instudyfindt: calculate the timeline in study when some or all subjects...

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

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))

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