Comparison of Regression Curves with Censored Responses

In this article, we introduce a procedure to test the equality of regression functions when the response variables are censored. The test is based on a comparison of Kaplan-Meier estimators of the distribution of the censored residuals. Kolmogorov-Smirnov- and Cramér-von Mises-type statistics are considered. Some asymptotic results are proved: weak convergence of the process of interest, convergence of the test statistics and behaviour of the process under local alternatives. We also describe a bootstrap procedure in order to approximate the critical values of the test. A simulation study and an application to a real data set conclude the paper. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..