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

Abstract

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.

The Effects of Cultivar, Nitrogen Supply and Soil Type on Radiation Use Efficiency and Harvest Index in Spring Wheat

“…All statistical analyses were made using the statistical software R version 3.6.1 [26]. In particular, the packages nlme [27] and lme4 [28] were used for fitting linear mixed models, multcomp [29] for pairwise comparisons and mmmVcov [30] for estimating the joint covariance matrix in the after-fitting approach used for the harvest index.…”

The Estimation of Excess Mortality during the COVID-19 Pandemic in Jakarta, Indonesia

“…The linear mixed model has the advantage over traditional analysis procedures, conducting simultaneous inferences for multiple outcomes by introducing random effects in the model. 24 This method gives forecast values with minor variance than the time series model. 7 The result revealed an excess number of 13,507 deaths in overall Jakarta, which was far higher than the official record of 1,881 deaths related to COVID-19 in 2020.…”

Model-based simultaneous inference for multiple subgroups and multiple endpoints

“…The cost of such multiple testing is conservativeness whereas it is reduced (with respect to Bonferroni) by taking the correlations between the test statistics into account. Using the mmm approach marginal models can be formulated as generalized linear mixed-effects models allowing the analysis of various primary endpoints occurring in RCTs, including multiple primary endpoints -even different scaled [19]. It controls the familywise error rate in simulations with a total sample size of greater than or equal to 500.…”