# Re: [R] coxph diagnostics plot for shape of hazard function?

From: Terry Therneau <therneau_at_mayo.edu>
Date: Tue, 11 Nov 2008 08:14:28 -0600 (CST)

> 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.

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