Fig. 3: Bayesian analysis of possible modeling architectures underlying a trial-derived observation of vaccine efficacy.
From: Addressing mechanism bias in model-based impact forecasts of new tuberculosis vaccines
A Absolute frequency density distributions of efficacy values \({{VE}}_{{dis}}\) obtained in sets of N = 2 × 106 clinical trial simulations per model, uniformly distributed across the intrinsic vaccine efficacy parameter ε (efficacy resolution: 0.005, with 10,000 realizations for each value of ε). Red horizontal lines mark the PoD efficacy observed in the M72/AS01E trial \({{VE}}_{{dis}}=49.7\%.\) Along with each bi-dimensional density cloud, we represent its marginalized frequencies over the vertical axis, obtained upon adding simulation results over all possible values of \(\varepsilon\) for each model. These density curves capture the marginalized likelihoods \(P\left({{VE}}_{{dis}}|i\right)\). Red dashed lines capture their value at the observed efficacy, that is \(P\left({{VE}}_{{dis}}=49.7\%|i\right)\). B Marginal posteriors \(P\left(i| {{VE}}_{{dis}}=49.7\%\right)\), capturing the relative compatibility of each model with respect to the efficacy observed in the M72AS01E trial. C Distribution \(P\left(\varepsilon| {{VE}}_{{dis}}=49.7\%,i\right)\) of the intrinsic vaccine efficacy parameter ε in each model type, given the observed efficacy \({{VE}}_{{dis}}=49.7\%\), along with mean and 95% confidence intervals associated to them. For M3, the CI was omitted, for it spans the entire range \(\varepsilon \in [{{{{\mathrm{0,1}}}}}]\), as the model fails systematically to produce simulation instances compatible with the observed \({{VE}}_{{dis}}=49.7\%.\) Source data are provided as a Source Data file.
