overallcovp1: calculate the first part of the overall covariance

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

calculate the first part of the overall covariance

Description

This will calculate the first part of the overall covariance accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

overallcovp1(tfix=2.0,tfix0=1.0,taur=5,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=rate51,ratec1=c(0.5,0.6),
                    rate10=rate11,rate20=rate10,rate30=rate31,
                    rate40=rate20,rate50=rate20,ratec0=ratec1,
                    tchange=c(0,1),type1=1,type0=1,
                    rp21=0.5,rp20=0.5,
                    eps=1.0e-2,veps=1.0e-2,beta=0,beta0=0)

Arguments

tfix	The upper point where the overall covariance is computed.
tfix0	The lower point where the overall covariance is computed.
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	A small number representing the error tolerance when calculating the utility function \Phi_l(x)=\frac{\int_0^x s^l e^{-s}ds}{x^{l+1}} with l=0,1,2.
veps	A small number representing the error tolerance when calculating the Fisher information.
beta	The value at which the covaraince is computed, upper bound
beta0	The value at which the covaraince is computed, lower bound

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

covbeta1	The first part of the covariance
EA1	The first score function

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

pwe,rpwe,qpwe,ovbeta,innervar

Examples

taur<-1.2
u<-c(1/taur,1/taur)
ut<-c(taur/2,taur)
r11<-c(1,0.5)
r21<-c(0.5,0.8)
r31<-c(0.7,0.4)
r41<-r51<-r21
rc1<-c(0.5,0.6)
r10<-c(1,0.7)
r20<-c(0.5,1)
r30<-c(0.3,0.4)
r40<-r50<-r20
rc0<-c(0.2,0.4)
getcov1<-overallcovp1(tfix=2.0,tfix0=1.0,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,
              eps=1.0e-2,veps=1.0e-2,beta=0,beta0=0)
getcov1$covbeta1

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