The Cox proportional hazards model for survival data with covariate ${\bf z}$ is defined through the hazard function $h(t,{\bf z})$ by $$ h(t,{\bf z}) = h_0(t)~\cdot\theta~~,~~~\theta = \theta(\beta, {\bf z}).$$The porportional odds model is sometimes given by
$$ O(t,{\bf z}) = O_0(t)\cdot\theta $$ where
$O_0(t) = O(t,{\bf 0})$ and $$ O(t,{\bf z}) = \frac{1-S(t,{\bf z})}{S(t,{\bf z})}$$ is the odds of an event occurring in the time interval $(0,t)$ for an individual with covariate ${\bf z}.$
My question is this: Is there a way to define the proportional odds model via its hazard function?