rmstcov: 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)

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

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.

Author

Xiaodong Luo

Details

More details

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

Run this code

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

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