# [R] help on pspline in coxph

Lei Liu liulei at virginia.edu
Wed Apr 6 23:06:47 CEST 2011

```Hi there,

I have a question on how to extract the linear term in the penalized
spline in coxph. Here is a sample code:

n=100

set.seed(1)

x=runif(100)

f1 = cos(2*pi*x)

hazard = exp(f1)

T = 0

for (i in 1:100) {

T[i] = rexp(1,hazard[i])

}

C = runif(n)*4

cen = T<=C

y = T*(cen) + C*(1-cen)

data.tr=cbind(y,cen,x)

fit=coxph(Surv(data.tr[,1], data.tr[,2])~pspline(data.tr[,3]) )

If I use summary(fit), it will show the following results:

summary(fit)
Call:
coxph(formula = Surv(data.tr[, 1], data.tr[, 2]) ~ pspline(data.tr[,
3]))

n= 100
coef  se(coef) se2   Chisq DF   p
pspline(data.tr[, 3]), li 0.495 0.437    0.437  1.28 1.00 2.6e-01
pspline(data.tr[, 3]), no                      43.79 3.08 1.9e-09

exp(coef) exp(-coef) lower .95 upper .95
ps(data.tr[, 3])2     0.4404      2.270   0.08164     2.376
ps(data.tr[, 3])3     0.2065      4.842   0.01701     2.507
ps(data.tr[, 3])4     0.0951     10.512   0.00695     1.302
ps(data.tr[, 3])5     0.0493     20.274   0.00387     0.628
ps(data.tr[, 3])6     0.0280     35.741   0.00230     0.340
ps(data.tr[, 3])7     0.0192     52.068   0.00156     0.237
ps(data.tr[, 3])8     0.0219     45.605   0.00178     0.271
ps(data.tr[, 3])9     0.0473     21.156   0.00399     0.561
ps(data.tr[, 3])10    0.1432      6.983   0.01250     1.640
ps(data.tr[, 3])11    0.3936      2.541   0.03436     4.509
ps(data.tr[, 3])12    0.9449      1.058   0.06885    12.969
ps(data.tr[, 3])13    2.2406      0.446   0.07643    65.683

Iterations: 3 outer, 9 Newton-Raphson
Theta= 0.697
Degrees of freedom for terms= 4.1
Rsquare= 0.385   (max possible= 0.994 )
Likelihood ratio test= 48.6  on 4.08 df,   p=7.74e-10
Wald test            = 45.1  on 4.08 df,   p=4.29e-09

My question is how to extract the linear coefficient (0.495) in
pspline(data.tr[, 3]). I tried coef(fit) but it fails to display this
term. Your help is greatly appreciated!

Lei Liu
Associate Professor
Division of Biostatistics and Epidemiology
Department of Public Health Sciences
University of Virginia School of Medicine

http://people.virginia.edu/~ll9f/

```