Inference in segmented line regression: a simulation study

Abstract A segmented line regression model has been used to describe changes in cancer incidence and mortality trends Kim, H.-J., Fay, M.P., Feuer, E.J. and Midthune, D.N., 2000, Permutation tests for joinpoint regression with applications to cancer rates. Statistics in Medicine, 19, 335–351. Kim, H.-J., Fay, M.P., Yu, B., Barrett., M.J. and Feuer, E.J., 2004, Comparability of segmented line regression models. Biometrics, 60, 1005–1014.. The least squares fit can be obtained by using either the grid search method proposed by Lerman Lerman, P.M., 1980, Fitting segmented regression models by grid search. Applied Statistics, 29, 77–84. which is implemented in Joinpoint 3.0 available at http://srab.cancer.gov/joinpoint/index.html, or by using the continuous fitting algorithm proposed by Hudson Hudson, D.J., 1966, Fitting segmented curves whose join points have to be estimated. Journal of the American Statistical Association, 61, 1097–1129. which will be implemented in the next version of Joinpoint software. Following the least squares fitting of the model, inference on the parameters can be pursued by using the asymptotic results of Hinkley Hinkley, D.V., 1971, Inference in two-phase regression. Journal of the American Statistical Association, 66, 736–743. and Feder Feder, P.I., 1975a, On asymptotic distribution theory in segmented regression Problems-Identified Case. The Annals of Statistics, 3, 49–83. Feder Feder, P.I., 1975b, The log likelihood ratio in segmented regression. The Annals of Statistics, 3, 84–97. Via simulations, this paper empirically examines small sample behavior of these asymptotic results, studies how the two fitting methods, the grid search and the Hudson's algorithm affect these inferential procedures, and also assesses the robustness of the asymptotic inferential procedures. Keywords: Joinpoint regressionGrid searchContinuous fittingChange-points