The quasiparticle approximation and corrections beyond it are derived from expansion in the spirit of the virial corrections. This way, the Boltzmann equation for electrons in semiconductors is recovered from the nonequilibrium Green's functions without unjustified neglect of the former theory. The present approach gives higher-order contributions to the scattering rates and provides observables as functionals of the quasiparticle distribution. The application scheme is of the same simplicity as the one based on the quasiparticle approximation. Five applications to phenomena beyond the scope of the quasiparticle approximation are presented: two-phonon scattering rates, compensation of wave-function remormalization for isotropic elastic scattering, quasiparticle backflow, backflow current of waves, and discussion of the collisional broadening.