| ssLong.multiTime {powerMediation} | R Documentation |
Sample size calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with more than 2 time points
Description
Sample size calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with more than 2 time points.
Usage
ssLong.multiTime(es, power, nn, sx2, rho = 0.5, alpha = 0.05)
Arguments
es |
effect size |
power |
power |
nn |
number of observations per subject |
sx2 |
within subject variance |
rho |
within subject correlation |
alpha |
type I error rate |
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 sample size calculation formula is (Equation on page 30 of Diggle et al. (1994)):
m=\frac{2\left(Z_{1-\alpha}+z_{power}\right)^2 \left(1-\rho\right)}{
nn s_x^2 es^2}
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.
Value
subject per group
Note
The test is a two-sided test. For one-sided tests, please double the
significance level. For example, you can set alpha=0.10
to obtain one-sided test at 5% significance level.
Author(s)
Weiliang Qiu stwxq@channing.harvard.edu
References
Diggle PJ, Liang KY, and Zeger SL (1994). Analysis of Longitundinal Data. page 30. Clarendon Press, Oxford
See Also
Examples
# subject per group = 196
ssLong.multiTime(es=0.5/10, power=0.8, nn=3, sx2=4.22, rho = 0.5, alpha=0.05)