Permutation tests for joinpoint regression with applications to cancer rates

The identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data. We apply a joinpoint r egression model to describe such continuous changes and use the grid-search method to fit the regression function with unknown joinpoints assuming con stant variance and uncorrelated errors. We find the number of significant j oinpoints by performing several permutation tests, each of which has a corr ect significance level asymptotically. Each p-value is found using Monte Ca rlo methods, and the overall asymptotic significance level is maintained th rough a Bonferroni correction. These tests are extended to the situation wi th non-constant variance to handle rates with Poisson variation and possibl y autocorrelated errors. The performance of these tests are studied via sim ulations and the tests are applied to U.S. prostate cancer incidence and mo rtality rates. Copyright (C) 2000 John Wiley & Sons, Ltd.