rmstcov: Calculation of the variance and covariance of estimated...

In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

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

PWEALL documentation built on Aug. 9, 2023, 9:08 a.m.