rmstpower {PWEALL}

Calculate powers at different cut-points based on difference of restricted mean survival times (RMST)

Description

A function to calculate powers at different cut-points based on difference of restricted mean survival times (RMST) account for delayed treatment, discontinued treatment and non-uniform entry

Usage

rmstpower(tcut=2,tstudy=seq(tcut,tcut+2,by=0.5),alpha=0.05,twosided=1,
          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,
          eps=1.0e-2,veps=1.0e-2,n=1000)

Arguments

tcut

timepoint at which rmst is calculated

tstudy

a vector of study time points, which must be not smaller than tcut

alpha

type-1 error rate

twosided

twosided test=1 or not

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 for the treatment group

rp20

re-randomization prob for the control group

eps

error tolerence

veps

error tolenrence for calculating variance

n

total number of subjects, both groups combined

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.

Value

power

power

rmst1

rmst in the treatment group

se1

standard error of the rmst in the treatment group

rmst0

rmst in the control group

se0

standard error of the rmst in the control group

drmst

rmst1-rmst0

sed

standard error of the mean difference

Note

This calculates the restricted mean survival times between the treatment and control groups and their standard errors

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

Examples

tcut<-3.0
tstudy<-seq(3,6,by=1)
taur<-1.2
u<-c(1/taur,1/taur)
ut<-c(taur/2,taur)
r11<-c(0.2,0.1)
r21<-r11
r31<-c(0.03,0.02)
r41<-r51<-r21
rc1<-c(0.01,0.02)
r10<-c(0.2,0.2)
r20<-r10
r30<-c(0.02,0.01)
r40<-r50<-r20
rc0<-c(0.02,0.01)
getrmst<-rmstpower(tcut=tcut,tstudy=tstudy,alpha=0.05,twosided=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,rp21=0.5,rp20=0.5,n=1000)
###powers at each time point
cbind(tstudy,getrmst$power)