Stochastic-interventional vaccine efficacy (SVE)

Using modified treatment policies (MTPs), we can define a counterfactual mean under a \(\delta\)-shift of the natural post-vaccination immune response \(S\):

\[ \text{SVE}(\delta) = 1 - \frac{\E[\Pr(Y = 1 \mid S = d(s, l; \delta), A = 1, L = l)]} {\E[\Pr(Y=1 \mid A = 0, L = l)]} \]

SVE summarizes how VE would change under hypothetical, biologically plausible shifts \(\delta\) of candidate immune correlate \(S\) (Gilbert et al., 2021; Hejazi et al., 2021).

Identification

Causal identification assumptions differ slightly for CVE and SVE, but both require

1. SUTVA (consistency, no interference)
2. no unmeasured confounders of the
   • \(A\)–\(S\) relationship (fulfilled by randomization of \(A\))
   • \(A\)–\(Y\) relationship (fulfilled by randomization of \(A\))
   • \(S\)–\(Y\) relationship (needed, conditional on \(L\))

For structural positivity, SVE provides more flexibility than CVE:

• for CVE, the assumption is analogous to that of static interventions on \(A\).
• for SVE, the assumption is based on that of MTPs: \(s \in \mathcal{S} \implies d(s, l) \in \mathcal{S}\) for all \(l \in \mathcal{L}\), where \(\mathcal{S}\) denotes the support of \(S\) conditional on \(L = l\)

Estimation

Both doubly robust one-step (bias-corrected) and targeted minimum loss (TML) estimators based on the efficient influence function (EIF) have been developed;

• both allow for the use of ensemble machine learning (e.g., Super Learner (van der Laan et al., 2007)) for initial estimation of nuisance functions, and
• both remain consistent under forms of nuisance function misspecification.

Use of two-phase sampling requires correction by an IPCW augmentation of the EIF, which re-weights based on the (known) sampling mechanism, improving efficiency and providing further robustness (Hejazi et al., 2021; Rose and van der Laan, 2011).

SVE in practice: COVE trial of the mRNA-1273 vaccine

Predicted VE under hypothetical shifts to Day 57 pseudovirus neutralizing antibody titer in vaccine recipients (Hejazi et al., 2023; Huang et al., 2023).

• SVE measured for COVID-19 disease 7-100 days post Day-57 visit.
• Sharp gains in VE for upward shifts; negative shifts show a wide range of deteriorating VE.

nAb responses to variants pooling phase 1 studies

Pseudovirus neutralizing antibody (PsV nAb) titer distributions across variants of SARS-CoV-2 from pooled phase 1 studies. These were used to calibrate choices of \(\delta\) for SVE, informing the immunobridging application (Hejazi et al., 2023).

Bridging VE across SARS-CoV-2 variants

Using the immune correlate to bridge VE estimates to variants not directly observed in the trial (Hejazi et al., 2023).

• SVE prediction shows sharp changes in VE with shifts to the GM titer of the PsV nAb correlate in vaccinees.
  • Positive \(\delta\): saturates at nearly 100%.
  • Negative \(\delta\): large range, from -20% to 92%.
• Bridging VE across variants indicates VE drops but stabilizes at 50%, if the model based on ancestral D614G strain holds.
• Post-2 dose: For most variants (excepting omicron), the VE estimate ranges from 50% (mu) to about 80% (lambda).
• SVE predictions and real-world VE estimates well-correlated, but SVE predictions may be underestimates, as PsV nAb is an imperfect causal mediator of total VE.

The big picture

• SVE and CVE propose shifted- versus fixed-value interventions on \(S\), both used, developed by the CoVPN biostatistics response team (Gilbert et al., 2021).
• Case-cohort (two-phase) sampling helps reduce cost of measuring candidate immune correlates but introduces selection bias requiring analytic correction.
• Stochastic interventions (SVE) and static contrasts (CVE) are complementary tools for causal mediation analysis to assess immune correlates of protection.
  • Both admit doubly/multiply robust, asymptotically efficient estimators that are compatible with modern ensemble machine learning.
  • Open-source software (txshift, haldensify, vaccine) implement these methods for widespread use (Hejazi and Benkeser, 2020).

Causal mediation analysis can be leveraged to assess causally grounded evidence for/against an immune marker’s value as a surrogate endpoint.

Thank you! Questions?

Based on joint work with the CoVPN Biostatistics Response team (led by Peter Gilbert, Fred Hutch and UW)

  nimahejazi.org/research

  @nshlab  and  @nhejazi

  Core methods for SVE framework (Biometrics)

  SVE translational and bridging application (IJID)

  Application of SVE in the COVE RCT (Viruses)

  Core methods for CVE framework (Biostatistics)

  CoVPN arsenal for assessing CoPs (Vaccine)

References

Breslow, N., McNeney, B. and Wellner, J. A. (2003) Large sample theory for semiparametric regression models with two-phase, outcome dependent sampling. The Annals of Statistics, 31, 1110–1139. Institute of Mathematical Statistics.

Dı́az, I. and van der Laan, M. J. (2012) Population intervention causal effects based on stochastic interventions. Biometrics, 68, 541–549. Wiley Online Library.

Follmann, D. (2006) Augmented designs to assess immune response in vaccine trials. Biometrics, 62, 1161–1169. Oxford University Press.

Gilbert, P. B., Fong, Y., Benkeser, D., et al. (2021) CoVPN COVID-19 vaccine efficacy trial immune correlates statistical analysis plan. DOI: 10.6084/m9.figshare.13198595.

Gilbert, P. B., Fong, Y., Kenny, A., et al. (2023) A controlled effects approach to assessing immune correlates of protection. Biostatistics, 24, 850–865. Oxford University Press. DOI: 10.1093/biostatistics/kxac024.

Gilbert, P. B., Fong, Y., Hejazi, N. S., et al. (2024) Four statistical frameworks for assessing an immune correlate of protection (surrogate endpoint) from a randomized, controlled, vaccine efficacy trial. Vaccine, 42, 2181–2190. Elsevier. DOI: 10.1016/j.vaccine.2024.02.071.

Haneuse, S. and Rotnitzky, A. (2013) Estimation of the effect of interventions that modify the received treatment. Statistics in Medicine, 32, 5260–5277. Wiley Online Library.

Hejazi, N. S. and Benkeser, D. C. (2020) txshift: Efficient estimation of the causal effects of stochastic interventions in R. Journal of Open Source Software, 5, 2447. The Open Journal. DOI: 10.21105/joss.02447.

Hejazi, N. S., van der Laan, M. J., Janes, H. E., et al. (2021) Efficient nonparametric inference on the effects of stochastic interventions under two-phase sampling, with applications to vaccine efficacy trials. Biometrics. Wiley Online Library. DOI: 10.1111/biom.13375.

Hejazi, N. S., Shen, X., Carpp, L. N., et al. (2023) Stochastic interventional approach to assessing immune correlates of protection: Application to the COVE mRNA-1273 vaccine trial. International Journal of Infectious Diseases, 137, 28–39. Elsevier. DOI: 10.1016/j.ijid.2023.09.012.

Huang, Y., Hejazi, N. S., Blette, B., et al. (2023) Stochastic interventional vaccine efficacy and principal surrogate analyses of antibody markers as correlates of protection against symptomatic COVID-19 in the COVE mRNA-1273 trial. Viruses, 15, 2029. MDPI. DOI: 10.3390/v15102029.

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Rose, S. and van der Laan, M. J. (2011) A targeted maximum likelihood estimator for two-stage designs. The International Journal of Biostatistics, 7, 1–21.

van der Laan, M. J., Polley, E. C. and Hubbard, A. E. (2007) Super learner. Statistical Applications in Genetics and Molecular Biology, 6. De Gruyter. DOI: 10.2202/1544-6115.1309.