Likelihood free and likelihood based approaches to modeling and analysis of functional antibody titers with applications to group B Streptococcus vaccine development.

Opsonophagocytic killing assays (OPKA) are routinely used for the quantification of bactericidal antibodies against Gram-positive bacteria in clinical trial samples. The OPKA readout, the titer, is traditionally estimated using non-linear dose-response regressions as the highest serum dilution yielding a predefined threshold level of bacterial killing. Therefore, these titers depend on a specific killing threshold value and on a specific dose-response model. This thesis describes a novel OPKA titer definition, the threshold free titer, which preserves biological interpretability whilst not depending on any killing threshold. First, a model-free version of this titer is presented and shown to be more precise than the traditional threshold-based titers when using simulated and experimental group B Streptococcus (GBS) OPKA experimental data. Second, a model-based threshold-free titer is introduced to automatically take into account the potential saturation of the OPKA killing curve. The posterior distributions of threshold-based and threshold-free titers is derived for each analysed sample using importance sampling embedded within a Markov chain Monte Carlo sampler of the coefficients of a 4PL logistic dose-response model. The posterior precision of threshold-free titers is again shown to be higher than that of threshold-based titers. The biological interpretability and operational characteristics demonstrated here indicate that threshold-free titers can substantially improve the routine analysis of OPKA experimental and clinical data.