overallcov {PWEALL} | R Documentation |
calculate the overall covariance
Description
This will calculate the overall covariance accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.
Usage
overallcov(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=rate21,ratec1=c(0.5,0.6),
rate10=c(1,0.7),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 |
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
with |
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
covbeta |
The covariance the score functions |
covbeta1 |
The first part of the cov |
covbeta2 |
The second part of the cov |
covbeta3 |
The third part of the cov |
covbeta4 |
The fourth part of the cov |
EA1 |
The first score function |
EA2 |
The second score function |
Note
Version 1.0 (7/19/2016)
Author(s)
Xiaodong Luo
References
Luo, et al. (2017)
See Also
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)
getcov<-overallcov(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)
getcov$covbeta