instudyfindt: 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)

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

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

Author

Xiaodong Luo

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.

References

Luo, et al. (2017)

Examples

Run this code

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))

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