Longitudinal characterization of cognitive change in late-life has received increasing attention to better understand age-related cognitive aging and cognitive changes reflecting pathology-related and mortality-related processes. Several mixed-effects models have been proposed to accommodate the non-linearity of cognitive decline and assess the putative influence of covariates on it. In this work, we examine the standard linear mixed model (LMM) with a linear function of time and five alternative models capturing non-linearity of change over time, including the 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 deceased participants from two prospective cohorts with annual cognitive testing, we compared the interpretation of the models by investigating the association of education on cognitive change before death. Finally, we performed a simulation study to empirically evaluate the models and provide practical recommendations. In particular, models were challenged by increasing follow-up spacing, increasing missing data, and decreasing sample size. With the exception of the LMM with a quadratic term, the fit of all models was generally adequate to capture non-linearity of cognitive change and models were relatively robust. Although spline-based models do not have interpretable nonlinearity parameters, their convergence was easier to achieve and they allow for graphical interpretation. In contrast the piecewise and the sigmoidal models, with interpretable non-linear parameters may require more data to achieve convergence.

翻译：对晚年认知变化的纵向表征日益受到关注，以更好地理解与年龄相关的认知老化，以及反映病理和死亡相关过程的认知变化。已有多种混合效应模型被提出，用以适应认知衰退的非线性特征，并评估协变量对其的潜在影响。在本研究中，我们考察了标准线性混合模型（LMM）以及五种捕捉时间变化非线性的替代模型，包括带二次项的LMM、带样条的LMM、函数型混合模型、分段线性混合模型和S形混合模型。我们首先从理论上描述了这些模型。接着，利用两个前瞻性队列中已故参与者的年度认知测试数据，通过探讨教育程度与死亡前认知变化的关联，比较了这些模型的解释方式。最后，我们进行了模拟研究以经验性地评估模型，并提供实用建议。特别地，模型面临随访间隔增加、缺失数据增多以及样本量减少的挑战。除带二次项的LMM外，所有模型的拟合通常都能充分捕捉认知变化的非线性，且模型相对稳健。尽管基于样条的模型缺乏可解释的非线性参数，但其收敛更易实现，并允许图形化解释。相比之下，具有可解释非线性参数的分段模型和S形模型可能需要更多数据才能实现收敛。