pwecxpwu: Integration of the density of piecewise exponential...

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

Integration of the density of piecewise exponential distribution with crossover effect, censoring and recruitment function

Description

This will calculate the functions according to the piecewise exponential distribution with crossover

Usage

pwecxpwu(t=seq(0,10,by=0.5),taur=5,
        u=c(1/taur,1/taur),ut=c(taur/2,taur),
        rate1=c(1,0.5),rate2=rate1,rate3=c(0.7,0.4),
        rate4=rate2,rate5=rate2,ratec=c(0.5,0.6),
        tchange=c(0,1),type=1,rp2=0.5,eps=1.0e-2)

Arguments

t	a vector of time points
taur	recruitment time
u	recruitment rate
ut	recruitment interval, must have the same length as u
rate1	piecewise constant event rate before crossover
rate2	piecewise constant event rate after crossover
rate3	piecewise constant event rate for crossover
rate4	additional piecewise constant event rate for more complex crossover
rate5	additional piecewise constant event rate for more complex crossover
ratec	censoring piecewise constant event rate
tchange	a strictly increasing sequence of time points starting from zero at which event rate changes. The first element of tchange must be zero. The above rates rate1 to ratec and tchange must have the same length.
type	type of crossover, i.e. markov, semi-markov and hybrid
rp2	re-randomization prob
eps	tolerance

Details

This is to calculate the function (and its derivative)

\xi(t)=\int_0^t G_E(t-s)\widetilde{f}(s)S_C(s)ds,

where G_E is the accrual function defined by taur, u and ut, S_C is the piecewise exponential survival function of the censoring time, defined by tchange and ratec, and \widetilde{f} is the density for the event distribution subject to crossover defined by tchange, rate1 to rate5 and type.

Value

du	the function
duprime	its derivative

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

rpwe

Examples

taur<-2
u<-c(0.6,0.4)
ut<-c(1,2)
r1<-c(0.6,0.3)
r2<-c(0.6,0.6)
r3<-c(0.1,0.2)
r4<-c(0.5,0.4)
r5<-c(0.4,0.5)
rc<-c(0.5,0.6)
exu<-pwecxpwu(t=seq(0,10,by=0.5),taur=taur,u=u,ut=ut,
        rate1=r1,rate2=r2,rate3=r3,rate4=r4,rate5=r5,ratec=rc,
        tchange=c(0,1),type=1,eps=1.0e-2)
c(exu$du,exu$duprime)

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