Optical conductivity of an interacting polaron gas is calculated within an extended random phase approximation which takes into account mixing of collective excitations of the electron gas with LO phonons. This mixing is important for the optical response of strongly polar crystals where the static dielectric constant is rather high, as in the case of strontium titanate. The present calculation sheds light on unexplained features of experimentally observed optical conductivity spectra in $n$-doped SrTiO$_{3}$. These features appear to be due to dynamic screening of the electron-electron interaction by polar optical phonons and hence do not require additional mechanisms for their explanation.