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Principal Investigator  
Principal Investigator's Name: Sonia Dembowska
Institution: University of Leeds
Department: Department of Statistics
Country:
Proposed Analysis: Images are frequently used in clinical setting for diagnosis, monitoring or prediction of dis- ease. Our work is focused on task brain functional Magnetic Resonance Imaging (fMRI) data, made up of three dimensional images taken over time. Brain fMRI data is a set of cuboid elements (i.e. voxels). Most commonly, fMRI images are analysed with a per-voxel approach which includes generalized linear models (GLMs) and time series models. Other methods include single-time point dimensionality reduction on a vectorised image or the full 3D image. Modelling four-dimensional data proves challenging, on one hand, per-voxel analysis considers the complete dataset but involves parametric and spatial assumptions that treat neighbouring voxels as independent. On the other hand, dimensionality reduction methods respect spatial relations but ignore the temporal component. We have created a model that retains the spatial structure of an image whilst considering the temporal component. Our method extends on the model introduced by Park and Staicu (2015) which models curves captured over time, to 3D images. We develop an algorithm for the estimation of model parameters. We use the functional data analysis (FDA) framework, which regards each datum as a realization of a random object in an infinite- dimensional functional space. Dimensionality reduction methods create a latent space that will allow for the representation and interpretation of the original data. We propose a model using the FDA framework that expands on the model from Park and Staicu (2015) and a new, efficient estimation method based on the algorithm introduced in Li et al. (2019) that circumvents calculating the 8 dimensional covariance matrix. Our model will represent the data using spatial principal components whilst the score will contain temporal information. We want to use the ADNI dataset to expand on our existing work that models fMRI images. fMRI images are captured at regular time intervals which creates a dense temporal array of 3D images. When modelling disease progression, we are interested in sparse time points often happening at irregular and longer intervals. We aim to use our extended Functional Principal Component Analysis model to decompose the data into two functions: the principal components (PCs) and the score functions. The PCs will hold the spatial information from the brains whilst the scores will be patient-specific functions that will span over time. This was each score function can relate a patients information to the relevant PCs. As this is a longitudinal study, the score function will undergo smoothing to account for sparse time points. The score functions provide summaries of patient data that can be further used in a survival analysis model for disease progression.
Additional Investigators  
Investigator's Name: Jeanine Houwing-Duistermaat
Proposed Analysis: The same as for Sonia Dembowska
Investigator's Name: Haiyan Liu
Proposed Analysis: The same as for Sonia Dembowska