powerLong.multiTime: Power calculation for testing if mean changes for 2 groups are the
same or not for longitudinal study with more than 2 time points
Description
Power calculation for testing if mean changes for 2 groups are the
same or not for longitudinal study with more than 2 time points.
Usage
powerLong.multiTime(es, m, nn, sx2, rho = 0.5, alpha = 0.05)
Arguments
es
effect size
m
number of subjects
nn
number of observations per subject
sx2
within subject variance
rho
within subject correlation
alpha
type I error rate
Value
power
Details
We are interested in comparing the slopes of the 2 groups $A$ and $B$:
$$\beta_{1A} = \beta_{1B}$$
where
$$Y_{ijA}=\beta_{0A}+\beta_{1A} x_{jA} + \epsilon_{ijA}, j=1, \ldots, nn; i=1, \ldots, m$$
and
$$Y_{ijB}=\beta_{0B}+\beta_{1B} x_{jB} + \epsilon_{ijB}, j=1, \ldots, nn; i=1, \ldots, m$$
The power calculation formula is (Equation on page 30 of Diggle et al. (1994)):
$$power=\Phi\left[
-z_{1-\alpha} + \sqrt{\frac{m nn s_x^2 es^2}{2(1-\rho)}}
\right]$$
where $es=d/\sigma$, $d$ is the meaninful differnce of interest,
$sigma^2$ is the variance of the random error,
$\rho$ is the within-subject correlation, and
$s_x^2$ is the within-subject variance.
References
Diggle PJ, Liang KY, and Zeger SL (1994).
Analysis of Longitundinal Data. page 30.
Clarendon Press, Oxford