Cox proportional-hazards model

The Cox model writes $h(t\mid z)=h_0(t)e^{{\beta }^{T}z}$ with an unspecified baseline hazard.

The Cox partial likelihood conditions each event on its risk set, eliminating the baseline hazard.

A stratified Cox model gives each stratum its own baseline hazard while sharing regression coefficients.

A stratum is a subgroup assigned its own nuisance baseline.