WLR.test.cov: Estimate the covariance and correlation between two arbitrary...
In lilywang1988/IAfrac: Tools for weighted log-rank tests

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

View source: R/Hasegawa2016.R

These two functions estimate the covariance and correlations between the two arbitrary weight functions, which are not necessary to be Fleming-Harrington family.

WLR.test.cov(
  survival,
  delta,
  trt,
  w1 = function(v, ...) {     1 },
  w2 = function(v, ...) {     1 }
)

WLR.test.cor(
  survival,
  delta,
  trt,
  w1 = function(v, ...) {     1 },
  w2 = function(v, ...) {     1 }
)

`survival`	The time to event or censoring, not that, it's the follow-up time after entoring, you may also consider as the total at-risk time.
`delta`	The event indicator, with 1 indicating observed events, and 0 indicating censoring.
`trt`	The treatment assignment indicator, with 1 indicating treatment group, and 0 as control group.
`w1`	It has the default function which will return standard log-rank test with weight 1 and thus the function will be reduced to a variance for log-rank tests, and correlation always equals 1. If the two weights are identical, `WLR.test.cov` is equivalent to the estimated variance, and `WLR.test.cor` is always equal to 1. The function can be any non-negative functions with a basic argument v as the input time vector, which are corresponding to the follow-up times. Optionally, there are two additional variables,follow-up time `survival` and event indicator `delta` to make the weights dependent on the survival functions (like the Fleming-Harrington family). It would be better if the function itself has `...` as the last argument, so that it can be robust to any misspecification of the variable names, and thus, it will just ignore the misspecified ones. Please refer to the examples to figure out how to define the Fleming-Harrington and any other weight functions.
`w2`	Same requirements as the other argument `w1`. Just not that if they are identical, `WLR.test.cov` returns the variance like `I.t`, and `WLR.test.cor` always returns 1.

Any two weight functions can be assigned to arguments w1 and w2. Two examples, one is Fleming-Harrington family and the other is not, are demonstrated in the examples section.

The two functions, WLR.test.cov returns the covariance, WLR.test.cor returns the correlation coefficient estimate solely based on the input data.

Lili Wang

Hasegawa, T. (2016). Group sequential monitoring based on the weighted log‐rank test statistic with the Fleming–Harrington class of weights in cancer vaccine studies. Pharmaceutical statistics, 15(5), 412-419.

cor.0,cor.1, I_t.

# install.packages("devtools")
# library(devtools)
# install_github("keaven/nphsim")
library(nphsim)

eps<-2 # delayed effect
p<-0.5 #treatment assignment
b<-30 # an intrinsic parameter to decide the number of intervals per time unit
tau<- 18 # end of the study
R<-14 # accrual period [0,R]
omega<- tau-R
lambda<-log(2)/6 # control group risk hazard
theta<-0.7 # hazard ratio
lambda.trt<- lambda*theta #hazard after the change point for the treatment arm
rho<- 0 # parameter for the weights
gamma<-1 #parameter for the weights
alpha<-0.025 #type 1 error
beta<-0.1 #type 2 error
# First we decide the sample size:
size_FH <- sample.size_FH(eps,p,b,tau,omega,lambda,lambda.trt,rho, gamma,alpha,beta)
n_FH <-size_FH$n
n_event_FH<-size_FH$n_event
d_fixed<-ceiling(-0.6*n_event_FH)
accrual.rt<-n_FH/R # the needed arrual rate
#Generate data accordingly, use eta=1e-5 to inhibit censoring
data_temp <- nphsim(nsim=1,lambdaC=lambda, lambdaE = c(lambda,lambda.trt),
                  ssC=ceiling(n_FH*(1-p)),intervals = c(eps),ssE=ceiling(n_FH*p),
                            gamma=accrual.rt, R=R, eta=1e-5, fixEnrollTime = TRUE)$simd
# Example 1 for WLR.test.cov and WLR.test.cor: Fleming-Harrington family Weights
# I will let w1 be the default 1
# define a WLRT for w2 accodring to the rho and gamma defined above.
w2<-function(...){survKM_minus(...)^rho*(1-survKM_minus(...))^gamma}
data_interim<-data.trim.d(d_fixed,data_temp)[[1]] #data trimmed at the interim stage, the second enry on the list is the interim time, refer to function data.trim.d for details.
data_final<-data.trim.d(n_event_FH,data_temp)[[1]] #data trimmed at the final stage
WLR.test.cov(survival=data_interim$survival,delta=data_interim$delta,trt=data_interim$trt,w2=w2)
WLR.test.cor(survival=data_interim$survival,delta=data_interim$delta,trt=data_interim$trt,w2=w2)

# The variance should be identical to the output from I_t and correlation is 1 if two weights are identical.
WLR.test.cov(survival=data_interim$survival,delta=data_interim$delta,trt=data_interim$trt,w1=w2,w2=w2)
I_t.2(data_interim,data_interim,rho,gamma)
WLR.test.cor(survival=data_interim$survival,delta=data_interim$delta,trt=data_interim$trt,w1=w2,w2=w2)

#Example 2 for WLR.test.cov and WLR.test.cor: any Weights
w2_2<-function(v,...){1-exp(-v*0.25)}
WLR.test.cov(survival=data_interim$survival,delta=data_interim$delta,trt=data_interim$trt,w2=w2_2)
WLR.test.cor(survival=data_interim$survival,delta=data_interim$delta,trt=data_interim$trt,w2=w2_2)