Testing the proportionality assumption for specified covariate in the cox model

In this paper, I propose a test for proportional hazards assumption for specified covariates. The testis based on a general alternative in sense that hazards rates under different values of covariates therate is not only constant as in the Cox model, but it may cross, go away, and may be monotonicwith time. The limit distribution of the test statistic is derived. Finite samples properties of thetest power are analyzed by simulation. Application of the proposed test on Real data examples areconsidered