Compute a basis for a natural cubic spline, by default using the parameterisation described by Royston and Parmar (2002). Used for flexible parametric survival models.

## Arguments

- knots
Vector of knot locations in increasing order, including the boundary knots at the beginning and end.

- x
Vector of ordinates to compute the basis for.

- spline
`"rp"`

to use the natural cubic spline basis described in Royston and Parmar.`"splines2ns"`

to use the alternative natural cubic spline basis from the`splines2`

package (Wang and Yan 2021), which may be better behaved due to the basis being orthogonal.

## Value

A matrix with one row for each ordinate and one column for each knot.

`basis`

returns the basis, and `dbasis`

returns its derivative
with respect to `x`

.

`fss`

and `dfss`

are the same, but with the order of the
arguments swapped around for consistency with similar functions in other R
packages.

## Details

The exact formula for the basis is given in `flexsurvspline`

.

## References

Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197.

Wang W, Yan J (2021). Shape-Restricted Regression Splines with R Package splines2. Journal of Data Science, 19(3), 498-517.