Simulation of Piecewise Constant Hazard Model (Cox)

Simulates data from a piecewise constant baseline hazard that can also be of Cox type. Censors data at the highest value of the break points.

Usage

rchaz(cumhazard, rr, n = NULL, entry = NULL, cause = 1, extend = FALSE)

Arguments

cumhazard: Cumulative hazard matrix (columns: time, cumulative hazard), or piece-constant rates for periods defined by the first column of input.
rr: Relative risk vector for simulations, or alternatively when rr=1 specify n.
n: Number of simulations if rr not given.
entry: Delayed entry time for simulations (optional).
cause: Name/code of the event cause (default 1).
extend: To extend piecewise constant with constant rate beyond the last break point. Default is FALSE. If TRUE, extends with average rate over time from cumulative. If numeric, uses the given rate.

Value

A data frame containing:

entry: Entry times.
time: Event/censoring times.
status: Event status (1=event, 0=censored).
rr: Relative risks used.

Attributes include:

cumhaz: The cumulative hazard used.
extend.rate: The extension rate if used.

Details

For a piecewise linear cumulative hazard, the inverse is easy to compute. With delayed entry $x$, we compute: $$\Lambda^{-1}(\Lambda(x) + E/RR)$$ where $RR$ are the relative risks and $E$ is exponential with mean 1. This quantity has survival function: $$P(T > t | T>x) = \exp(-RR (\Lambda(t) - \Lambda(x)))$$

Author

Thomas Scheike

Examples

chaz <-  c(0,1,1.5,2,2.1)
breaks <- c(0,10,   20,  30,   40)
cumhaz <- cbind(breaks,chaz)
n <- 10
X <- rbinom(n,1,0.5)
beta <- 0.2
rrcox <- exp(X * beta)

pctime <- rchaz(cumhaz,n=10)
pctimecox <- rchaz(cumhaz,rrcox,entry=runif(n))