Probability density, distribution, quantile, random generation, hazard,
cumulative hazard, mean and restricted mean functions for the Royston/Parmar
spline model. These functions have all parameters of the distribution collecte together in a single argument gamma
. For the equivalent functions with one argument per parameter, see Survsplinek
.
dsurvspline( x, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0, log = FALSE ) psurvspline( q, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0, lower.tail = TRUE, log.p = FALSE ) qsurvspline( p, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0, lower.tail = TRUE, log.p = FALSE ) rsurvspline( n, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0 ) Hsurvspline( x, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0 ) hsurvspline( x, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0 ) rmst_survspline( t, gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0, start = 0 ) mean_survspline( gamma, beta = 0, X = 0, knots = c(-10, 10), scale = "hazard", timescale = "log", offset = 0 )
x, q, t | Vector of times. |
---|---|
gamma | Parameters describing the baseline spline function, as
described in |
beta | Vector of covariate effects (deprecated). |
X | Matrix of covariate values (deprecated). |
knots | Locations of knots on the axis of log time, supplied in
increasing order. Unlike in This may in principle be supplied as a matrix, in the same way as for
|
scale |
|
timescale |
|
offset | An extra constant to add to the linear predictor \(\eta\). |
log, log.p | Return log density or probability. |
lower.tail | logical; if TRUE (default), probabilities are \(P(X \le x)\), otherwise, \(P(X > x)\). |
p | Vector of probabilities. |
n | Number of random numbers to simulate. |
start | Optional left-truncation time or times. The returned restricted mean survival will be conditioned on survival up to this time. |
dsurvspline
gives the density, psurvspline
gives the
distribution function, hsurvspline
gives the hazard and
Hsurvspline
gives the cumulative hazard, as described in
flexsurvspline
.
qsurvspline
gives the quantile function, which is computed by crude
numerical inversion (using qgeneric
).
rsurvspline
generates random survival times by using
qsurvspline
on a sample of uniform random numbers. Due to the
numerical root-finding involved in qsurvspline
, it is slow compared
to typical random number generation functions.
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.
Christopher Jackson <chris.jackson@mrc-bsu.cam.ac.uk>
## reduces to the weibull regscale <- 0.786; cf <- 1.82 a <- 1/regscale; b <- exp(cf) dweibull(1, shape=a, scale=b)#> [1] 0.1137858#> [1] 0.1137858#> [1] 0.1407338#> [1] 0.1407338# should be the same