A comparison of approaches for simultaneous inference of fixed effects for multiple outcomes using linear mixed models

Longitudinal studies with multiple outcomes often pose challenges for the statistical analysis. A joint model including all outcomes has the advantage of incorporating the simultaneous behavior but is often difficult to fit due to computational challenges. We consider 2 alternative approaches to quantify and assess the loss in efficiency as compared with joint modelling when evaluating fixed effects. The first approach is pairwise fitting of pseudolikelihood functions for pairs of outcomes. The second approach recovers correlations between parameter estimates across multiple marginal linear mixed models. The methods are evaluated in terms of a data example both from a study on the effects of milk protein on health in young adolescents and in an extensive simulation study. We find that the 2 alternatives give similar results in settings where an exchangeability condition is met, but otherwise, pairwise fitting shows a larger loss in efficiency than the marginal models approach. Using an alternative to the joint modelling strategy will lead to some but not necessarily a large loss of efficiency for small sample sizes.