Modeling adaptive response profiles in a vaccine clinical trial

Vaccine clinical studies typically provide time-resolved data on adaptive response read-outs in response to the administration of that particular vaccine to a cohort of individuals. However, modeling such data is challenged by the properties of these time-resolved profiles such as non-linearity, scarcity of measurement points, scheduling of the vaccine at multiple time points. Linear Mixed Models (LMM) are often used for the analysis of longitudinal data but their use in these time-resolved immunological data is not common yet. Apart from the modeling challenges mentioned earlier, selection of the optimal model by using information-criterion-based measures is far from being straight-forward. The aim of this study is to provide guidelines for the application and selection of LMMs that deal with the challenging characteristics of the typical data sets in the field of vaccine clinical studies.

We used antibody measurements in response to Hepatitis-B vaccine with five different adjuvant formulations for demonstration purposes. We built piecewise-linear, piecewise-quadratic and cubic models with transformations of the axes with pre-selected or optimized knot locations where time is a numerical variable. We also investigated models where time is categorical and random effects are shared intercepts between different measurement points. We compared all models by using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Deviance Information Criterion (DIC), variations of conditional AIC and by visual inspection of the model fit in the light of prior biological information.

There are various ways of dealing with the challenges of the data which have their own advantages and disadvantages. We explain these in detail here. Traditional information-criteria-based measures work well for the coarse selection of the model structure and complexity, however are not efficient at fine tuning of the complexity level of the random effects.

We show that common statistical measures for optimal model complexity are not sufficient. Rather, explicitly accounting for model purpose and biological interpretation is needed to arrive at relevant models.

Clinical trial registration number for this study: NCT00805389, date of registration: December 9, 2008 (pro-active registration).