ccsize: Power and sample size for case-cohort design

Description

The power of the test is according to $$\Phi\left(Z_\alpha+m^{1/2}\theta\sqrt{\frac{p_1p_2p_D}{q+(1-q)p_D}}\right)$$ where $\alpha$ is the significance level, $\theta$ is the log-hazard ratio for two groups, $p_j$, j=1, 2, are the proportion of the two groups in the population. $m$ is the total number of subjects in the subcohort, $p_D$ is the proportion of the failures in the full cohort, and $q$ is the sampling fraction of the subcohort.

Alternatively, the sample size required for the subcohort is $$m=nBp_D/(n-B(1-p_D))$$ where $B=(Z_{1-\alpha}+Z_\beta)^2/(\theta^2p_1p_2p_D)$, and $n$ is the size of cohort.

When infeaisble configurations are specified, a sample size of -999 is returned.

Usage

ccsize(n,q,pD,p1,alpha,theta,power=NULL,verbose=FALSE)

Arguments

the total number of subjects in the cohort

the sampling fraction of the subcohort

the proportion of the failures in the full cohort

proportions of the two groups (p2=1-p1)

alpha

significant level

theta

log-hazard ratio for two groups

power

if specified, the power for which sample size is calculated

verbose

error messages are explicitly printed out

Value

The returned value is a value indicating the power or required sample size.

References

Cai J, Zeng D. Sample size/power calculation for case-cohort studies. Biometrics 2004, 60:1015-1024

Examples

Run this code

# Table 1 of Cai & Zeng (2004).
outfile <- "table1.txt"
cat("n","pD","p1","theta","q","power
",file=outfile,sep="t")
alpha <- 0.05
n <- 1000
for(pD in c(0.10,0.05))
{
   for(p1 in c(0.3,0.5))
   {
      for(theta in c(0.5,1.0))
      {
         for(q in c(0.1,0.2))
         {
            power <- ccsize(n,q,pD,p1,alpha,theta)
            cat(n,"t",pD,"t",p1,"t",theta,"t",q,"t",signif(power,3),"",
                file=outfile,append=TRUE)
         }
      }
   }
}
n <- 5000
for(pD in c(0.05,0.01))
{
   for(p1 in c(0.3,0.5))
   {
      for(theta in c(0.5,1.0))
      {
         for(q in c(0.01,0.02))
         {
            power <- ccsize(n,q,pD,p1,alpha,theta)
            cat(n,"t",pD,"t",p1,"t",theta,"t",q,"t",signif(power,3),"",
                file=outfile,append=TRUE)
         }
      }
   }
}
table1<-read.table(outfile,header=TRUE,sep="t")
unlink(outfile)
# ARIC study
outfile <- "aric.txt"
n <- 15792
pD <- 0.03
p1 <- 0.25
alpha <- 0.05
theta <- c(1.35,1.40,1.45)
beta1 <- 0.8
s_nb <- c(1463,722,468)
cat("n","pD","p1","hr","q","power","ssize
",file=outfile,sep="t")
for(i in 1:3)
{
  q <- s_nb[i]/n
  power <- ccsize(n,q,pD,p1,alpha,log(theta[i]))
  ssize <- ccsize(n,q,pD,p1,alpha,log(theta[i]),beta1)
  cat(n,"t",pD,"t",p1,"t",theta[i],"t",q,"t",signif(power,3),"t",ssize,"",
      file=outfile,append=TRUE)
}
aric<-read.table(outfile,header=TRUE,sep="t")
unlink(outfile)
# EPIC study
outfile <- "epic.txt"
n <- 25000
alpha <- 0.00000005
power <- 0.8
s_pD <- c(0.3,0.2,0.1,0.05)
s_p1 <- seq(0.1,0.5,by=0.1)
s_hr <- seq(1.1,1.4,by=0.1)
cat("n","pD","p1","hr","alpha","ssize
",file=outfile,sep="t")
# direct calculation
for(pD in s_pD)
{
   for(p1 in s_p1)
   {
      for(hr in s_hr)
      {
         ssize <- ccsize(n,q,pD,p1,alpha,log(hr),power)
         if (ssize>0) cat(n,"t",pD,"t",p1,"t",hr,"t",alpha,"t",ssize,"",
                          file=outfile,append=TRUE)
      }
   }
}
epic<-read.table(outfile,header=TRUE,sep="t")
unlink(outfile)
# exhaustive search
outfile <- "search.txt"
s_q <- seq(0.01,0.5,by=0.01)
cat("n","pD","p1","hr","nq","alpha","power
",file=outfile,sep="t")
for(pD in s_pD)
{
   for(p1 in s_p1)
   {
      for(hr in s_hr)
      {
         for(q in s_q)
         {
            power <- ccsize(n,q,pD,p1,alpha,log(hr))
            cat(n,"t",pD,"t",p1,"t",hr,"t",q*n,"t",alpha,"t",power,"",
                file=outfile,append=TRUE)
         }
      }
   }
}
search<-read.table(outfile,header=TRUE,sep="t")
unlink(outfile)