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In this article, we propose an omnibus test for comparing two survival functions under non-proportional hazards. The test statistic is based on a product-limit estimate of the restricted distance correlation, which is closely related to the distance between survival curves. The strong consistency is established under mild regularity conditions. Our simulation studies show that the new test has satisfactory power under proportional hazard and various non-proportional hazards settings including delayed treatment effect, diminishing effect, and crossing survival curves; therefore, it can be a competitive alternative to the existing omnibus tests such as Kolmogorov-Smirnov test, Cramer-von Mises test, two-stage test, and the maxCombo test based on weighted log-rank statistics. Two extensions of the new test to one-sided alternatives and a Gaussian kernel are also discussed
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Fasano-Franceschini Test: an Implementation of a 2-Dimensional Kolmogorov-Smirnov test in R
The univariate Kolmogorov-Smirnov (KS) test is a non-parametric statistical test designed to assess whether two samples come from the same underlying distribution. The versatility of the KS test has made it a cornerstone of statistical analysis across the scientific disciplines. However, the test proposed by Kolmogorov and Smirnov does not naturally extend to multidimensional distributions. Here, we present the fasano.franceschini.test package, an R implementation of the 2-D KS two-sample test as defined by Fasano and Franceschini (Fasano and Franceschini 1987) and provide multiple use cases across the scientific disciplines. The fasano.franceschini.test package provides three improvements over the current 2-D KS test on the Comprehensive R Archive Network (CRAN): (i) the Fasano and Franceschini test has been shown to run in O(n2) versus the Peacock implementation which runs in O(n3); (ii) the package implements a procedure for handling ties in the data; and (iii) the package implements a parallelized permutation procedure for improved significance testing. Ultimately, the fasano.franceschini.test package presents a robust statistical test for analyzing random samples defined in 2-dimensions.
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- Award ID(s):
- 1764421
- PAR ID:
- 10336398
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.48550/arXiv.2106.10539
