Alexander McLain | Searcharxiv

arXiv2024

Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression

Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. For example, Aphasia Quotient (AQ) is a critical measure of language impairment and informs treatment decisions, but it is challenging to measure in stroke patients. It is of interest to use high-resolution T2 neuroimages of brain damage to predict AQ. However, sparse regression models show marked evidence of heteroscedastic error even after transformations are applied. This violation of the homoscedasticity assumption can lead to bias in estimated coefficients, prediction intervals (PI) with improper length, and increased type I errors. Bayesian heteroscedastic linear regression models relax the homoscedastic error assumption but can enforce restrictive prior assumptions on parameters, and many are computationally infeasible in the high-dimensional setting. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization (H-PROBE) algorithm. H-PROBE is a computationally efficient maximum a posteriori estimation approach that requires minimal prior assumptions and can incorporate covariates hypothesized to impact heterogeneity. We apply this method by using high-dimensional neuroimages to predict and provide PIs for AQ that accurately quantify predictive uncertainty. Our analysis demonstrates that H-PROBE can provide narrower PI widths than standard methods without sacrificing coverage. Narrower PIs are clinically important for determining the risk of moderate to severe aphasia. Additionally, through extensive simulation studies, we exhibit that H-PROBE results in superior prediction, variable selection, and predictive inference compared to alternative methods.

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arXiv2022

A Generalization of Ripley's K Function for the Detection of Spatial Clustering in Areal Data

Spatial clustering detection has a variety of applications in diverse fields, including identifying infectious disease outbreaks, assessing land use patterns, pinpointing crime hotspots, and identifying clusters of neurons in brain imaging applications. While performing spatial clustering analysis on point process data is common, applications to areal data are frequently of interest. For example, researchers might wish to know if census tracts with a case of a rare medical condition or an outbreak of an infectious disease tend to cluster together spatially. Since few spatial clustering methods are designed for areal data, researchers often reduce the areal data to point process data (e.g., using the centroid of each areal unit) and apply methods designed for point process data, such as Ripley's K function or the average nearest neighbor method. However, since these methods were not designed for areal data, a number of issues can arise. For example, we show that they can result in loss of power and/or a significantly inflated type I error rate. To address these issues, we propose a generalization of Ripley's K function designed specifically to detect spatial clustering in areal data. We compare its performance to that of the traditional Ripley's K function, the average nearest neighbor method, and the spatial scan statistic with an extensive simulation study. We then evaluate the real world performance of the method by using it to detect spatial clustering in land parcels containing conservation easements and US counties with high pediatric overweight/obesity rates.

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