Mathematical Modelling for Optimal Vaccine Dose Finding: Maximising Efficacy and Minimising Toxicity

Abstract

Vaccination is a key tool to reduce global disease burden. Vaccine dose can affect vaccine efficacy and toxicity. Given the expense of developing vaccines, optimising vaccine dose is essential. Mathematical modelling has been suggested as an approach for optimising vaccine dose by quantitatively establishing the relationships between dose and efficacy/toxicity. In this work, we performed simulation studies to assess the performance of modelling approaches in determining optimal dose. We found that the ability of modelling approaches to determine optimal dose improved with trial size, particularly for studies with at least 30 trial participants, and that, generally, using a peaking or a weighted model-averaging-based dose–efficacy relationship was most effective in finding optimal dose. Most methods of trial dose selection were similarly effective for the purpose of determining optimal dose; however, including modelling to adapt doses during a trial may lead to more trial participants receiving a more optimal dose. Clinical trial dosing around the predicted optimal dose, rather than only at the predicted optimal dose, may improve final dose selection. This work suggests modelling can be used effectively for vaccine dose finding, prompting potential practical applications of these methods in accelerating effective vaccine development and saving lives.

The Correlated Beta Dose Optimisation Approach: Optimal Vaccine Dosing Using Mathematical Modelling and Adaptive Trial Design

“…Previous work has investigated mathematical modelling for the selection of optimal dose with regard to a single-administration vaccine [2,13,21]. In this work we would also like to consider optimising dose 'prime/boost' paradigm vaccines, which are vaccines that are administered as two or more doses at separate time points [37,38].…”

“…The 'Parametric' DOA uses parametric models to describe dose-efficacy and dosetoxicity, as described in [21,35]. Specifically, we used the latent quadratic model [35,48] for modelling dose-efficacy for single-administration dose-optimisation problems.…”

“…These calibrated models were then used to predict dose-utility. The method of trial dose selection for each cohort was the softmax selection method described in both [21,51,52] and Supplementary Materials S4. The method of final dose selection was to choose the dose with the maximum utility according to the predictions of the calibrated model.…”

“…Previous work has shown that for some vaccines an increase in dose leads to increased efficacy responses, but that for other vaccines there is a maximum efficacy dose after which an increased dose leads to decreased vaccine efficacy [13,19,20].This means that there may be uncertainty in the correct models to use. Selecting optimal vaccine dose using models which are 'misspecified', meaning they are not appropriate for describing the dose-response relationship for the purposes of selecting optimal dose, could lead to suboptimal vaccine dosing, decreasing efficacy or increasing toxicity [21][22][23].…”

“…We have previously discussed the use of model averaging to account for this uncertainty [21]. Alternatively, others have suggested that non-parametric models can be effective for locating optimal dose in the case of model uncertainty [24][25][26].Whilst the assumption of parametric models is that vaccine dose-response follows some pre-specified equation/shape, non-parametric models do not assume a predefined equation/shape.…”