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Last data update: 2014.03.03

R: Sample size calculations for difference in slopes between two...

diggle.linear.power

R Documentation

Sample size calculations for difference in slopes between two groups.

Description

This function performs the sample size calculation for difference in slopes between two groups. See Diggle et al (2002) for parameter definitions and other details.

Usage

diggle.linear.power(n = NULL, delta = NULL, t = NULL, sigma2 = 1,
  R = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided",
  "one.sided"), tol = .Machine$double.eps^2)

Arguments

`n`	sample size per group
`delta`	group difference in slopes
`t`	the observation times
`sigma2`	the residual variance
`R`	the working correlation matrix (or variance-covariance matrix if `sigma2` is 1). If `R` is a scalar, an exchangeable working correlation matrix will be assumed.
`sig.level`	Type I error
`power`	power
`alternative`	one- or two-sided test
`tol`	numerical tolerance used in root finding.

Details

See Diggle, et al (1997) and package vignette for more details.

Value

The number of subject required per arm to attain the specified power given sig.level and the other parameter estimates.

Author(s)

Michael C. Donohue, Steven D. Edland

References

Diggle P.J., Heagerty P.J., Liang K., Zeger S.L. (2002) Analysis of longitudinal data. Second Edition. Oxford Statistical Science Series.

Examples


## Not run: 
browseVignettes(package = "longpower")

## End(Not run)

# Reproduces the table on page 29 of Diggle et al
n = 3
t = c(0,2,5)
rho = c(0.2, 0.5, 0.8)
sigma2 = c(100, 200, 300)
tab = outer(rho, sigma2, 
      Vectorize(function(rho, sigma2){
        ceiling(diggle.linear.power(
          delta=0.5,
          t=t,
          sigma2=sigma2,
          R=rho,
          alternative="one.sided",
          power = 0.80)$n)}))
colnames(tab) = paste("sigma2 =", sigma2)
rownames(tab) = paste("rho =", rho)
tab

# An Alzheimer's Disease example using ADAS-cog pilot estimates
# var of random intercept
sig2.i = 55
# var of random slope
sig2.s = 24
# residual var
sig2.e = 10
# covariance of slope and intercep
cov.s.i <- 0.8*sqrt(sig2.i)*sqrt(sig2.s)

cov.t <- function(t1, t2, sig2.i, sig2.s, cov.s.i){
        sig2.i + t1*t2*sig2.s + (t1+t2)*cov.s.i 
}

t = seq(0,1.5,0.25)
n = length(t)
R = outer(t, t, function(x,y){cov.t(x,y, sig2.i, sig2.s, cov.s.i)})
R = R + diag(sig2.e, n, n)

diggle.linear.power(d=1.5, t=t, R=R, sig.level=0.05, power=0.80)