A test of fit for a semiparametric additive risk model

Kolmogorov-Smirnov and Cramer-von Mises type test statistics based on the standardised cumulative hazard process are proposed. It is very difficult to evaluate their asymptotic distributions, but they can be approximated by the use of the bootstrap. The advantages of the goodness-of-fit test are that arbitrary partitions of the time axis and covariate spaces are not needed for evaluating test statistics and that it has excellent consistency properties. The test is applied to data from the Mayo Clinic trial in primary biliary cirrhosis of the liver. A simulation study indicates that the proposed test is suitable for practical use.