The ability to predict the pressure dependence of chemical reaction rates would be a great boon to kinetic modeling of processes such as combustion and atmospheric chemistry. This pressure dependence is intimately related to the rate of collision-induced transitions in energy E and angular momentum J. We present a scheme for predicting this pressure dependence based on coupling trajectory-based determinations of moments of the E, J-resolved collisional transfer rates with the two-dimensional master equation. This completely a priori procedure provides a means for proceeding beyond the empiricism of prior work. The requisite microcanonical dissociation rates are obtained from ab initio transition state theory. Predictions for the CH4 = CH3 + H and C2H3 = C2H2 + H reaction systems are in excellent agreement with experiment.