# lmmpower: Sample size calculations for linear mixed models of rate of... In longpower: Sample Size Calculations for Longitudinal Data

## Description

These functions compute sample size for linear mixed models based on the formula due to Diggle (2002) or Liu and Liang (1997). These formulae are expressed in terms of marginal model or Generalized Estimating Equations (GEE) parameters. These functions translate pilot mixed effect model parameters (e.g. random intercept and/or slope, fixed effects, etc.) into marginal model parameters so that either formula can be applied to equivalent affect. Pilot estimates are assumed to be from an appropriate "placebo" group and the parameter of interest is assumed to be the rate of change over time of the outcome.

## Usage

 ```1 2 3 4 5 6 7 8``` ```## S3 method for class 'double' lmmpower(object = NULL, n = NULL, parameter = 2, pct.change = NULL, delta = NULL, t = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "one.sided"), beta = NULL, beta.CI = NULL, delta.CI = NULL, sig2.i = NULL, sig2.s = NULL, sig2.e = NULL, cov.s.i = NULL, R = NULL, method = c("edland", "diggle", "liuliang"), tol = .Machine\$double.eps^2, ...) ```

## Arguments

 `object` an object returned by lme4 `n` sample size per group of a mixed-effects model object to placebo data assumed to have either a random intercept, or a random intercept and random effect for time (slope); and fixed effect representing the rate of change in a placebo group. `parameter` the name or position of the rate of change parameter of interest, e.g. (`"time"`, `"t"`, or `2` if it is the second specified fixed effect). `pct.change` the percent change in the pilot estimate of the parameter of interest (`beta`, the placebo/null effect) `delta` the change in the pilot estimate of the parameter of interest, computed from `pct.change` if left missing. `t` vector of time points `sig.level` Type I error `power` power `alternative` `"two.sided"` or `"one.sided"` `beta` pilot estimate of the placebo effect (slope or rate of change in the outcome) `beta.CI` 95% confidence limits of the pilot estimate of beta `delta.CI` 95% confidence limits of the effect size `sig2.i` pilot estimate of variance of random intercept `sig2.s` pilot estimate of variance of random slope `sig2.e` pilot estimate of residual variance `cov.s.i` pilot estimate of covariance of random slope and intercept `R` pilot estimate of a marginal model working correlation matrix `method` the formula to use. Defaults to `"diggle"` for Diggle et al (2002). Alternatively `"liuliang"` can be selected for Liu & Liang (1997). `tol` numerical tolerance used in root finding. `...` other arguments

## Details

Any parameters not explicitly stated are extracted from the fitted `object`.

## Value

An object of class `power.htest` giving the calculated sample size, N, per group and other parameters.

## Author(s)

Michael C. Donohue

## References

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

Liu, G., and Liang, K. Y. (1997) Sample size calculations for studies with correlated observations. Biometrics, 53(3), 937-47.

`liu.liang.linear.power` `diggle.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 27 28 29 30 31 32``` ```## Not run: browseVignettes(package = "longpower") ## End(Not run) lmmpower(delta=1.5, t = seq(0,1.5,0.25), sig2.i = 55, sig2.s = 24, sig2.e = 10, cov.s.i=0.8*sqrt(55)*sqrt(24), power = 0.80) lmmpower(n=208, t = seq(0,1.5,0.25), sig2.i = 55, sig2.s = 24, sig2.e = 10, cov.s.i=0.8*sqrt(55)*sqrt(24), power = 0.80) lmmpower(beta = 5, pct.change = 0.30, t = seq(0,1.5,0.25), sig2.i = 55, sig2.s = 24, sig2.e = 10, cov.s.i=0.8*sqrt(55)*sqrt(24), power = 0.80) ## Not run: library(lme4) fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy) lmmpower(fm1, pct.change = 0.30, t = seq(0,9,1), power = 0.80) library(nlme) fm2 <- lme(Reaction ~ Days, random=~Days|Subject, sleepstudy) lmmpower(fm2, pct.change = 0.30, t = seq(0,9,1), power = 0.80) # random intercept only fm3 <- lme(Reaction ~ Days, random=~1|Subject, sleepstudy) lmmpower(fm3, pct.change = 0.30, t = seq(0,9,1), power = 0.80) library(gee) fm4 <- gee(Reaction ~ Days, id = Subject, data = sleepstudy, corstr = "exchangeable") lmmpower(fm4, pct.change = 0.30, t = seq(0,9,1), power = 0.80) ## End(Not run) ```