ccsize {gap} | R Documentation |
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.
ccsize(n,q,pD,p1,alpha=0.05,theta,power=NULL)
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 |
The returned value is a value indicating the power or required sample size.
Cai J, Zeng D. Sample size/power calculation for case-cohort studies. Biometrics 2004, 60:1015-1024
Programmed for EPIC study
Jing Hua Zhao
# Table 1 of Cai & Zeng (2004). options(echo=FALSE) cat("n\tpD\tp1\ttheta\tq\tpower\n") 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,digits=3),"\n") } } } } 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,digits=3),"\n") } } } } options(echo=TRUE) # ARIC study options(echo=FALSE) n <- 15792 pD <- 0.03 p1 <- 0.25 alpha <- 0.05 theta <- c(1.35,1.40,1.45) power <- 0.8 s_nb <- c(1463,722,468) 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]),power) cat(n,"\t",pD,"\t",p1,"\t",theta[i],"\t",q,"\t",signif(power,digits=3),"\t",ceiling(ssize),"\n") } options(echo=TRUE) # EPIC study? options(echo=FALSE) n <- 25000 alpha <- 0.00000001 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_theta <- seq(1.2,1.8,by=0.2) s_q <- seq(0.01,0.5,by=0.01) # direct calculation for(pD in s_pD) { for(p1 in s_p1) { for(theta in s_theta) { ssize <- ccsize(n,q,pD,p1,alpha,log(theta),power) if(ssize>0) cat(n,"\t",pD,"\t",p1,"\t",theta,"\t",ssize,"\n") } } } # exhaustive search nrows <- length(s_pD) * length(s_p1) * length(s_theta) * length(s_q) powtable <- matrix(rep(0,nrows * 5),ncol=5,byrow=TRUE) ijkl <- 0 for(pD in s_pD) { for(p1 in s_p1) { for(theta in s_theta) { for(q in s_q) { ijkl <- ijkl + 1 power <- ccsize(n,q,pD,p1,alpha,log(theta)) powtable[ijkl,] <- c(pD,p1,theta,q*n,power) cat(n,"\t",pD,"\t",p1,"\t",theta,"\t",q*n,"\t",signif(power,digits=3),"\n") } } } } options(echo=TRUE)