AsympDiscSurv {SurvDisc}

Asymptotic Estimate of Mean and Variance of Log-hazard Ratio for Discrete Time Survival

Description

calculates the expected estimated log-hazard ratio and the estimated variance for large sample sizes when there are two groups with possibly non-proportional hazards and possible unequal randomization and censoring distributions.

Usage

AsympDiscSurv(h0,h1,p0,p1,method=c("efron","breslow","PrenticeGloeckler"),tol=1E-12)

Arguments

h0

vector of hazard rates in the control group

h1

vector of hazard rates in the treatment group

p0

vector of probabilities of being in the risk set and in the control group. See Details section below.

p1

vector of probabilities of being in the risk set and in the treatment group. See Details section below.

method

method for handling ties.

tol

a positive scalar giving the tolerance at which the maximum absolute value of the gradient is considered close enough to 0 to stop the algorithm.

Details

This calculates the asymptotic mean of the coefficient estimated by a proportional hazards regression model between two groups.

If there are r intervals, the vectors need only be of length r-1 since all subjects reaching the final interval will be assumed to have an event at some time in the last interval.

p0 and p1 are not the survival curves because they also include information about the allocation ratio between groups and the censoring distribution. The j^th element of p0 is the probability of being assigned to the control group and being at risk at time time[j]. p0+p1 is always less than or equal to 1 and should be close to 1 at the first time point and decreasing with time. Note that subjects censored at time[j] are not in the risk set, only subjects who have an event at this time or later or who are censored later. This definition of censoring time is the definition used in the reference and may be different than used in other places. Add 1 to all censored times if desired to force censoring to conform with the more standard ways. With equal allocation and no censoring, then p0[1]=p1[1]=0.5.

Value

A list which contains:

coefficients

the estimated coefficient (log-hazard ratio)

varn

the asymptotic variance multiplied by n where n is the total sample size combined in both groups

Author(s)

John Lawrence,[e-mail]

See Also

LongToSurv

Examples

set.seed(1234)
nsim=1
n=250
k=50
trt=c(rep(0,n),rep(1,n))
betaef=rep(0,nsim)
varef=betaef
betapg=betaef
varpg=betaef
m1=3.05
for (i in 1:nsim){
  x=rexp(2*n,1)
  x[(n+1):(2*n)]=x[(n+1):(2*n)]/2
  x=ceiling(x*(k-1)/m1)
  x=pmin(x,k)
  cens=rbinom(2*n,1,0.9)
  pg1=PrenticeGloeckler.test(x,cens,trt,k)
  betapg[i]=pg1$coefficient
  varpg[i]=(pg1$coefficient/pg1$wald.test)^2
  efron=survival::coxph(survival::Surv(x,cens)~trt,ties="efron")
  betaef[i]=efron$coef
  varef[i]=efron$var}

h0=0.9*(exp(-c(0:(k-2))*m1/(k-1))-exp(-c(1:(k-1))*m1/(k-1)))
h0=h0/(h0+exp(-c(1:(k-1))*m1/(k-1)))
p0=exp(-c(0:(k-1))*m1/(k-1))
p0=(p0[1:(k-1)]*0.9+p0[2:k]*0.1)/2
h1=0.9*(exp(-c(0:(k-2))*2*m1/(k-1))-exp(-c(1:(k-1))*2*m1/(k-1)))
h1=h1/(h1+exp(-c(1:(k-1))*2*m1/(k-1)))
p1=exp(-2*c(0:(k-1))*m1/(k-1))
p1=(p1[1:(k-1)]*0.9+p1[2:k]*0.1)/2

fa=AsympDiscSurv(h0=h0, h1=h1,p0=p0,p1=p1)
c(fa$estimate,fa$var/(2*n))
c(mean(betaef),var(betaef),mean(varef))