  We study the contributions from the connected and disconnected contraction
diagrams to the pion-kaon scattering amplitude within the framework of
SU$(4|1)$ partially-quenched chiral perturbation theory. Combining this with a
finite-volume analysis, we demonstrate that a lattice calculation of the easier
computable connected correlation functions is able to provide valuable
information of the noisier disconnected correlation functions, and may serve as
a theory guidance for the future refinement of the corresponding lattice
techniques.
