Exponentiating spline coefficients

Question

I am fitting a flexible parametric survival model with 1 df on the log cumulative baseline hazard (i.e. a Weibull model) but with a 1 df (linear term) on the interaction of X1 with log time, to account for non-proportional hazards.

The regression equation is:

stpm2(Surv(time = time, event = event) ~ X1 + X2 + X3 + X4, data = dat, df = 1, tvc = list(X1 = 1))

The output I get is attached as an image produced with flextable.

What I want to know is:

1. I presume it's valid to exponentiate the spline terms on the cumulative baseline hazard and the interaction of time with the covariate (bottom two rows of the table)?
2. Are these terms interpretable, especially for the covariate spline term? I would guess not, but am happy to be enlightened. The hazard ratio for X1 is 0.375 but this is meaningless by itself right, because there is the additional spline term that contributes to the X1:time association?

To my understanding with any model that contains spline terms, the only good way to interpret the model is by predicting/plotting covariate effects at different values.

Thanks

Answer 1

As the reference manual for the rstpm2 package notes, different packages use different spline bases for this type of modeling. Any interpretation of the spline coefficients thus would have to be package-specific. That's possible, but your sense is correct that "predicting/plotting covariate effects at different values" is the best way to go.

That also in part addresses your question about exponentiating spline coefficients: you can exponentiate anything that you want, but interpretation of what those exponentiated coefficients mean would depend on the package used to fit the model. Also note that the main spline coefficient has a very similar magnitude but opposite sign than the intercept has. With coefficients having such high magnitudes (+15 or -16), it would be safest to do all calculations in the original coefficient scales first and only exponentiate at the end if you want a hazard ratio.

Furthermore, the time-varying coefficient for X1 is represented as an interaction term between X1 and the spline for time. Under standard coding, each of the 2 individual coefficients is reported as the value when the interacting predictor is at a reference value, presumably 0 in this case. That might or might not be a scenario that makes sense, and the X1 coefficient would depend on whether time is measured in days (log(t)=0 at 1 day) or years (log(t)=0 at 1 year). There's nothing specific to a survival model or a spline in this respect; this is a general issue for regression modeling when predictors are involved in interactions. See this page and its links, among many others on this site.