A new approach is theoretically proposed to study the glass transition of active pharmaceutical ingredients and a glass-forming anisotropic molecular liquid at high pressures. We describe amorphous materials as a fluid of hard spheres. Effects of nearest neighbor interactions and cooperative motions of particles on glassy dynamics are quantified through a local and collective elastic barrier calculated using the elastically collective nonlinear Langevin equation theory. Inserting two barriers into Kramer's theory gives the structural relaxation time. Then, we formulate a new mapping based on the thermal expansion process under pressure to intercorrelate particle density, temperature, and pressure. This analysis allows us to determine the pressure and temperature dependence of a relaxation. From this, we estimate the effective elastic modulus of amorphous materials and capture the effects of conformation on the relaxation process. Remarkably, our theoretical results agree well with experiments.