Thorough understanding of neuropsychological data using state space modelling
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Abstract
Alzheimer's disease, and other related dementia diseases, are a worsening issue with an acceleration in today's aging population. Longitudinal cognitive assessment of those suffering from dementia offers vital insight into disease progression and allows for assessment of possible disease interventions. Difficulty in modeling such data arises as there are often non-linear and heterogenous patterns of decline from patient to patient. We propose the use of state space models (SSM), specifically a Local Linear Trend (LLT) model, as an alternative to the commonly used linear mixed effect models (LMEM) for longitudinal assessments. The proposed model includes the estimation of interpretable population linear effects on the outcome, while also allowing for subject-specific non-linearities in cognitive trajectories. To fit the LLT model, we utilize the traditional full likelihood estimation using the Kalman Filter and Kalman Smoother. We also compare the use of a partitioned LLT and a Bayesian LLT for computational efficiency. In two separate simulation analyses, we show the advantages of the LLT models over the predominant techniques. We go on to show that of the LLT methods, the Bayesian LLT excels. The LLT models are then used to estimate the effect of the APOE e4 allele on cognitive trajectory.
Running the LLT on a single outcome provides accurate estimation of linear effects, but multiple tests are often offered for better understanding of different cognitive domains. To gain a more thorough understanding of cognition and how it relates to Alzheimer's disease we propose the use of a multivariate local linear trend model (MLLT), which simultaneously models linear effects for multiple tests, while also measuring inter-correlation of the underlying cognitive state between tests. Lastly, we propose a factor MLLT (FMLLT) to clarify underlying factors of cognition. The FMLLT can be utilized in both a structured and unstructured approach. These tools are shown to provide a flexible and accurate framework for analyzing longitudinal neuropsychological data.