Analysis of multivariate longitudinal immuno-epidemiological data using a pairwise joint modelling approach

Immuno-epidemiologists are often faced with multivariate outcomes, measured repeatedly over time. Such data are characterised by complex inter- and intra-outcome relationships which must be accounted for during analysis. Scientific questions of interest might include determining the effect of a treatment on the evolution of all outcomes together, or grouping outcomes that change in the same way. Modelling the different outcomes separately may not be appropriate because it ignores the underlying relationships between outcomes. In such situations, a joint modelling strategy is necessary. This paper describes a pairwise joint modelling approach and discusses its benefits over more simple statistical analysis approaches, with application to data from a study of the response to BCG vaccination in the first year of life, conducted in Entebbe, Uganda.

The study aimed to determine the effect of maternal latent Mycobacterium tuberculosis infection (LTBI) on infant immune response (TNF, IFN-γ, IL-13, IL-10, IL-5, IL-17A and IL-2 responses to PPD), following immunisation with BCG. A simple analysis ignoring the correlation structure of multivariate longitudinal data is first shown. Univariate linear mixed models are then used to describe longitudinal profiles of each outcome, and are then combined into a multivariate mixed model, specifying a joint distribution for the random effects to account for correlations between the multiple outcomes. A pairwise joint modelling approach, where all possible pairs of bivariate mixed models are fitted, is then used to obtain parameter estimates.

Univariate and pairwise longitudinal analysis approaches are consistent in finding that LTBI had no impact on the evolution of cytokine responses to PPD. Estimates from the pairwise joint modelling approach were more precise. Major advantages of the pairwise approach include the opportunity to test for the effect of LTBI on the joint evolution of all, or groups of, outcomes and the ability to estimate association structures of the outcomes.

The pairwise joint modelling approach reduces the complexity of analysis of high-dimensional multivariate repeated measures, allows for proper accounting for association structures and can improve our understanding and interpretation of longitudinal immuno-epidemiological data.