Comparing heart PET scans: an adjustment of Kolmogorov-Smirnov test under spatial autocorrelation

Wenjun Zheng, Hongjian Zhu, K. Lance Gould and Dejian Lai

Journal of Applied Statistics, 2025, vol. 52, issue 1, 253-269

Abstract: The principle of independence is a fundamental yet often disregarded assumption in statistical inference. It is observed that the implications of correlations, if not considered, can lead to a conservative estimation of Type I error in the presence of positive linear correlations when utilizing the Kolmogorov-Smirnov (KS) test. Conversely, negative linear correlations may engender a liberal estimation of Type I error. To address the impact of spatial autocorrelation in the analysis of Positron Emission Tomography (PET) images, we have proposed an innovative methodology to reconstruct a grid map of human heart scans using spherical coordinates. We have examined the distribution of the KS test statistic under spatial autocorrelation through Monte Carlo (MC) simulation and have introduced a KS test with a spatial adjustment. The newly proposed KS test with spatial adjustment demonstrates a controlled Type I error and power that is not inferior when compared to the original KS test. This suggests its potential utility in the analysis of spatially autocorrelated data.

Date: 2025
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DOI: 10.1080/02664763.2024.2366300

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