pwecxcens: Integration of the density of piecewise exponential... In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

Description

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

Usage

 1 2 3 pwecxcens(t=seq(0,10,by=0.5),rate1=c(1,0.5),rate2=rate1, rate3=c(0.7,0.4),rate4=rate2,rate5=rate2,ratec=c(0.2,0.3), tchange=c(0,1),type=1,rp2=0.5,eps=1.0e-2)

Arguments

 t a vector of time points 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)

ξ(t)=\int_0^t \widetilde{f}(s)S_C(s)ds,

where 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 s the survival function of \widetilde{f} sc the survival function S_C

Xiaodong Luo

References

Luo, et al. (2017)

 1 2 3 4 5 6 7 8 9 10 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<-pwecxcens(t=seq(0,10,by=0.5),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)