ccsize: Power and sample size for case-cohort design

In gap: Genetic Analysis Package

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 = TRUE, 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

a value indicating the power or required sample size.

Note

Programmed for EPIC study. keywords misc

Author(s)

Jing Hua Zhao

References

\insertRef

cai04gap

See Also

pbsize

Examples

## Not run: 
# Table 1 of Cai & Zeng (2004).
alpha <- 0.05
table1 <- rbind(
  transform(
    within(expand.grid(
      pD = c(0.10, 0.05),
      p1 = c(0.3, 0.5),
      theta = c(0.5, 1.0),
      q = c(0.1, 0.2)
    ), {
      n <- 1000
      power <- mapply(ccsize,
        n = n, q = q, pD = pD, p1 = p1, theta = theta,
        MoreArgs = list(alpha = alpha)
      )
    }),
    power = signif(power, 3)
  ),
  transform(
    within(expand.grid(
      pD = c(0.05, 0.01),
      p1 = c(0.3, 0.5),
      theta = c(0.5, 1.0),
      q = c(0.01, 0.02)
    ), {
      n <- 5000
      power <- mapply(ccsize,
        n = n, q = q, pD = pD, p1 = p1, theta = theta,
        MoreArgs = list(alpha = alpha)
      )
    }),
    power = signif(power, 3)
  )
)

# ARIC study
aric <- within(
  data.frame(
    n = 15792,
    pD = 0.03,
    p1 = 0.25,
    hr = c(1.35, 1.40, 1.45),
    q = c(1463, 722, 468) / 15792
  ), {
    alpha <- 0.05
    beta <- 0.2
    power <- mapply(ccsize,
      n = n, q = q, pD = pD, p1 = p1, theta = log(hr),
      MoreArgs = list(alpha = alpha)
    )
    ssize <- mapply(ccsize,
      n = n, q = q, pD = pD, p1 = p1, theta = log(hr),
      MoreArgs = list(alpha = alpha, beta = beta, power = FALSE)
    )
    power <- signif(power, 3)
  }
)

# EPIC study
epic <- within(
  expand.grid(
    pD = c(0.3, 0.2, 0.1, 0.05),
    p1 = seq(0.1, 0.5, by = 0.1),
    hr = seq(1.1, 1.4, by = 0.1)
  ), {
    n <- 25000
    q <- 0.1
    alpha <- 5e-8
    beta <- 0.2
    ssize <- mapply(ccsize,
      n = n, q = q, pD = pD, p1 = p1, theta = log(hr),
      MoreArgs = list(alpha = alpha, beta = beta, power = FALSE)
    )
  }
)
epic <- subset(epic, !is.na(ssize) & ssize > 0)

# exhaustive search
search <- within(
  expand.grid(
    pD = c(0.3, 0.2, 0.1, 0.05),
    p1 = seq(0.1, 0.5, by = 0.1),
    hr = seq(1.1, 1.4, by = 0.1),
    q  = seq(0.01, 0.5, by = 0.01)
  ), {
    n <- 25000
    alpha <- 5e-8
    power <- mapply(ccsize,
      n = n, q = q, pD = pD, p1 = p1, theta = log(hr),
      MoreArgs = list(alpha = alpha)
    )
    nq <- n * q
  }
)

## End(Not run)

gap documentation built on May 28, 2026, 9:07 a.m.