| ssLong {powerMediation} | R Documentation |
Sample size calculation for longitudinal study with 2 time point
Description
Sample size calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with 2 time point.
Usage
ssLong(es,
rho = 0.5,
alpha = 0.05,
power = 0.8)
Arguments
es |
effect size of the difference of mean change. |
rho |
correlation coefficient between baseline and follow-up values within a treatment group. |
alpha |
Type I error rate. |
power |
power for testing for difference of mean changes. |
Details
The sample size formula is based on Equation 8.30 on page 335 of Rosner (2006).
n=\frac{2\sigma_d^2 (Z_{1-\alpha/2} + Z_{power})^2}{\delta^2}
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
n=\frac{4(1-\rho)(Z_{1-\alpha/2}+Z_{\beta})^2}{d^2}
where d=\delta/\sigma.
Value
required sample size 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
Rosner, B. Fundamentals of Biostatistics. Sixth edition. Thomson Brooks/Cole. 2006.
See Also
ssLongFull, powerLong,
powerLongFull.
Examples
# Example 8.33 on page 336 of Rosner (2006)
# n=85
ssLong(es=5/15, rho=0.7, alpha=0.05, power=0.8)