[R] andersen plot vs score process or scaled Schoenfeld residuals to test for proporti0nal hazards

Thomas Lumley tlumley at u.washington.edu
Fri Mar 31 17:48:16 CEST 2006

On Fri, 31 Mar 2006, singyee ling wrote:

> Dear all,
> I use the Andersen plot to check for proportional hazards assumption for a
> factor (say x) in the Cox regression model and obtained a straight line that
> pass through the origin. However, the formal test done by the  R-function
> cox.zph, which is based on the plot of Schonefeld residuals against time,
> indicates that proportional hazards assumption is violated. Further, a plot
> of the score process (cumulative sums of schoenfeld residuals) against time
> again give the same conclusion as the cox.zph function and i am really
> stumped by this. Klein et al (1997, pp 354) mentioned that graphical checks
> for proportional hazards assumption is often preferred to formal test as
> formal test based on a large enough sample (in my case is 4000 data
> entries), will often reject the null hypothesis of proportionality. Is that
> what is happening in my case? any suggestion?

If you plot the cox.zph object you should be able to see why the test is 
rejecting.  The plot includes a smooth curve that estimates the log hazard 
ratio as a function of time, and you can see if you think it departs 
importantly from a horizontal line.

The cox.zph tests are (approximately) score tests against particular 
one-dimensional alternatives and so are more powerful against those 
alternatives than a test based on the supremum of the score process.


Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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