Thanks for those clarifications, that is really helpful. My follow-up question then would be: how do I need to report the results of a model which uses restricted cubic splines to allow for others to validate such a model with their own data?

To give a concrete example: I am planning to estimate a risk prediction model based on the strategy from your text and the RMS short course (which are excellent resources by the way). Therefore I would want to model continuous variables using restricted cubic spilnes. How should I report the model to allow others to externally validate it using their own data? When others would want to follow the process outlined by Royston and Altman linked above, they would need predictions for the individuals in their dataset.

Given a hypothetical model created from data of the `survival`

package:

```
library(tidyverse)
library(rms)
df <- survival::pbc %>%
as_tibble() %>%
# Only allow one event state, not 2
mutate(event = as.numeric(status == 2))
dd <- datadist(df); options(datadist = "dd")
S <- Surv(time = df$time, event = df$event)
a <- cph(S ~ rcs(age, 5) + sex, df)
```

`print(a)`

would give me this:

```
print(a)
# Output:
Cox Proportional Hazards Model
cph(formula = S ~ rcs(age, 5) + sex, data = df)
Model Tests Discrimination
Indexes
Obs 418 LR chi2 28.20 R2 0.066
Events 161 d.f. 5 Dxy 0.225
Center 2.8692 Pr(> chi2) 0.0000 g 0.506
Score chi2 29.13 gr 1.658
Pr(> chi2) 0.0000
Coef S.E. Wald Z Pr(>|Z|)
age 0.0654 0.0597 1.10 0.2729
age' -0.0017 0.2675 -0.01 0.9950
age'' -0.3289 1.1103 -0.30 0.7671
age''' 0.9991 1.7020 0.59 0.5572
sex=f -0.2310 0.2280 -1.01 0.3109
```

And `Formula(a)`

would give me this:

```
Function(a)
# Output:
function(age = 51.000684,sex = "f") {-2.8692322+0.065446684* age-1.4362402e-06*pmax(age-33.839014,0)^3-0.00028313565*pmax(age-43.981314,0)^3+0.00086010403*pmax(age-51.000684,0)^3-0.00069649416*pmax(age-56.828131,0)^3+0.00012096202*pmax(age-67.920876,0)^3-0.23102847*(sex=="f") }
<environment: 0x00000293349704b8>
```

And `latex(a)`

would give me this:

Wouldn’t it be necessary to report this equation somewhere in the paper too? I had a look at an article that you co-authored and couldn’t find a formula or the regression coefficients that would allow me to calculate predictions. I did see that you provide a shiny app which I am planning to do too, but another researcher would still need the formula to calculate predictions, right? Or is there another way to externally validate your model? Or would it be more appropriate to refit the model using the same specification as mentioned in the paper?

Sorry, but I am only starting to get the full picture here.

Thanks in advance for any precious inputs!