ccsize {gap}

Power and sample size for case-cohort design

Description

Power and sample size for case-cohort design

Usage

ccsize(n, q, pD, p1, theta, alpha, beta = 0.2, power = FALSE, verbose = FALSE)

Arguments

n

the total number of subjects in the cohort.

q

the sampling fraction of the subcohort.

pD

the proportion of the failures in the full cohort.

p1

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

theta

log-hazard ratio for two groups.

alpha

type I error – significant level.

beta

type II error.

power

if specified, the power for which sample size is calculated.

verbose

error messages are explicitly printed out.

Details

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.

Value

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

Note

Programmed for EPIC study. keywords misc

Author(s)

Jing Hua Zhao

References

Cai J, Zeng D (2004). “Sample size/power calculation for case-cohort studies.” Biometrics, 60(4), 1015-24. ISSN 0006-341X (Print) 0006-341x, doi:10.1111/j.0006-341X.2004.00257.x.

See Also

pbsize

Examples

## Not run: 
# Table 1 of Cai & Zeng (2004).
outfile <- "table1.txt"
cat("n","pD","p1","theta","q","power\n",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),"\n",
                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),"\n",
                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\n",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,"\n",
      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\n",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,"\n",
                          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\n",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,"\n",
                file=outfile,append=TRUE)
         }
      }
   }
}
search<-read.table(outfile,header=TRUE,sep="\t")
unlink(outfile)

## End(Not run)