pwepower: Calculating the powers of various the test statistics for... In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

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

 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)

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 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.

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)

Xiaodong Luo

References

Luo, et al. (2017)