In this work we explore the effects of higher twist power corrections on the deeply virtual Compton scattering process. The calculation of the helicity amplitudes for all possible polarization combinations is performed within the framework of QCD operator product expansion. As a result the known accuracy of the amplitudes is improved to include the (kinematic) twist-4 contributions. For the most part the analysis focuses on spin-1/2 targets, the answers for scalar targets conveniently emerge as a byproduct. We investigate the analytical structure of these corrections and prove consistency with QCD factorization. We give an estimation of the numerical impact of the sub-leading twist contributions for proton targets with the help of a phenomenological model for the nonperturbative proton generalized parton distributions. We compare different twist approximations and relate predictions for physical observables to experiments performed by the Hall A, CLAS, HERMES, H1 and ZEUS collaborations. The estimate also includes a numerical study for planned COMPASS-II runs. Throughout the analysis special emphasis is put on the convention dependence induced by finite twist truncation of scattering amplitudes.