The screening effect is introduced into the recently presented perturbed hard-sphere-chain (PHSC) equation of state for copolymer systems. Using reactivity ratios of copolymerization kinetics, the model first computes the number of specific monomer sequences in the copolymer consisting of monomers A and B. Some of the AB and BA monomer sequences (i.e., diads) are then replaced by BE sequences to represent the screening effect of segment B on segment A in AB and BA sequences. The essential characteristic of the screening effect is the assumption that the solution properties of a copolymer correspond to those of another copolymer whose composition differs from that of the true copolymer. The screening effect theory is used to calculate miscibility maps for several poly(styrene-co-methyl methacrylate) random copolymers that exhibit lower critical solution temperature behavior and significant deviation from the classical Flory-Huggins model. For a fixed temperature, there is good agreement between the theoretical miscibility map and experiment. To represent the temperature dependence of the miscibility map with temperature-independent parameters, it is necessary to consider diad interactions by modeling the copolymer consisting of monomers A and B as a terpolymer consisting of monomers A, B, and C that represent AA, BE, and AB and BA diads, respectively, of the copolymer.