  We study the role of excited phonon populations in the relaxation rates of
nonequilibrium electrons using a nonequilibrium Green's function formalism. The
transient modifications in the phononic properties are accounted for by
self-consistently solving the Dyson equation for the electron and phonon
Green's functions. The pump induced changes manifest in both the electronic and
phononic spectral functions. We find that the excited phonon populations
suppress the decay rates of nonequilibrium electrons due to enhanced phonon
absorption. The increased phonon occupation also sets the nonequilibrium decay
rates and the equilibrium scattering rates apart. The decay rates are found to
be time-dependent, and this is illustrated in the experimentally observed
population decay of photoexcited $\mathrm{Bi}_{1.5}\mathrm{Sb}_{0.5}
\mathrm{Te}_{1.7}\mathrm{Se}_{1.3}$.
