diggle.linear.power {longpower}

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) and package vignette for more 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.

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.

See Also

lmmpower, diggle.linear.power

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[1])}))
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)