PWEALL (version 1.3.0.1)

rmstsim: simulating the restricted mean survival times

Description

This will simulate the test statistics accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

rmstsim(tcut=c(1,2),tstudy=tcut+0.2,taur=1.2,
        u=c(1/taur,1/taur),ut=c(taur/2,taur),pi1=0.5,
        rate11=c(1,0.5),rate21=rate11,rate31=c(0.7,0.4),
        rate41=rate21,rate51=rate21,ratec1=c(0.5,0.6),
        rate10=rate11,rate20=rate10,rate30=rate31,
        rate40=rate20,rate50=rate20,ratec0=c(0.6,0.5),
        tchange=c(0,1),type1=1,type0=1,rp21=0.5,rp20=0.5,
        n=1000,rn=200,eps=1.0E-08)

Value

outr

test statistics at each pair of tcut and tstudy in column and each simulation run in row

Arguments

tcut

a vector of time points at which rmst are calculated

tstudy

a vector of study time points, should be the same length as tcut and should be not less than tcut element-wise

taur

Recruitment time

u

Piecewise constant recuitment rate

ut

Recruitment intervals

pi1

Allocation probability for the treatment group

rate11

Hazard before crossover for the treatment group

rate21

Hazard after crossover for the treatment group

rate31

Hazard for time to crossover for the treatment group

rate41

Hazard after crossover for the treatment group for complex case

rate51

Hazard after crossover for the treatment group for complex case

ratec1

Hazard for time to censoring for the treatment group

rate10

Hazard before crossover for the control group

rate20

Hazard after crossover for the control group

rate30

Hazard for time to crossover for the control group

rate40

Hazard after crossover for the control group for complex case

rate50

Hazard after crossover for the control group for complex case

ratec0

Hazard for time to censoring for the control group

tchange

A strictly increasing sequence of time points at which the event rates changes. The first element of tchange must be zero. It must have the same length as rate11, rate21, rate31, etc.

type1

Type of crossover in the treatment group

type0

Type of crossover in the control group

rp21

re-randomization prob in the treatment group

rp20

re-randomization prob in the control group

n

number of subjects

rn

number of simulations

eps

tolerence for comparing event times

Author

Xiaodong Luo

Details

The hazard functions corresponding to rate11,...,rate51,ratec1, rate10,...,rate50,ratec0 are all piecewise constant function taking the form \(\lambda(t)=\sum_{j=1}^m \lambda_j I(t_{j-1}\le t<t_j)\), where \(\lambda_1,\ldots,\lambda_m\) are the corresponding elements of the rates and \(t_0,\ldots,t_{m-1}\) are the corresponding elements of tchange, \(t_m=\infty\). Note that all the rates must have the same tchange.

References

Luo et al. (2018) Design and monitoring of survival trials in complex scenarios, Statistics in Medicine <doi: https://doi.org/10.1002/sim.7975>.

See Also

pwe,rpwe,qpwe,ovbeta

Examples

tcuta<-c(2,3)
taur<-1.2
u<-c(1/taur,1/taur)
ut<-c(taur/2,taur)
r11<-c(1,0.5)
r21<-c(0.5,0.8)
r31<-c(0.7,0.4)
r41<-r51<-r21
rc1<-c(0.5,0.6)
r10<-c(1.5,0.7)
r20<-c(0.5,1)
r30<-c(0.3,0.4)
r40<-r50<-r20
rc0<-c(0.2,0.4)
ar<-rmstsim(tcut=tcuta,tstudy=tcuta+0.1,taur=taur,u=u,ut=ut,pi1=0.5,
            rate11=r11,rate21=r21,rate31=r31,rate41=r41,rate51=r51,ratec1=rc1,
            rate10=r10,rate20=r20,rate30=r30,rate40=r40,rate50=r50,ratec0=rc0,
            tchange=c(0,1),type1=1,type0=1,
            n=300,rn=200)
##Empirical power
apply(ar$outr>1.96,2,mean)