R help - Nov 2008 - coxph diagnostics plot for shape of hazard function?

Hi,

I've been banging my head against the following problem for a while
and thought the fine people on r-help might be able to help. I'm
using the survival package.

I'm studying the survival rate of a population with a preexisting
linear-like event rate (there are theoretical reasons to believe
it's linear, but of course it's subject to the usual sampling noise)

Some of the population exhibit predictor
X and some don't [I'm not trying to be cagey about the setting
here, it's just complicated to explain and I'm trying to keep my
message short.] When I plot the survival curves, there's a qualitatively
significant difference and this is confirmed by survdiff.

When I run cox.zph, however, it's pretty clear that the proportional
hazards assumption isn't satisfied:
> zph <- cox.zph(cox)
> zph
                         rho chisq        p
Initially.Vulnerable -0.0476  32.5 1.19e-08
>
Similarly, when I do plot(zph), B(t) is fairly non-constant.

This isn't inherently a problem for me. I don't need a hard single
number
to characterize the shape of the excess risk. However, I'd like to be
able to say
something qualitative about the shape of the excess risk for the predictor.
E.g., is it linear, monotonically increasing, monotonially decreasing, etc.
Is it safe to use the coxph diagnostic plot for this purpose?

I did try heuristically subtracting out the background and then fitting a spline
using locfit as described in the MASS supplement, but this seemed a little more
ad hoc than I was hoping for something more principled.

Thanks in advance.

-Ekr

> Similarly, when I do plot(zph), B(t) is fairly non-constant.
> This isn't inherently a problem for me. I don't need a hard single
number
> to characterize the shape of the excess risk. However, I'd like to be
> able to say
> something qualitative about the shape of the excess risk for the predictor.
> E.g., is it linear, monotonically increasing, monotonially decreasing, etc.
> Is it safe to use the coxph diagnostic plot for this purpose?
  Basically - yes you can.  There are a few caveats:
    1. As a computational shortcut cox.zph assumes that var(X) is approximately 
constant over time, where X is the matrix of covariates.  (Improving this has 
been on my to do list for some time). I have found this to be almost always 
true, but if you have a data set where e.g. everyone in treatment 1 is crossed 
over at 6 months, then you can get odd results for that covariate.  I've run
across 2-3 such data sets in 10+ years.

    2. The spline curve on the plot is "for the eye".  You can
certainly use
other smoothings, fit a line, etc.  Often you can find a simpler fit.
    	zpfit <- cox.zph(mycoxfit, transform='identity')
    	plot(zpfit$x, zpfit$y[,1], xlab='Time')  #look at variable 1
    	lines(lowess(zpfit$x, zpfit$y[,1]), col=2)
    	abline( lm(zpfit$y[,1] ~zpfit$x), col=3)
    	
    	plot(zpfit$x, zpfit$y[,1], log='x') #same as transform=log 
    	
    	etc.
    	
Sometimes the regression spline fit, the default for cox.zph, puts an extra 
"hook" on the end of the curve, somewhat like polynomials will.  
    	
    	Terry T.