pwe: Piecewise exponential distribution: hazard, cumulative...

In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

Piecewise exponential distribution: hazard, cumulative hazard, density, distribution, survival

Description

This will provide the related functions of the specified piecewise exponential distribution.

Usage

pwe(t=seq(0,5,by=0.5),rate=c(0,5,0.8),tchange=c(0,3))

Arguments

t	A vector of time points.
rate	A vector of event rates
tchange	A strictly increasing sequence of time points at which the event rate changes. The first element of tchange must be zero. It must have the same length as rate.

Details

Let \lambda(t)=\sum_{j=1}^m \lambda_j I(t_{j-1}\le t<t_j) be the hazard function, where \lambda_1,\ldots,\lambda_m are the corresponding elements of rate and t_0,\ldots,t_{m-1} are the corresponding elements of tchange, t_m=\infty. The cumulative hazard function

\Lambda(t)=\sum_{j=1}^m \lambda_j(t\wedge t_j-t\wedge t_{j-1}),

the survival function S(t)=\exp\{-\Lambda(t)\}, the distribution function F(t)=1-S(t) and the density function f(t)=\lambda(t)S(t).

Value

hazard	Hazard function
cumhazard	Cumulative hazard function
density	Density function
dist	Distribution function
surv	Survival function

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

rpwe,qpwe

Examples

t<-seq(0,3,by=0.1)
rate<-c(0.6,0.3)
tchange<-c(0,1.75)
pwefun<-pwe(t=t,rate=rate,tchange=tchange)
pwefun

PWEALL documentation built on Aug. 9, 2023, 9:08 a.m.