ccsize {gap} | R Documentation

## Power and sample size for case-cohort design

### Description

The power of the test is according to

Phi(Z_alpha+m^0.5*theta*sqrt(p_1p_2p_D/q+(1-q)p_D))

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

`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)
`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

### Note

Programmed for EPIC study

### Author(s)

Jing Hua Zhao

### 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)

[Package gap version 1.2.1 Index]