rmstcov {PWEALL}

Calculation of the variance and covariance of estimated restricted mean survival time

Description

A function to calculate the variance and covariance of estimated restricted mean survival time using data from different cut-off points accounting for delayed treatment, discontinued treatment and non-uniform entry

Usage

rmstcov(t1cut=2.0,t1study=2.5,t2cut=3.0,t2study=3.5,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,veps=1.0e-2)

Arguments

t1cut

time point at which rmst is calculated

t1study

the study time point from first patient in, it must be larger than t1cut. This will be used for study monitoring.

t2cut

time point at which rmst is calculated. t2cut must be not smaller than t1cut.

t2study

the study time point from first patient in, it must be larger than t2cut. This will be used for study monitoring.

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 pi2*r2(t-s)+(1-pi2)*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

t1cut

time point at which rmst is calculated

t1study

the study time point from first patient in, it must be larger than t1cut. This will be used for study monitoring.

t2cut

time point at which rmst is calculated. t2cut must be not smaller than t1cut.

t2study

the study time point from first patient in, it must be larger than t2cut. This will be used for study monitoring.

rmst

rmst at cut-point t1cut with study time t1study

rmst1

rmst at cut-point t2cut with study time t2study

rmstx

rmst at cut-point t1cut with study time t2study, which should be the same as rmst.

v

the variance of rmst

v1

the variance of rmst1

cov

the covariance of rmst and rmst1

cov1

another covariance of rmst and rmst1, should be the same as cov

Note

This calculates the "true" variance and covariance 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)
rmcov<-rmstcov(t1cut=2.0,t1study=2.5,t2cut=3.0,t2study=3.5,taur=5,
        rate1=r1,rate2=r2,rate3=r3,rate4=r4,rate5=r5,ratec=rc,
        tchange=c(0,1),type=1)
rmcov