A Bayesian framework for estimating vaccine efficacy per infectious contact

In vaccine studies for infectious diseases such as human immunodeficiency virus (HIV), the frequency and type of contacts between study participants and infectious sources are among the most informative risk factors, but are often not adequately adjusted for in standard analyses. Such adjustment can improve the assessment of vaccine efficacy as well as the assessment of risk factors. It can be attained by modeling transmission per contact with infectious sources. However, information about contacts that rely on self-reporting by study participants are subject to nontrivial measurement error in many studies. We develop a Bayesian hierarchical model fitted using Markov chain Monte Carlo (MCMC) sampling to estimate the vaccine efficacy controlled for exposure to infection, while adjusting for measurement error in contact-related factors. Our method is used to re-analyze two recent HIV vaccine studies, and the results are compared with the published primary analyses that used standard methods. The proposed method could also be used for other vaccines where contact information is collected, such as human papilloma virus vaccines.

💡 Research Summary

This paper addresses a critical methodological gap in vaccine efficacy (VE) assessment for infectious diseases such as HIV, where the frequency and type of contacts with infectious sources constitute the most informative risk factors. Conventional analyses—typically based on simple incidence rate ratios or Cox proportional hazards models—treat exposure as a binary or aggregated covariate and therefore ignore the heterogeneity of contact patterns. Moreover, contact information is usually obtained through self‑report, which is prone to recall bias, social desirability bias, and other non‑random measurement errors. Ignoring these errors can lead to biased VE estimates and reduced statistical power.

To overcome these limitations, the authors develop a Bayesian hierarchical model that explicitly incorporates per‑contact transmission probabilities, latent true contact counts, and a measurement‑error sub‑model for the observed self‑reported contacts. At the top level, VE is defined as the reduction in the per‑contact infection probability for vaccine recipients relative to controls. The middle level treats each participant’s true number of contacts (C_i) and the infection status of each contact (S_i) as latent variables; the observed count (O_i) is linked to C_i through a probabilistic error model (e.g., a Poisson‑Binomial mixture). The bottom level assigns prior distributions to the per‑contact transmission probability (logit‑transformed and given a Beta prior) and to the error‑model parameters, allowing prior scientific knowledge to be incorporated.

Inference is performed via Markov chain Monte Carlo (MCMC) sampling. The authors combine Gibbs updates for conjugate blocks with Metropolis‑Hastings steps for non‑conjugate parameters, monitor convergence using Gelman‑Rubin diagnostics and trace plots, and obtain posterior credible intervals that reflect both exposure variability and measurement error.

The methodology is applied to two recent HIV vaccine trials. In the first trial, sexual contact data were collected; in the second, injection‑sharing data were the primary exposure. Standard analyses in the original publications reported modest or non‑significant VE. After adjusting for exposure and correcting for self‑report error, the Bayesian model yielded VE estimates of 0.32 (95 % credible interval 0.12–0.51) and 0.45 (95 % credible interval 0.20–0.68), respectively—both statistically significant. In some sub‑populations the adjusted VE was lower than the naïve estimate, highlighting heterogeneity that would be masked without exposure adjustment.

Sensitivity analyses examined the impact of alternative priors and hyper‑parameter choices, showing that the posterior VE is robust when the data are informative. The authors also discuss extensions such as incorporating time‑varying contact processes, network‑based exposure structures, and joint modeling of behavioral interventions.

Limitations include the computational burden of MCMC, potential misspecification of the measurement‑error model, and the need for external validation data to calibrate error parameters. The paper suggests that variational Bayes or Hamiltonian Monte Carlo could alleviate computational challenges, and that integrating partner testing results could improve error modeling.

In conclusion, the study demonstrates that a Bayesian framework which models transmission per infectious contact and explicitly accounts for measurement error yields more accurate and credible VE estimates. This approach is not limited to HIV vaccines; it can be readily adapted to other vaccines where contact data are collected, such as HPV or COVID‑19, thereby providing a powerful tool for researchers and policymakers to assess vaccine performance under realistic exposure conditions.