lpl (version 0.13)

rsurv: The Survival Distribution

Description

Density, distribution function, quantile function and random variable generation for a survival distribution with a provided hazard function or cumulative hazard function

Usage

dsurv(x, h0 = NULL, H0 = function(x){x}, log=FALSE)
  psurv(q, h0 = NULL, H0 = function(x){x}, low.tail=TRUE, log.p=FALSE) 
  qsurv(p, h0 = NULL, H0 = function(x){x}, low.tail=TRUE)
  rsurv(n, h0 = NULL, H0 = function(x){x})
  rcoxph(n, h0 = NULL, H0 = function(x){x}, lp = 0)

Value

{ dsurv } gives the density h(x)/S(x), { psurv } gives the distribution function, { qsurv } gives the quantile function, { rsurv } generates random survival time, and { rcoxph } generates random survival time with Cox proportional hazards model.

The length of the result is determined by n for rsurv and rcoxph.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

h0

hazard function, default is h0 = NULL.

H0

cumulative hazard function, default is H0(x) = x.

lp

linear predictor for rcoxph, H(x) = H0(x)exp(lp).

log, log.p

logical; if TRUE, probabilities p are give as log(p).

low.tail

logical; if TRUE, probabilities are P[X < or = x] otherwise, S(x) = P[X>x].

Author

Bingshu E. Chen

Details

If { h0 } or { H0 } are not specified, they assume the default values of h0(x) = 1 and H0(x) = x, respectively.

The survival distribution function is given by,

S(x) = exp(-H0(x)),

where H0(x) is the cumulative hazard function. Only one of h0 or H0 can be specified, if h0 is given, then H0(x) = integrate(h0, 0, x, subdivisions = 500L)

To calculate the restricted mean survival time for Weibull distribution with

H = function(x) x^2 h = function(x) 2*x

use

rmst(tua, h0 = h)

or

rmst(tua, H0 = H)

when both h0 and H0 are provided, only h0 will be used and H0 will be ignored.

To generate Cox PH survival time, use

u = exp(-H(t)*exp(lp))

then, -log(u)*exp(-lp) = H(t). Find t such that H(t) = -log(u)exp(-lp).

References

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, volume 1. Wiley, New York.

See Also

Distributions for other standard distributions, including dweibull for the Weibull distribution.

Examples

#### use qsurv to generate quantiles for weibull distribution
H1 = function(x) x^3
qsurv(seq(0.1, 0.9, 0.2), H0 = H1) ### shall be the same as
qweibull(seq(0.1, 0.9, 0.2), 3)
#### to get random survival time from the cumulative hazard function H1(t)
rsurv(15, H0 = H1)