Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

1 2 3 4 5 6 7 8 9 | ```
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)
``` |

`t` |
a vector of time points at which power is calculated, |

`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 |

`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 |

The hazard functions corresponding to `rate11`

,...,`rate51`

,`ratec1`

, `rate10`

,...,`rate50`

,`ratec0`

are all piecewise constant function taking the form *λ(t)=∑_{j=1}^m λ_j I(t_{j-1}≤ t<t_j)*, where *λ_1,…,λ_m* are the corresponding elements of the rates and *t_0,…,t_{m-1}* are the corresponding elements of tchange, *t_m=∞*. Note that all the rates must have the same `tchange`

.

`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. |

Version 1.0 (7/19/2016)

Xiaodong Luo

Luo, et al. (2017)

`pwe`

,`rpwe`

,`qpwe`

,`ovbeta`

,`innervar`

,
`pwepowerni`

,`pwepowereq`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
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)])
``` |

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