> On examining non-linearity of Cox coefficients with penalized splines - I > have not been able to dig up a completely clear description of the test > performed in R or S-plus.
One "iron clad" way to test is to fit a model that has the variable of interest "x" as a linear term, then a second model with splines, and do a likelihood ratio test with 2*(difference in log-likelihood) on (difference in df) degrees of freedom. With a penalized model this test is conservative: the chi-square is not quite the right distribution, the true dist has the same mean but smaller variance. The pspline function uses an evenly spaced set of symmetric basis functions. A neat consequence of this is that the Wald test for linear vs 'more general' is a test that the coefficients of the spline terms fall in a linear series. That is, a linear trend test on the coefficients. This is what coxph does. As with the LR test, the chi-square dist is conservative. I have not worked at putting in the more correct distribution. See Eilers and Marx, Statistical Science 1986. > And what is the null for the non-linear test? The linear test is "is a linear better than nothing", the non-linear one is a sequential test "is the non-linear better than the linear". The second test of course depends on the total number of df you allowed for the pspline fit. As a silly example adding "+ pspline(x, df=200)" would likely show that the nonlinear term was not a significant addition, i.e., not worth 199 more degrees of freedom. Terry Therneau ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.