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 than with Varilrix

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 (NCT00492648) 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 found between the B-cell 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 to 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, this approach allows testing for differences in immunological processes between vaccines or schedules. 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.