Sunday, Aug 3: 2:00 PM - 3:50 PM
4013
Contributed Papers
Music City Center
Room: CC-101B
Main Sponsor
Section on Statistics in Imaging
Presentations
An isometric embedding of a Riemannian manifold in Euclidean space is an embedding such that the Riemannian structure on each tangent space is induced by the scalar product in the ambient space; such an embedding preserves path lengths, angles, areas and volumes. Such a mapping preserves much of the geometric information contained in the original Riemannian manifold where the data is valued allowing for some computationally advantages. In addition if the Riemmanian manifold is homogeneous then we would also want the such an embedding, to be equivariant. The Veronese-Whitney (VW) embedding is an isometric equivariant embedding for 3D projective shape data. It is in fact the only embedding used in the analysis of 3D projective shape data, at the present time. In this paper we consider a novel equivariant isometric embedding, the Nash embedding into a Euclidean space of a lower dimension than the Euclidean space where the Veronese-Whitney embedding is valued . We compare the performance of the novel Nash embedding-based statistical techniques with those based on the VW embedding in Monte Carlo studies and a real data example.
Keywords
Extrinsic shape analysis
Nash embedding
Nonparametric test
Three-dimensional projective shape analysis
Despite advances in Alzheimer's disease (AD) research, limited information exists regarding the absolute risk of mild cognitive impairment (MCI) in cognitively unimpaired (CU) individuals with abnormal AD biomarkers, particularly when accounting for competing risks of death. We included 5,858 participants from the Mayo Clinic Study of Aging (MCSA) to evaluate AD amyloid stage as a predictor of clinical progression to MCI or dementia. The data includes long-term follow-up information on death and dementia beyond active study participation, which mitigates potential bias due to dropout. We predicted 10-year and lifetime risks of MCI and dementia, accounting for the competing risks of death, given amyloid PET stages, sex, APOE4 status, and baseline age. Results are based on a hidden Markov model. AD amyloid staging based on amyloid PET Centiloid values was the strongest predictor of lifetime risk for MCI or for dementia. Higher Centiloid levels amplified age effects on the risk of MCI, whereas for dementia, amyloid stage effects surpassed age effects. For 10-year risk, age was the dominant factor, whereas for lifetime risk, amyloid stages had a greater influence.
Keywords
Hidden Markov Models
Alzheimer's Disease
Absolute Risk
Co-Author(s)
Terry Therneau, Mayo Clinic
Clifford Jack, Mayo Clinic
Heather Wiste, Mayo Clinic
Prashanthi Vemuri, Mayo Clinic
Jon Graff-Radford, Mayo Clinic
Ronald Petersen, Mayo Clinic
Dave Knopman, Mayo Clinic
Val Lowe, Mayo Clinic
First Author
Mingzhao Hu, Mayo Clinic
Presenting Author
Mingzhao Hu, Mayo Clinic
Spatial proteomic technologies reveal immune cells organization, offering critical information about immune function and disease mechanisms. Standard methods for assessing immune cell interactions rely on simplistic summary statistics that fail to accommodate variations in scan orientation, cell count, and location variations across individuals, thereby do not directly evaluate spatial structures.
To address this, we use topological data analysis (TDA) with persistent homology (PH) to capture spatial structure. PH systematically translates spatial information of cells into topological summaries, producing k*n persistence diagrams-one for each cell type per individual. Pairwise L1 distances between persistence diagrams for individual cell types form k n*n distance matrices that capture structural differences across the population. The Kernel RV is then used to identify associations between the spatial structures of different immune cell types. Simulations and real data analyses show our approach is often more powerful, particularly at assessing global structures, while still protecting type I error, serving as a powerful new approach investigating spatial immune cell interaction.
Keywords
Spatial Proteomic Imaging Data
Persistent Homology
Kernel RV
Topological Data Analysis
One popular technique in Topological Data Analysis (TDA) called persistent homology (PH) is used to describe holes in an image through their dimension and the functional values (e.g., thresholds or scales) at which they are created and filled. While TDA has been successfully applied to identifying shape in a static image through its hole structure, estimating the changes in that hole structure within a time-evolving image set is relatively understudied. We develop a method which first identifies statistically significant topological features in the spatial and temporal dimensions simultaneously. These higher-dimensional topological features are then used to establish temporal connections between the lower-dimensional features they are built from, effectively separating spatial connections from temporal connections. The spatial structure of the lower-dimensional features can be analyzed at each time-point separately and their temporal evolution represented on a ZigZag diagram (topological summary statistic focused on time dynamics). The method's effectiveness in capturing the emergence and progression of topological features is tested on a time series of images from cell wounds.
Keywords
Image Processing
, Spatiotemporal Analysis
Topological Data Analysis
High Dimensional Statistics
The generalized Gaussian distribution (GGD) is a versatile parametric family extensively used in signal and image processing for its ability to model diverse data distributions. In image compression algorithms like JPEG, the distributions of discrete cosine transform coefficients for a broad range of images are often represented by the GGD, encompassing widely used distributions such as Laplace and Gaussian. While extensive research focuses on estimating the GGD's shape parameter, fewer studies have developed accurate and optimal approaches for estimating the scale parameter, which is critical for controlling distribution spread and compression performance. We propose a novel optimal estimator for the GGD scale parameter and derive its exact mean squared error (MSE). We show analytically that our estimator has a uniformly smaller MSE than that of the maximum likelihood estimator. When applied to Lloyd-Max quantization of real images, our estimator demonstrates excellent performance, balancing feature preservation, compression efficiency, and minimal distortion.
Keywords
Optimal Scale Estimator
Generalized Gaussian Distribution
Maximum Likelihood Estimator
Mean Squared Error
Image Compression
Lloyd-Max Quantization
Estimated glomerular filtration rate (eGFR) is a continuous biomarker of kidney function and an important clinical outcome in glomerular and other kidney diseases. The use of demographic, clinical, and kidney biopsy image data to predict future eGFR and quantify prediction uncertainty is crucial for risk stratification and clinical decision-making. Conformal quantile regression (CQR) provides a statistical framework to estimate prediction intervals around continuous outcomes with statistical guarantees about coverage of the true outcomes. However, CQR has not been explored in the context of predicting eGFR using image data that include generated regressors. In this study, we conducted a simulation study to test the performance of CQR in constructing prediction intervals of continuous outcomes from generated regressors. We demonstrated that CQR is robust to additive measurement error in the generated regressors but large samples are required for optimal coverage with functionally misspecified regressors. Finally, we used real-world glomerular disease kidney biopsy image features to predict eGFRs and demonstrated that CQR prediction intervals provide reliable coverage in real data.
Keywords
Computational pathology
Conformal quantile regression
Image features
Generated regressors
Prediction intervals