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

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  • Wenjun Zheng
  • Hongjian Zhu
  • K. Lance Gould
  • Dejian Lai

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.

Suggested Citation

  • Wenjun Zheng & Hongjian Zhu & K. Lance Gould & Dejian Lai, 2025. "Comparing heart PET scans: an adjustment of Kolmogorov-Smirnov test under spatial autocorrelation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 52(1), pages 253-269, January.
    • Handle: RePEc:taf:japsta:v:52:y:2025:i:1:p:253-269
    DOI: 10.1080/02664763.2024.2366300
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