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 power calculation formula is (Equation on page 30 of Diggle et al. (1994)):
$$
power=\Phi\left[
-z_{1-\alpha} + \sqrt{\frac{m nn s_x^2 es^2}{2(1-\rho)}}
\right]
$$
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.