Testing the proportionality assumption for specified covariate in the cox model

Abstract

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