A quick omnibus test for the proportional hazards model of random censorship

In case of censored observations, we present a simple procedure for testing the hypothesis of the proportional hazards model in which the survival function of the censoring variables is some power of the survival function of the lifetimes. The test is based on the number of runs in the sequence of censoring indicators associated with the ordered values of the observable minima of lifetimes and censoring times. The procedure is proved to be consistent against general alternatives, and it is illustrated on three well-known data sets.