Probability density and distribution function for the Royston/Parmar spline model.
1 2 3 4  dsurvspline(x, gamma, beta=0, X=0, knots=c(10,10), scale="hazard", offset=0)
psurvspline(q, gamma, beta=0, X=0, knots=c(10,10), scale="hazard", offset=0)
hsurvspline(x, gamma, beta=0, X=0, knots=c(10,10), scale="hazard", offset=0)
Hsurvspline(x, gamma, beta=0, X=0, knots=c(10,10), scale="hazard", offset=0)

x,q 
Vector of times. 
gamma 
Vector of parameters describing the baseline spline
function, as described in 
beta 
Vector of covariate effects. 
X 
Matrix of covariate values. 
knots 
Locations of knots on the axis of log time, supplied in
increasing order. Unlike in 
scale 

offset 
An extra constant to add to the linear predictor eta. 
dsurvspline
gives the density, psurvspline
gives the distribution
function, hsurvspline
gives the hazard and Hsurvspline
gives the cumulative hazard, as described in flexsurvspline
.
Christopher Jackson <chris.jackson@mrcbsu.cam.ac.uk>
Royston, P. and Parmar, M. (2002). Flexible parametric proportionalhazards and proportionalodds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):21752197.
1 2 3 4 5 6 7 8 9 10 11  ## reduces to the weibull
regscale < 0.786; cf < 1.82
a < 1/regscale; b < exp(cf)
dweibull(1, shape=a, scale=b)
dsurvspline(1, gamma=c(log(1 / b^a), a)) # should be the same
## reduces to the lognormal
meanlog < 1.52; sdlog < 1.11
dlnorm(1, meanlog, sdlog)
dsurvspline(1, gamma = c(meanlog/sdlog, 1/sdlog), scale="normal")
# should be the same

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