Joint Modeling and Dynamic Ensemble Forecasting of Influenza Vaccine Responses from Complex Longitudinal Trajectories

This Github page provides code and data for reproducing the results in the manuscript: ``Joint Modeling and Dynamic Ensemble Forecasting of Influenza Vaccine Responses from Complex Longitudinal Trajectories'' by Y. Chen, Y. Zhang, and Y. Shen.

Real-world implications

The forecasts and simulations using advance statistics models can enhance our understanding of vaccine-induced immunity, aligning well with the goals of the Computational Models of Immunity to Pertussis Booster Vaccinations (CMI-PB) Project.

Summary

Longitudinal measurement trajectories have become increasingly valuable for deepening our predictive understanding of vaccine-induced immunity. However, the complexity of immune interaction patterns inherent in these trajectories, along with their incompleteness and high heterogeneity, introduces significant methodological challenges for predictive modeling. To address these challenges, we introduce both parametric and nonparametric Joint Modeling and Dynamic Forecasting (JMDF) frameworks to enhance vaccine response prediction. JMDF provides four key advances:

• Adaptive use of non-missing longitudinal measurements as covariates without requiring imputation;
• A novel application of Gaussian Markov random fields (GMRFs) to enable information sharing across individuals, thereby achieving efficient modeling and interpretation of complex interactions;
• Joint forecasting of responses to multiple vaccine subtypes while allowing deep within-individual dependencies across viral subtypes; and
• An efficient ensemble forecasting strategy that integrates vaccination trajectory patterns.

This work advances modern statistical modeling in public health, particularly in the area of vaccine response prediction and immune response simulation, with the potential to support personalized vaccination strategies.

Data from the human influenza vaccine cohort study

To understand vaccine-induced immunity, an ongoing human influenza vaccine cohort study is being conducted. The cohort was initiated in 2013 at two sites: one in Florida (FL) and the other in Pennsylvania (PA). Since 2016, the study has been primarily conducted at the University of Georgia (UGA) in Athens, Georgia, United States. Data were illustrated in Figure 1.

Figure 1: Incomplete longitudinal trajectories of pre- and post-vaccination HAI titers collected from 30 randomly selected participants over eleven years.

Simulations

Furthermore, JMDF-GMRF successfully recovers complex interaction patterns, whether generated from smoothing functions (Figure 2) or simulated from Matérn fields.

Figure 2: Two-dimensional surfaces. The four panels from left to right show the true smooth surface g(x, z) = sin(0.1x) cos(0.1z) + 0.001xz, and its approximations using the proposed different JMDF-GMRF models.

Real data analysis using the UGA cohort

Methods consistently reveal similar nonlinear associations between BMI and vaccination responses, showing positive effects at both low and high BMI levels, as shown in Figure 3.

Figure 3: Estimated nonlinear functions with respect to BMI, along with 95% credible intervals via JMDF-LR and JMDF-GMRF.

The following maps characterize the interaction effects between human age and historical longitudinal pre-vaccination HAI titers on future vaccination responses.

Figure 4: Recovered Gaussian Markov random fields between human age and longitudinal pre-vaccination HAI titers.