Several mixed-effects models for longitudinal data have been proposed to accommodate the non-linearity of late-life cognitive trajectories and assess the putative influence of covariates on it. No prior research provides a side-by-side examination of these models to offer guidance on their proper application and interpretation. In this work, we examined five statistical approaches previously used to answer research questions related to non-linear changes in cognitive aging: the linear mixed model (LMM) with a quadratic term, LMM with splines, the functional mixed model, the piecewise linear mixed model, and the sigmoidal mixed model. We first theoretically describe the models. Next, using data from two prospective cohorts with annual cognitive testing, we compared the interpretation of the models by investigating associations of education on cognitive change before death. Lastly, we performed a simulation study to empirically evaluate the models and provide practical recommendations. Except for the LMM-quadratic, the fit of all models was generally adequate to capture non-linearity of cognitive change and models were relatively robust. Although spline-based models have no interpretable nonlinearity parameters, their convergence was easier to achieve, and they allow graphical interpretation. In contrast, piecewise and sigmoidal models, with interpretable non-linear parameters, may require more data to achieve convergence.

翻译：为适应晚年认知轨迹的非线性特征并评估协变量对其潜在影响，研究者提出了多种纵向数据混合效应模型。目前尚无研究对这些模型进行并列比较，以指导其合理应用与解读。本研究系统考察了五种此前用于回答认知老化非线性变化相关研究问题的统计学方法：含二次项的线性混合模型、含样条函数的线性混合模型、函数型混合模型、分段线性混合模型及S形混合模型。我们首先从理论层面描述各模型特性。继而利用两个前瞻性队列的年度认知测试数据，通过探究教育程度对临终前认知变化的影响来比较各模型的解释力。最后开展模拟研究对各模型进行实证评估并提出实践建议。除含二次项的线性混合模型外，其余模型均能有效捕捉认知变化的非线性特征且具有较好的稳健性。尽管基于样条函数的模型缺乏可解释的非线性参数，但其收敛性更易实现且支持图形化解读。相反，具有可解释非线性参数的分段模型与S形模型可能需要更多数据才能达到收敛。