approx.I: Approximate information for an arbitrary survival function

In lilywang1988/IAfrac: Tools for weighted log-rank tests

Description

An approximation alternative to the regular prediction of the information/covariance based on the assumed survival functions.

Usage

approx.I(
  t.star,
  p,
  S1 = function(x) {     1 },
  S0 = function(x) {     1 },
  func = function(x) {     1 },
  n.length = 1e+06
)

Arguments

t.star	The ending time of the cumulative informaiton or covariance prediciton.
p	Treatment assignment probability.
S1	Survival function for the treatment group.
S0	Survival function for the control gorup.
func	The integrand function.
n.length	The number of intervals spitted to obtain the approximate integration.

Author(s)

Lili Wang

References

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.

Examples

# Examples for approx.I
eps<-2 # delayed effect
p<-0.5 #treatment assignment
tau<-18 # end of the study
R<-14 # accrual period [0,R]
lambda<-log(2)/6 # control group risk hazard
theta<-0.7 # hazard ratio
lambda.trt<- lambda*theta
rho<- 0 # parameter for the weights
gamma<-1 #parameter for the weights
S1<-function(x){
  ifelse(x>eps,exp(-theta*lambda*x)*getc(theta,lambda,eps),exp(-lambda*x))
  }
  S0<-function(x){
    exp(-lambda*x)
    }
    S_pool<-function(x){
      p*S1(x)+(1-p)*S0(x)
      }
      func<-function(x){
        min((tau-x)/R,1)*(S_pool(x)^rho*(1-S_pool(x))^gamma)^2
        }
 approx.I(t.star=tau,p,S1=S1,S0=S0,fun=func,n.length=1e6)
 I.1(rho,gamma,lambda,theta,eps,R,p,tau)
 # Change the cumulative information up to 10 instead of taus
 func2<-function(x){
   min((10-x)/R,1)*(S_pool(x)^rho*(1-S_pool(x))^gamma)^2
   }
   approx.I(t.star=10,p,S1=S1,S0=S0,fun=func2,n.length=1e6)
   I.1(rho,gamma,lambda,theta,eps,R,p,t.star=10)
   # Covariance approximation for two weights: 1 and G(0,1)
   rho1=rho2=0
   gamma1=0
   gamma2=1
   func3<-function(x){
  min((10-x)/R,1)*(S_pool(x)^rho1*(1-S_pool(x))^gamma1)*(S_pool(x)^rho2*(1-S_pool(x))^gamma2)
  }
  approx.I(t.star=10,p,S1=S1,S0=S0,fun=func3,n.length=1e6)
  I.1.cov(rho1,gamma1,rho2,gamma2,lambda,theta,eps,R,p,t.star=10)

lilywang1988/IAfrac documentation built on March 11, 2021, 11:53 a.m.