Current methods of power and sample size calculations for the design of longitudinal studies to evaluate mediation effects are mostly based on simulation studies and do not provide closed-form formulae. A further challenge due to the longitudinal study design is the consideration of missing data, which almost always occur in longitudinal studies due to staggered entry or drop out. In this article, we consider the product of coefficients as a measure for the longitudinal mediation effect and evaluate three methods for testing the hypothesis on the longitudinal mediation effect: the joint significant test, the normal approximation and the test of b methods. Formulae for power and sample size calculations are provided under each method while taking into account missing data. Performance of the three methods under limited sample size are examined using simulation studies. An example from the Einstein aging study is provided to illustrate the methods.