| powerLong {powerMediation} | R Documentation |
Power calculation for longitudinal study with 2 time point
Description
Power calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with 2 time point.
Usage
powerLong(es,
n,
rho = 0.5,
alpha = 0.05)
Arguments
es |
effect size of the difference of mean change. |
n |
sample size per group. |
rho |
correlation coefficient between baseline and follow-up values within a treatment group. |
alpha |
Type I error rate. |
Details
The power formula is based on Equation 8.31 on page 336 of Rosner (2006).
power=\Phi\left(-Z_{1-\alpha/2}+\frac{\delta\sqrt{n}}{\sigma_d \sqrt{2}}\right)
where \sigma_d = \sigma_1^2+\sigma_2^2-2\rho\sigma_1\sigma_2, \delta=|\mu_1 - \mu_2|,
\mu_1 is the mean change over time t in group 1,
\mu_2 is the mean change over time t in group 2,
\sigma_1^2 is the variance of baseline values within a treatment group,
\sigma_2^2 is the variance of follow-up values within a treatment group,
\rho is the correlation coefficient between baseline and follow-up values within a treatment group,
and Z_u is the u-th percentile of the standard normal distribution.
We wish to test \mu_1 = \mu_2.
When \sigma_1=\sigma_2=\sigma, then formula reduces to
power=\Phi\left(-Z_{1-\alpha/2} + \frac{|d|\sqrt{n}}{2\sqrt{1-\rho}}\right)
where d=\delta/\sigma.
Value
power for testing for difference of mean changes.
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
Rosner, B. Fundamentals of Biostatistics. Sixth edition. Thomson Brooks/Cole. 2006.
See Also
ssLong, ssLongFull,
powerLongFull.
Examples
# Example 8.34 on page 336 of Rosner (2006)
# power=0.75
powerLong(es=5/15, n=75, rho=0.7, alpha=0.05)