pwecxpwuforvar {PWEALL} | R Documentation |
calculate the utility function used for varaince calculation
Description
This is a utility function to calculate the overall variance accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.
Usage
pwecxpwuforvar(tfix=10,t=seq(0,10,by=0.5),taur=5,u=c(1/taur,1/taur),ut=c(taur/2,taur),
rate1=c(1,0.5),rate2=rate1,rate3=c(0.7,0.4),rate4=rate2,rate5=rate2,ratec=c(0.5,0.6),
tchange=c(0,1),type=1,rp2=0.5,eps=1.0e-2)
Arguments
tfix |
The upper point where the integral is computed. |
t |
A vector of lower bounds where the integral is computed. |
taur |
Recruitment time |
u |
Piecewise constant recuitment rate |
ut |
Recruitment intervals |
rate1 |
Hazard before crossover |
rate2 |
Hazard after crossover |
rate3 |
Hazard for time to crossover |
rate4 |
Hazard after crossover for complex case |
rate5 |
Hazard after crossover for complex case |
ratec |
Hazard for time to censoring |
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 |
type |
Type of crossover |
rp2 |
re-randomization prob |
eps |
A small number representing the error tolerance when calculating the utility function
with |
Details
This is to calculate the function
B_l(t,s)=\int_0^s x^l G_E(t-x)\widetilde{f}(x)S_C(x)dx,
where G_E
is the accrual function defined by taur
, u
and ut
, S_C
is the piecewise exponential survival function of the censoring time, defined by tchange
and ratec
, and \widetilde{f}
is the density for the event distribution subject to crossover defined by tchange
, rate1
to rate5
and type
. This function is useful when calculating the overall varaince and covariance.
Value
f0 |
the integral when |
f1 |
the integral when |
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)
getf<-pwecxpwuforvar(tfix=3,t=seq(0,3,by=1),taur=taur,u=u,ut=ut,
rate1=r11,rate2=r21,rate3=r31,rate4=r41,rate5=r51,ratec=rc1,
tchange=c(0,1),type=1,eps=1.0e-2)
getf