R help - Mar 2006 - andersen plot vs score process or scaled Schoenfeld residuals to test for proporti0nal hazards

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?

Thanks!

kind regards,
singyee ling

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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

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