Checking a semiparametric additive risk model.

McKeague and Sasieni [A partly parametric additive risk model. Biometrika 81 (1994) 501] propose a restriction of Aalen's additive risk model by the additional hypothesis that some of the covariates have time-independent influence on the intensity of the observed counting process. We introduce goodness-of-fit tests for this semiparametric Aalen model. The asymptotic distribution properties of the test statistics are derived by means of martingale techniques. The tests can be adjusted to detect particular alternatives. As one of the most important alternatives we consider Cox's proportional hazards model. We present simulation studies and an application to a real data set.