2024 - Rome - Italy

PAGE 2024: Lewis Sheiner Student Session
Julie Dudasova

Logistic regression-based approach to assess heterogeneity in vaccine efficacy using immunogenicity measurements in phase 3 clinical trials

Julie Dudasova (1,2), Zdenek Valenta (3), Andreea Magalie (4), Jeffrey R. Sachs (4)

(1) Quantitative Pharmacology and Pharmacometrics, MSD Czech Republic, Prague, Czech Republic, (2) First Faculty of Medicine, Charles University, Prague, Czech Republic, (3) Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic, (4) Quantitative Pharmacology and Pharmacometrics, Merck & Co., Inc., Rahway, NJ, USA


This work introduces a novel use of immune response biomarkers to help identify baseline covariates affecting vaccine efficacy (VE). 

Phase 3 clinical trials assessing VE typically provide data on binary clinical endpoints (e.g., disease or infection) along with subject-specific demographic or clinical characteristics (e.g., age or age group, sex, weight, height, race and ethnicity, geographical region, or pre-vaccination exposure to a wild-type virus) collected before the time of randomization (i.e., baseline covariates). While overall VE (marginal vaccination effect) is estimated from data for the entire enrolled population sample it can also be of interest to estimate VE in specific subgroups defined by baseline covariates (conditional vaccination effect). This is because the baseline covariates may not only influence clinical endpoint (incidence of disease can vary with age, for example), but they can also impact vaccination effect on the clinical endpoint (VE can vary with age, for example). This phenomenon is often referred to as vaccination effect heterogeneity [1]. Understanding how covariates affect VE is essential to informed decisions by vaccine developers and regulatory authorities. However, evaluating VE in demographic subgroups presents challenges when standard case-counting-based methods [2] are used. Most vaccine phase 3 clinical trials are designed (powered) to assess overall VE as the primary endpoint and attempts to estimate VE in subgroups often lead to confidence intervals (CI) being too wide to reliably inform on potential differences in VE between those subgroups. 

In most efficacy trials, participants’ immune response post-vaccination (immunogenicity) data are collected, typically roughly one month after vaccination. When an immunogenicity biomarker can reliably predict protection against disease or infection, it is termed “correlate of protection” (CoP) [3]. In this work, the term “CoP” is used for a biomarker that meets Prentice criteria [4] and fully mediates the vaccine effect. It has been demonstrated that CoP-based VE prediction is more precise than case-counting-based VE estimation [5]. This work is motivated by the need to evaluate a natural extension of that result: inclusion of CoP data could increase statistical efficiency of identifying covariates affecting VE and comparing VE between subgroups (by reducing the width of CoP-based CI as compared to case-counting). 

Application objectives:

Use the data from immunogenicity substudy [6] to the phase 3 Shingles Prevention Study (SPS) [7]:

  • To characterize the relationship between fold rise in varicella-zoster virus (VZV) antibody titers and probability of herpes zoster (HZ, shingles).
  • To estimate immunogenicity-based efficacy of high-potency live-attenuated herpes zoster vaccine (Zoster Vaccine Live, Merck Sharp & Dohme LLC, a subsidiary of Merck & Co., Inc., Rahway, NJ, USA) in the younger (≤69 years of age) and older (≥70 years of age) subgroups. 

Methodological objectives:

  • To evaluate accuracy and precision of CoP-based VE estimation in demographic subgroups with logistic function as a probability of disease (PoD) curve. 

Implementation objectives:

  • To implement the method for estimating VE using the logistic regression and immunogenicity data in the vaxpmx R package.


The best-fitting logistic model (with linear or quadratic term for immunogenicity; with or without a covariate predictor; with or without an interaction between immunogenicity and a covariate) is used to estimate the relationship between immunogenicity and probability of disease (PoD). VE is calculated as described by Coudeville et al. [8]. The 95% CI associated with estimated VE includes uncertainty (on the PoD curve and on the immunogenicity data) via parametric resampling of posterior distribution for the PoD curve parameters and bootstrapping the observed immunogenicity data.


Results of our analysis of the zoster vaccine data complement and agree with previous findings that (i) fold rise in VZV antibody titers (measured by glycoprotein ELISA) is a correlate of protection against HZ [5,9], and (ii) VE is higher in younger subjects compared to older subjects (reported in phase 3 study [7]; 38546 subjects; 456 HZ cases in the younger group, 501 HZ cases in the older group).

In our analysis, the logistic model with fold rise as a predictor using data from only 1326 subjects provided VE estimates significantly different from 0 in both the younger (with 17 cases of HZ) and older (15 cases) subgroups and found a trend of higher VE in younger subjects (point estimates, 58% for younger, 52% for older). Model-predicted difference in VE was not statistically significant (confidence intervals were overlapping) and was driven by the difference in immunogenicity between the age groups (no significant difference in the relationships between immunogenicity and probability of HZ was identified). Results based on case-counting alone did not indicate VEs significantly different from 0 (the lower bound of 95% CI was below 0) in these subgroups and estimated that VE in younger subjects was lower than in the older group (point estimates of 55% for younger, 67% for older; the difference was not statistically significant).

We performed clinical trial simulations which showed that logistic regression and use of CoP data provide accurate estimates of VE with better precision (lower variability of VE point estimates and hence narrower CI) in covariate-defined subgroups compared to case-counting. For all simulated scenarios used here: the true PoD curve was sigmoid or logistic; the true age effect on the PoD curve causes 30% or 0% VE difference between age groups; the immunogenicity distribution is the same in the younger and older populations; there were a total of 15000 subjects with 10000 vaccinated, 5000 control, ~3800 older, ~11200 younger, ~200 disease cases, and ~14800 non-cases (subjects who did not have disease symptoms during observation period).


Our analysis of the zoster vaccine data and simulated data representing typical phase 3 vaccine efficacy trials demonstrates that inclusion of CoP data in logistic models can increase precision in estimating efficacy (i.e., yield narrower confidence intervals) in demographic subgroups, and thus can help support even better-informed decisions by vaccine developers and public health authorities. The method for efficacy estimation using logistic regression and immunogenicity data is implemented in the vaxpmx R package [10].

[1] Halloran ME, Haber M, Longini IM. Interpretation and Estimation of Vaccine Efficacy under Heterogeneity. American Journal of Epidemiology, 1992, 136(3):328-343.
[2] Halloran ME, Longini IM, Struchiner CJ. Design and Analysis of Vaccine Studies. Springer, 2010.
[3] Orenstein WA, Offit PA, Edwards KM, Plotkin SA. Plotkin’s Vaccines. Elsevier, 2017.
[4] Prentice RL. Surrogate endpoints in clinical trials: definition and operational criteria. Statistics in Medicine, 1989, 8(4):431-440.
[5] Dudasova J et al. A method to estimate probability of disease and vaccine efficacy from clinical trial immunogenicity data. NPJ Vaccines, 6:133, 2021.
[6] Levin MJ et al. Varicella-zoster virus–specific immune responses in elderly recipients of a herpes zoster vaccine. The Journal of Infectious Diseases, 2008, 197(6):825-835.
[7] Oxman MN et al. A vaccine to prevent herpes zoster and postherpetic neuralgia in older adults. The New England Journal of Medicine, 2005, 352(22):2271-2284.
[8] Coudeville L, Andre P, Bailleux F, Weber F, Plotkin SA. A new approach to estimate vaccine efficacy based on immunogenicity data applied to influenza vaccines administered by the intradermal or intramuscular routes. Human Vaccines, 2010, 6(10):841–848.
[9] Gilbert PB et al. Fold rise in antibody titers by measured by glycoprotein-based enzyme-linked immunosorbent assay is an excellent correlate of protection for a herpes zoster vaccine, demonstrated via the vaccine efficacy curve. The Journal of Infectious Diseases, 2014, 210(10):1573-1581.
[10] https://cran.r-project.org/web/packages/vaxpmx/index.html

Reference: PAGE 32 (2024) Abstr 10855 [www.page-meeting.org/?abstract=10855]
Oral: Lewis Sheiner Student Session
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