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Analyzing the progression of Alzheimer's disease (AD) is challenging due to lacking sensitivity in currently available measures. AD stages are typically defined based on cognitive cut-offs, but this results in heterogeneous patient groups. More accurate modeling of the continuous progression of the disease would enable more accurate patient prognosis. To address these issues, we propose a new multivariate continuous-time disease progression (MCDP) model. The model is formulated as a nonlinear mixed-effects model that aligns patients based on their predicted disease progression along a continuous latent disease timeline. The model is evaluated using long-term follow-up data from 2152 participants in the Alzheimer's Disease Neuroimaging Initiative. The MCDP model was used to simultaneously model three cognitive scales; the Alzheimer's Disease Assessment Scale-cognitive subscale, the Mini-Mental State Examination, and the Clinical Dementia Rating scale-sum of boxes. Compared with univariate modeling and previously proposed multivariate disease progression models, the MCDP model showed superior ability to predict future patient trajectories. Finally, based on the multivariate disease timeline estimated using the MCDP model, the sensitivity of the individual items of the cognitive scales along the different stages of disease was analyzed. The analysis showed that delayed memory recall items had the highest sensitivity in the early stages of disease, whereas language and attention items were sensitive later in disease. [ABSTRACT FROM AUTHOR]

Summary: We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. We introduce a class of generally applicable models where warping effects are modelled through non‐linear transformation of latent Gaussian variables and systematic shape differences are modelled by Gaussian processes. To model cross‐covariance between sample co‐ordinates we propose a class of low dimensional cross‐covariance structures that are suitable for modelling multivariate functional data. We present a method for doing maximum likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body markers are tracked in three dimensions over time. The second data set consists of longitudinal height and weight measurements for Danish boys. The third data set consists of three‐dimensional spatial hand paths from a controlled obstacle avoidance experiment. We use the method to estimate the cross‐covariance structure and use a classification set‐up to demonstrate that the method outperforms state of the art methods for handling misaligned curve data. [ABSTRACT FROM AUTHOR]

A goodness-of-fit test for continuous-time models is developed that examines if the parameter estimates are consistent with another for different sampling frequencies. The test compares parameter estimates obtained from estimating functions for downsamples of the data. We prove asymptotic results for stationary and ergodic processes, and apply the downsampling test to linear drift diffusions. Simulations indicate that the test is quite powerful in detecting non-Markovian deviations from the linear drift diffusions. [ABSTRACT FROM AUTHOR]