# edland.linear.power: Linear mixed model sample size calculations. In longpower: Sample Size Calculations for Longitudinal Data

## Description

This function performs the sample size calculation for a linear mixed model with random slope.

## Usage

 ```1 2 3``` ```edland.linear.power(n = NULL, delta = NULL, t = NULL, sig2.s = 0, sig2.e = 1, 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 `sig2.s` variance of random slope `sig2.e` residual variance `sig.level` type one error `power` power `alternative` one- or two-sided test `tol` numerical tolerance used in root finding.

## Details

This function will also provide sample size estimates for linear mixed models with random intercept only simply by setting `sig2.s = 0`

## 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

Edland, S.D. (2009) Which MRI measure is best for Alzheimer's disease prevention trials: Statistical considerations of power and sample size. Joint Stat Meeting Proceedings. 4996-4999.

`lmmpower`, `diggle.linear.power`, `liu.liang.linear.power`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```## 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(edland.linear.power( delta=0.5, t=t, sig2.e=sigma2*(1-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 t = seq(0,1.5,0.25) n = length(t) edland.linear.power(delta=1.5, t=t, sig2.s = 24, sig2.e = 10, sig.level=0.05, power = 0.80) ```