An Application of Spatially Adjusted Kolmogorov-smirnov Test in Comparing Heart PET Scans

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Wenjun Zheng
Dejian Lai
Zhe Wang
Nils P. Johnson
K. Lance Gould

Abstract

The Kolmogorov-Smirnov (KS) test has been popular in many applied fields. Published research has suggested the utility of the KS test in image processing, histogram analysis, and PET/CT scans. However, the fundamental assumption of independence in a statistical model is easily overlooked. When the KS test is applied to spatial analysis, autocorrelation may cause the KS test to have an inflated type I error (small p-values) if no adjustments for spatial correlation are applied. To adjust for autocorrelation, the KS test must incorporate spatial adjustment. The spatially-adjusted KS has a controlled type I error and non-inferior power compared to the original KS test. Utilizing the KS test with spatial adjustment, we reanalyzed a trial comparing two types of stress medications: regadenoson (administered using different timings) versus dipyridamole. To analyze the PET scans with spatial autocorrelation, we introduced a novel way of reconstructing the shape of the human heart using spherical coordinates, and compared the KS test with spatial adjustment to a KS test with adjustment for correlation. The results showed that the reconstructed PET scans analyzed by the KS test with spatial adjustment have


controlled p-values.

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