absolute difference of the mean changes between the two groups: $\delta=|\mu_1 - \mu_2|$ where
$\mu_1$ is the mean change over time $t$ in group 1,
$\mu_2$ is the mean change over time $t$ in group 2.
sigma1
the variance of baseline values within a treatment group
sigma2
the variance of follow-up values within a treatment group
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 $\mu_1 = \mu_2$.
References
Rosner, B.
Fundamentals of Biostatistics. Sixth edition. Thomson Brooks/Cole. 2006.