On fitting Cox's regression model with time-dependent coefficients

This paper examines goodness-of-fit testing in the Cox regression model with time-varying regression coefficients. Arjas' (1988) approach is used to define test statistics of the Kolmogorov-Smirnov and Cramer-von Mises types. Their asymptotic limits are shown to be well-known functionals of standard Brownian motion, leading to the construction of formal goodness-of-fit tests. Some numerical studies are also included to illustrate the performance of the tests for moderate sample sizes.