An ODE-based mixed modelling approach for B- and T-cell dynamics induced by Varicella-Zoster Virus vaccines in adults shows higher T-cell proliferation with Shingrix compared to Varilrix
Authors: Keersmaekers Nina , Ogunjimi Benson , Van Damme Pierre , Beutels Philippe , Hens Niel 
Published: June 2018

Clinical trials covering the immunogenicity of a vaccine aim to study the longitudinal dynamics of certain immune cells after vaccination. The corresponding immunogenicity datasets are mainly analyzed by the use of statistical (mixed effects) models. This paper proposes the use of mathematical ordinary differential equation (ODE) models, combined with a mixed effects approach. ODE models are capable of translating underlying immunological post vaccination processes into mathematical formulas thereby enabling a testable data analysis. Mixed models include both population-averaged parameters (fixed effects) and individual-specific parameters (random effects) for dealing with inter-and intra-individual variability, respectively.

This paper models B-cell and T-cell datasets of a phase I/II, open-label, randomized, parallel-group study in which the immunogenicity of a new Herpes Zoster vaccine (Shingrix) is compared with the original Varicella Zoster Virus vaccine (Varilrix).

Since few significant correlations were assessed between the B-cell datasets and T-cell datasets, each dataset was modeled separately. By following a general approach to both the formulation of several different models and the procedure of selecting the most suitable model, we were able propose a mathematical ODE mixed-effects model for each dataset. As such, the use of ODE-based mixed effects models offers a suitable framework for handling longitudinal vaccine immunogenicity data. Moreover, it is possible to test differences in immunological processes between the two vaccines.

We found that the Shingrix vaccination schedule led to a more pronounced proliferation of T-cells, without a difference in T-cell decay rate compared to the Varilrix vaccination schedule.

Author summary

Upon vaccination, B-cells and T-cells are activated to induce an immune response against the vaccine antigen at hand. In this paper, we study and compare the longitudinal dynamics of the specific immune response based on a vaccine trial in which the immunogenicity of a new Herpes Zoster vaccine (Shingrix) is compared with the original Varicella Zoster Virus vaccine (Varilrix). We combine the use of ordinary differential equations (ODEs), i.e. mathematical models which are used to describe the dynamics of the immune response, with advanced regression analyses enabling us to infer the model parameters describing these dynamics. The resulting ODE-based mixed effects models enable describing the immune response dynamics allowing for both inter-and intra-individual variability; comparing the dynamics induced by the two vaccines and studying the B-and T-cell interactions. We found a more pronounced proliferation of T-cells for the Shingrix vaccination schedule as compared to the Varilrix vaccination schedule. The proposed methodology offers a suitable framework for better understanding the immunogenicity of vaccines.