Tests for the proportional intensity assumption based on the score process.

Proportional intensity models are widely used for describing the relationship between the intensity of a counting process and associated covariates. A basic assumption in this model is the proportionality, that each covariate has a multiplicative effect on the intensity. We present and study tests for this assumption based on a score process which is equivalent to cumulative sums of the Schoenfeld residuals. Tests within principle power against any type of departure from proportionality can be constructed based on this score process. Among the tests studied, in particular an Anderson-Darling type test turns out to be very useful by having good power properties against general alternatives. A simulation study comparing various tests for proportionality indicates that this test seems to be a good choice for an omnibus test for proportionality.