instudyfindt {PWEALL}

calculate the timeline in study when some or all subjects have entered

Description

This will calculate the timeline from some timepoint in study when some/all subjects have entered accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

instudyfindt(target=400,y=exp(rnorm(300)),z=rbinom(300,1,0.5),
                  d=rep(c(0,1,2),each=100),
                  tcut=2,blinded=1,type0=1,type1=type0,
                  rp20=0.5,rp21=0.5,tchange=c(0,1),
                  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),
                  rate11=rate10,rate21=rate20,rate31=rate30,
                  rate41=rate40,rate51=rate50,ratec1=ratec0,
                  withmorerec=1,
                  ntotal=1000,taur=5,u=c(1/taur,1/taur),ut=c(taur/2,taur),pi1=0.5,
                  ntype0=1,ntype1=1,
                  nrp20=0.5,nrp21=0.5,ntchange=c(0,1),
                  nrate10=rate10,nrate20=rate20,nrate30=rate30,nrate40=rate40,
                  nrate50=rate50,nratec0=ratec0,
                  nrate11=rate10,nrate21=rate20,nrate31=rate30,nrate41=rate40,
                  nrate51=rate50,nratec1=ratec0,
                  eps=1.0e-2,init=tcut*1.1,epsilon=0.001,maxiter=100)

Arguments

target

target number of events

y

observed times

z

observed treatment indicator when blinded=0, z=1 denotes the treatment group and 0 the control group

d

event indicator, 1=event, 0=censored, 2=no event or censored up to tcut, the data cut-point

tcut

the data cut-point

blinded

blinded=1 if the data is blinded,=0 if it is unblinded

type0

type of the crossover for the observed data in the control group

type1

type of the crossover for the observed data in the treatment group

rp20

re-randomization prob for the observed data in the control group

rp21

re-randomization prob for the observed data in the treatment 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 ratejk, j=1,2,3,4,5,c; k=0,1

rate10

Hazard before crossover for the old subjects in the control group

rate20

Hazard after crossover for the old subjects in the control group

rate30

Hazard for time to crossover for the old subjects in the control group

rate40

Hazard after crossover for the old subjects in the control group for complex case

rate50

Hazard after crossover for the old subjects in the control group for complex case

ratec0

Hazard for time to censoring for the old subjects in the control group

rate11

Hazard before crossover for the old subjects in the treatment group

rate21

Hazard after crossover for the old subjects in the treatment group

rate31

Hazard for time to crossover for the old subjects in the treatment group

rate41

Hazard after crossover for the old subjects in the treatment group for complex case

rate51

Hazard after crossover for the old subjects in the treatment group for complex case

ratec1

Hazard for time to censoring for the old subjects in the treatment group

withmorerec

withmorerec=1 if more subjects are needed to be recruited; =0 otherwise

ntotal

total number of the potential new subjects

taur

recruitment time for the potential new subjects

u

Piecewise constant recuitment rate for the potential new subjects

ut

Recruitment intervals for the potential new subjects

pi1

Allocation probability to the treatment group for the potential new subjects

ntype0

type of the crossover for the potential new subjects in the control group

ntype1

type of the crossover for the potential new subjects in the treatment group

nrp20

re-randomization prob for the potential new subjects in the control group

nrp21

re-randomization prob for the potential new subjects in the treatment group

ntchange

A strictly increasing sequence of time points at which the event rates changes. The first element of ntchange must be zero. It must have the same length as nratejk, j=1,2,3,4,5,c; k=0,1

nrate10

Hazard before crossover for the potential new subjects in the control group

nrate20

Hazard after crossover for the potential new subjects in the control group

nrate30

Hazard for time to crossover for the potential new subjects in the control group

nrate40

Hazard after crossover for the potential new subjects in the control group for complex case

nrate50

Hazard after crossover for the potential new subjects in the control group for complex case

nratec0

Hazard for time to censoring for the potential new subjects in the control group

nrate11

Hazard before crossover for the potential new subjects in the treatment group

nrate21

Hazard after crossover for the potential new subjects in the treatment group

nrate31

Hazard for time to crossover for the potential new subjects in the treatment group

nrate41

Hazard after crossover for the potential new subjects in the treatment group for complex case

nrate51

Hazard after crossover for the potential new subjects in the treatment group for complex case

nratec1

Hazard for time to censoring for the potential new subjects in the treatment 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. The hazard functions corresponding to nrate11,...,nrate51,nratec1, nrate10,...,nrate50,nratec0 are all piecewise constant functions and all must have the same ntchange.

Value

t1

the calculated timeline

dvalue

the number of events

dvprime

the derivative of the event cummulative function at time t1

tvar

the variance of the timeline estimator

ny

total number of subjects that could be in the study

eps

final tolerance

iter

Number of iterations performed

t1hist

the history of the iteration for timeline

dvaluehist

the history of the iteration for the event count

dvprimehist

the history of the iteration for the derivative of event count with respect to time

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

pwe,rpwe,qpwe,pwecxpwufindt

Examples

n<-1000
target<-550
ntotal<-1000
pi1<-0.5
taur<-2.8
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)
tchange<-c(0,1.873)
tcut<-2

####generate the data
E<-T<-C<-Z<-delta<-rep(0,n)
E<-rpwu(nr=n,u=u,ut=ut)$r
Z<-rbinom(n,1,pi1)
n1<-sum(Z)
n0<-sum(1-Z)
C[Z==1]<-rpwe(nr=n1,rate=rc1,tchange=tchange)$r
C[Z==0]<-rpwe(nr=n0,rate=rc0,tchange=tchange)$r
T[Z==1]<-rpwecx(nr=n1,rate1=r11,rate2=r21,rate3=r31,
                rate4=r41,rate5=r51,tchange=tchange,type=1)$r
T[Z==0]<-rpwecx(nr=n0,rate1=r10,rate2=r20,rate3=r30,
                rate4=r40,rate5=r50,tchange=tchange,type=1)$r
y<-pmin(pmin(T,C),tcut-E)
y1<-pmin(C,tcut-E)
delta[T<=y]<-1
delta[C<=y]<-0
delta[tcut-E<=y & tcut-E>0]<-2
delta[tcut-E<=y & tcut-E<=0]<--1

ys<-y[delta>-1]
Zs<-Z[delta>-1]
ds<-delta[delta>-1]

nplus<-sum(delta==-1)
nd0<-sum(ds==0)
nd1<-sum(ds==1)
nd2<-sum(ds==2)


ntaur<-taur-tcut
nu<-c(1/ntaur,1/ntaur)
nut<-c(ntaur/2,ntaur)

###calculate the timeline at baseline
xt<-pwecxpwufindt(target=target,ntotal=n,taur=taur,u=u,ut=ut,pi1=pi1,
              rate11=r11,rate21=r21,rate31=r31,ratec1=rc1,
              rate10=r10,rate20=r20,rate30=r30,ratec0=rc0,
              tchange=tchange,eps=0.001,init=taur,epsilon=0.000001,maxiter=100)
###calculate the timeline in study
yt<-instudyfindt(target=target,y=ys,z=Zs,d=ds,
                       tcut=tcut,blinded=0,type1=1,type0=1,tchange=tchange,
                       rate10=r10,rate20=r20,rate30=r30,ratec0=rc0,
                       rate11=r11,rate21=r21,rate31=r31,ratec1=rc1,
                       withmorerec=1,
                       ntotal=nplus,taur=ntaur,u=nu,ut=nut,pi1=pi1,
                       ntype1=1,ntype0=1,ntchange=tchange,
                       nrate10=r10,nrate20=r20,nrate30=r30,nratec0=rc0,
                       nrate11=r11,nrate21=r21,nrate31=r31,nratec1=rc1,
                       eps=1.0e-2,init=2,epsilon=0.001,maxiter=100)
##timelines                       
c(yt$t1,xt$t1)
##standard errors of the timeline estimators 
c(sqrt(yt$tvar/yt$ny),sqrt(xt$tvar/n))
###95 percent CIs
c(yt$t1-1.96*sqrt(yt$tvar/yt$ny),yt$t1+1.96*sqrt(yt$tvar/yt$ny))
c(xt$t1-1.96*sqrt(xt$tvar/n),xt$t1+1.96*sqrt(xt$tvar/n))