Dataset for: 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 two alternative approaches in order to quantify and assess the loss in efficiency as compared to joint modelling when evaluating fixed effects. The first approach is pairwise fitting of pseudo-likelihood functions for pairs of outcomes. The second approach recovers correlations between parameter estimates across multiple marginal linear mixed models. The methods are evaluated both in terms of a data example from a study on the effects of milk protein on health in young adolescents and in an extensive simulation study. We find that the two 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.多结局纵向研究往往给统计分析带来挑战。纳入全部结局的联合模型（joint model）虽可同时刻画变量间的关联行为，但受限于计算层面的难题，往往难以拟合。为量化并评估在评估固定效应（fixed effects）时，相较于联合建模策略的效率损失，本文提出两种替代分析方法。第一种方法为针对每一对结局变量，分别拟合伪似然函数（pseudo-likelihood function）；第二种方法则通过多个边际线性混合模型（marginal linear mixed model），恢复各模型参数估计值之间的相关性。本文通过两项实验对所提方法进行验证：一是一项针对青少年乳蛋白摄入对健康影响的真实数据集案例，二是大规模模拟研究。研究结果表明：当满足可交换性条件（exchangeability condition）时，两种替代方法的分析结果相近；而在不满足该条件的场景下，成对拟合法的效率损失要大于边际模型法。对于小样本场景，采用联合建模的替代策略虽会带来一定程度的效率损失，但未必会造成显著的效率损耗。