rpwexp: The Piecewise Exponential Distribution

Description Usage Arguments Details Examples

View source: R/rpwexp.r

Description

The piecewise exponential distribution allows a simple method to specify a distribtuion where the hazard rate changes over time. It is likely to be useful for conditions where failure rates change, but also for simulations where there may be a delayed treatment effect or a treatment effect that that is otherwise changing (e.g., decreasing) over time. rpwexp() is to support simulation both the Lachin and Foulkes (1986) sample size method for (fixed trial duration) as well as the Kim and Tsiatis(1990) method (fixed enrollment rates and either fixed enrollment duration or fixed minimum follow-up); see gsDesign.

Usage

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rpwexp(n, rate = 1, intervals = NULL, cumulative = FALSE)

Arguments

n

Number of observations. If length(n) > 1, the length is taken to be the number required.

rate

Vector containing exponential failure rates in intervals described by intervals

intervals

Vector containing positive values indicating interval lengths where the exponential rates provided in rate apply. Note that the length of intervals is 1 less than that of rate and that the final value rate in rate applies after time 'sum(intervals)'.

cumulative

FALSE (the default) generates n independent, identically distributed piecewise exponential failure rates according to the distribution specified by intervals and rate. TRUE generates independent inter-arrival times with the rates of arrival in each interval specified by intervals determined by rate.

Details

Using the cumulative=TRUE option, enrollment times that piecewise constant over time can be generated.

Examples

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# get 10k piecewise exponential failure times
# failure rates are 1 for time 0-.5, 3 for time .5 - 1 and 10 for >1.
# intervals specifies duration of each failure rate interval
# with the final interval running to infinity
x <- rpwexp(10000, rate = c(1, 3, 10), intervals = c(.5,.5))
plot(sort(x),(10000:1)/10001,log="y", main="PW Exponential simulated survival curve",
xlab="Time",ylab="P{Survival}")
# piecewise uniform (piecewise exponential inter-arrival times) for 10k patients enrollment
# enrollment rates of 5 for time 0-100, 15 for 100-300, and 30 thereafter
x <- rpwexp(10000, rate = c(5, 15, 30), intervals = c(100,200), cumulative=TRUE)
plot(x,1:10000,
     main="Piecewise uniform enrollment simulation",xlab="Time",
     ylab="Enrollment")
# exponential enrollment
x <- rpwexp(10000, rate = .03, intervals = NULL, cumulative=TRUE)
plot(x,1:10000,main="Simulated exponential inter-arrival times",
     xlab="Time",ylab="Enrollment")
# exponential failure times
x <- rpwexp(10000, rate = 5)

plot(sort(x),(10000:1)/10001,log="y", main="Exponential simulated survival curve",
     xlab="Time",ylab="P{Survival}")

library(ggplot2)
qplot(sort(x),(10000:1)/10001,geom="line") + scale_y_log10(breaks=c(1,.1,.01)) +
  ggtitle("Exponential simulated survival curve") +
  xlab("Time")+ylab("P{Survival}")

keaven/nphsim documentation built on July 2, 2018, 1:10 a.m.