ssLong: 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.
Value
required sample size per group
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 $d=\delta/\sigma$.
References
Rosner, B.
Fundamentals of Biostatistics. Sixth edition. Thomson Brooks/Cole. 2006.