Restricted Cubic Spline output in R rms package after cph

Question

I am developing a COX regression model in R.
The model I am currently using is as follows

fh <- cph(S ~ rcs(MPV,4) + rcs(age,3) + BMI + smoking + hyperten + gender +
    rcs(FVCPP,3) + TLcoPP, x=TRUE, y=TRUE, surv=TRUE, time.inc=2*52) 

If I then want to look at this with

print(fh, latex = TRUE) 

I get 3 coefs/SE/Wald etc for MPV (MVP, MVP' and MVP'') and 2 for age (age, age') .
Could someone please explain to me what these outputs are? ie I believe they are to do with the restricted cubic splines I have added.

Answer 1

When you write rcs(MPV,4) , you define the number of knots to use in the spline; in this case 4. Similarly, rcs(age,3) defines a spline with 3 knots. Due to identifiability constraints, 1 knot from each spline is subtracted out. You can think of this as defining an intercept for each spline. So rcs(Age,3) is a linear combination of 2 nonlinear basis functions and an intercept, while rcs(MPV,4) is a linear combination of 3 nonlinear basis functions and an intercept, ie,

and

In the notation above, what you get out from the print statement are the regression coefficients and , with corresponding standard errors, p-values etc. The intercepts and are typically set to zero, but they are important, because without them, the model fitting routine how have no idea of where on the y-axis to constrain the splines.

As a final note, you might actually be more interested in the output of summary(fh) .