rmstutil {PWEALL}

A utility function to calculate the true restricted mean survival time (RMST) and its variance account for delayed treatment, discontinued treatment and non-uniform entry

Description

A utility function to calculate the true restricted mean survival time (RMST) and its variance account for delayed treatment, discontinued treatment and non-uniform entry

Usage

rmstutil(tcut=2.0,tstudy=5.0,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,veps=1.0e-2)

Arguments

tcut

time point at which rmst is calculated

tstudy

the study time point from first patient in, it must be not smaller than tcut.

taur

Recruitment time

u

Piecewise constant recuitment rate

ut

Recruitment intervals

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

Hazard for time to censoring

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, 1=markov, 2=semi-markov, 3=hybrid

rp2

re-randomization probability to receive the rescue treatment when semi-markov crossover occurs. When it happens, the overall hazard will be rp2*r2(t-s)+(1-rp2)*r4(t), where r2 is the hazard for the semi-markov rescue treatment and r4 is hazard for the markov rescue treatment.

eps

A small number representing the error tolerance when calculating the utility function

\Phi_l(x)=\frac{\int_0^x s^l e^{-s}ds}{x^{l+1}}

with l=0,1,2.

veps

A small number representing the error tolerance when calculating the variance.

Details

More details

Value

tcut

time point at which rmst is calculated

tstudy

the study time point from first patient in, it must be not smaller than tcut

rmst

rmst at cut-point tcut

var

the variance of rmst

vadd

the additional variance term of rmst

Note

This calculates the "true" variance of restricted mean survival times

Author(s)

Xiaodong Luo

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>.

Examples

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(0.1,0.1)
rmt<-rmstutil(tcut=2.0,tstudy=5.0,taur=5,
        rate1=r1,rate2=r2,rate3=r3,
        rate4=r4,rate5=r5,ratec=rc,
        tchange=c(0,1),type=1,rp2=0.5,
        eps=1.0e-2,veps=1.0e-2)
rmt