  We propose inference procedures for general nonparametric factorial survival
designs with possibly right-censored data. Similar to additive Aalen models,
null hypotheses are formulated in terms of cumulative hazards. Thereby,
deviations are measured in terms of quadratic forms in Nelson-Aalen-type
integrals. Different to existing approaches this allows to work without
restrictive model assumptions as proportional hazards. In particular, crossing
survival or hazard curves can be detected without a significant loss of power.
For a distribution-free application of the method, a permutation strategy is
suggested. The resulting procedures' asymptotic validity as well as their
consistency are proven and their small sample performances are analyzed in
extensive simulations. Their applicability is finally illustrated by analyzing
an oncology data set.
