pwepower: Calculating the powers of various the test statistics for...

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

Calculating the powers of various the test statistics for superiority trials

Description

This will calculate the powers for the test statistics accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

pwepower(t=seq(0.1,3,by=0.5),alpha=0.05,twosided=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-4,iterbeta=25,
             n=1000)

Arguments

t	a vector of time points at which power is calculated, t must be positive
alpha	type-1 error rate
twosided	twosided test or not
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 for the treatment group
rp20	re-randomization prob for 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

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

power

powers for various test statistics. Columns 2-6 are for log-rank and columns 12-16 are for cox model. Column 2 is the exact power based on log-rank/score test; column 3 uses variance approximated by Fisher information, i.e. Lakatos's method; column 4 uses approximated Fisher info by number of events i.e. 4/D(t); column 5 uses approximated Fisher info by assuming exp dist. 1/D1(t)+1/D0(t); column 6 uses Fisher information at beta. Column 12 is the exact power based on Wald test; column 13 uses variance approximated by Fisher information; column 14 uses approximated Fisher info by number of events i.e. 4/D(t); column 15 uses approximated Fisher info by assuming exp dist. 1/D1(t)+1/D0(t); column 16 uses Fisher information at beta=0.

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

pwe,rpwe,qpwe,ovbeta,innervar, pwepowerni,pwepowereq

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[,c(2:4,12:14)])

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