pwecxpwufindt {PWEALL}

calculate the timeline when certain number of events accumulates

Description

This will calculate the timeline from study inception accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

pwecxpwufindt(target=400,ntotal=1000,taur=5,u=c(1/taur,1/taur),ut=c(taur/2,taur),pi1=0.5,
                         rate11=c(1,0.5),rate21=c(0.8,0.9),rate31=c(0.7,0.4),
                         rate41=rate21,rate51=rate21,ratec1=c(0.5,0.6),
                         rate10=c(1,0.7),rate20=c(0.9,0.7),rate30=c(0.4,0.6),
                         rate40=rate20,rate50=rate20,ratec0=c(0.3,0.3),
                         tchange=c(0,1),type1=1,type0=1,
                         rp21=0.5,rp20=0.5,eps=1.0e-2,
                         init=taur,epsilon=0.000001,maxiter=100)

Arguments

target

target number of events

ntotal

total number of subjects

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 in the treatment group

rp20

re-randomization prob in the control group

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.

init

initital value of the timeline estimate

epsilon

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

maxiter

Maximum number of iterations when calculating the timeline

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

t1

the calculated timeline

tvar

the true variance of the timeline estimator

eps

final tolerance

iter

Number of iterations performed

Note

Version 1.0 (7/19/2016)

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>.

See Also

pwe,rpwe,qpwe,instudyfindt

Examples

target<-400
ntotal<-2000
taur<-1.2
u<-c(1/taur,1/taur)
ut<-c(taur/2,taur)
r11<-c(1,0.5)
r21<-c(0.5,0.8)
r31<-c(0.7,0.4)
r41<-r51<-r21
rc1<-c(0.5,0.6)
r10<-c(1,0.7)
r20<-c(0.5,1)
r30<-c(0.3,0.4)
r40<-r50<-r20
rc0<-c(0.2,0.4)
gettimeline<-pwecxpwufindt(target=target,ntotal=ntotal,
                taur=5,u=c(1/taur,1/taur),ut=c(taur/2,taur),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,eps=1.0e-2,init=taur,epsilon=0.000001,maxiter=100)
gettimeline$t1