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Biometrika 1997 84(4):901-908; doi:10.1093/biomet/84.4.901
© 1997 by Biometrika Trust
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On fitting Cox's regression model with time-dependent coefficients

LESZEK MARZEC and PAWEL MARZEC

Mathematical Institute, University of Wroclaw 50-384 Wroclaw, Poland e-mail: lmarzec{at}hera.math.uni.wroc.pl pmarzec{at}hera.math.uni.wroc.pl

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 Cramér-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.

Key Words: Counting process • Cox regression model • Goodness of fit • Survival analysis • Time-dependent coefficients • Weak convergence


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