pwepowerfindt: Calculating the timepoint where a certain power of the...

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

Calculating the timepoint where a certain power of the specified test statistics is obtained

Description

This will calculate the timepoint where a certain power of the specified test statistics is obtained accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

pwepowerfindt(power=0.9,alpha=0.05,twosided=1,tupp=5,tlow=1,taur=1.2,
                     u=c(1/taur,1/taur),ut=c(taur/2,taur),pi1=0.5,
                     rate11=c(1,0.5),rate21=rate11,rate31=c(0.7,0.4),
                     rate41=rate21,rate51=rate21,ratec1=c(0.5,0.6),
                     rate10=rate11,rate20=rate10,rate30=rate31,
                     rate40=rate20,rate50=rate20,ratec0=c(0.6,0.5),
                     tchange=c(0,1),type1=1,type0=1,
                     rp21=0.5,rp20=0.5,eps=1.0e-2,veps=1.0e-2,
                     epsbeta=1.0e-04,iterbeta=25,
                     n=1000,testtype=1,maxiter=20,itereps=0.001)

Arguments

power	the desired power
alpha	type-1 error
twosided	twoside test or not
tupp	an upper time point where the power should be larger than power
tlow	a lower time point where the power should be smaller than power
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	error tolerence
veps	error tolenrence for calculating variance
epsbeta	error tolerance for calculating overall log HR
iterbeta	maximum number of iterations for calculating overall log HR
n	total number of subjects
testtype	test statistics, =1 log-rank;=2 Cox model; =3 log-rank with robust variance
maxiter	maximum number of bi-section iterations
itereps	error tolerance of power

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

testtype	type of statistic, =1 log-rank;=2 Cox model; =3 log-rank with robust variance
time	time calculated when the iterations stop
power	the power at time
err	distance from the desired power
k	number of bi-section iterations performed

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

pwe,rpwe,qpwe,ovbeta,innervar

Examples

t<-seq(3,6,by=1)
taur<-1.2
u<-c(1/taur,1/taur)
ut<-c(taur/2,taur)
r11<-c(0.2,0.1)
r21<-r11
r31<-c(0.03,0.02)
r41<-r51<-r21
rc1<-c(0.01,0.02)
r10<-c(0.2,0.2)
r20<-r10
r30<-c(0.02,0.01)
r40<-r50<-r20
rc0<-c(0.02,0.01)
getpower<-pwepower(t=t,alpha=0.05,twosided=1,taur=taur,u=u,ut=ut,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,n=1000)
###powers at each time point
cbind(t,getpower$power[,1:3])

###90% power should be in (3,3.5)
getpwtime<-pwepowerfindt(power=0.9,alpha=0.05,twosided=1,tupp=3.5,tlow=3,taur=taur,
        u=u,ut=ut,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,n=1000,testtype=1,maxiter=30)
getpwtime

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