PWEALL (version 1.3.0.1)

pwecxpwu: 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)

Value

du

the function

duprime

its derivative

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

Author

Xiaodong Luo

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.

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)