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The joinpoint regression model and permutation tests for identifying changes in trend are described in:
Methods Citation:
H. - J.Kim, H. - S.Chen, J.Byrne, B.Wheeler, and E.J.Feuer (2022),
Twenty Years since Joinpoint 1.0: Two Major Enhancements, Their Justification, and Impact. Statistics in Medicine 20; 41(16) : 3102 - 3130.
Kim HJ, Fay MP, Feuer EJ, Midthune DN. Permutation tests for joinpoint regression with applications to cancer rates.Stat Med. 2000 Feb 15;
19(3):335-51. doi:10.1002/(sici)1097-0258(20000215)19:3<335::aid-sim336>3.0.co;2-z.
Erratum in : Stat Med 2001 Feb 28; 20(4) : 655. PMID : 10649300.
Software Citation:
Surveillance Research Program , National Cancer Institute (2025). Joinpoint Regression Software, Version 5.4.0 - April 2025. (https://surveillance.cancer.gov/joinpoint)