pwepowerfindt: 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)

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

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

Author

Xiaodong Luo

Details

The hazard functions corresponding to rate11,...,rate51,ratec1, rate10,...,rate50,ratec0 are all piecewise constant function taking the form $λ (t) = \sum_{j = 1}^{m} λ_{j} I (t_{j - 1} \leq t < t_{j})$ , where $λ_{1}, \dots, λ_{m}$ are the corresponding elements of the rates and $t_{0}, \dots, t_{m - 1}$ are the corresponding elements of tchange, $t_{m} = \infty$ . Note that all the rates must have the same tchange.

References

Luo, et al. (2017)

Examples

Run this code

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

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