A state-space approach for longitudinal outcomes: An application to neuropsychological outcomes

Longitudinal assessments are crucial in evaluating the disease state and trajectory in patients with neurodegenerative diseases. Neuropsychological outcomes measured over time often have a non-linear trajectory with autocorrelated residuals and a skewed distribution. We propose the adjusted local linear trend model, an extended state-space model in lieu of the commonly used linear mixed-effects model in modeling longitudinal neuropsychological outcomes. Our contributed model has the capability to utilize information from the stochasticity of the data while accounting for subject-specific trajectories with the inclusion of covariates and unequally spaced time intervals. The first step of model fitting involves a likelihood maximization step to estimate the unknown variances in the model before parsing these values into the Kalman filter and Kalman smoother recursive algorithms. Results from simulation studies showed that the adjusted local linear trend model is able to attain lower bias, lower standard errors, and high power, particularly in short longitudinal studies with equally spaced time intervals, as compared to the linear mixed-effects model. The adjusted local linear trend model also outperforms the linear mixed-effects model when data is missing completely at random, missing at random, and, in certain cases, even in data with missing not at random.