# Can I estimate the COX regression using OLS

I am wondering if I can estimate the Cox regression $$h(t,z)= h_0(t)exp(\beta_1 z_1+\dots+\beta_x z_x)$$ model using OLS. The idea would be to rewrite the model with regards to the structure of a simple linear regression. This would allow me to estimate with OLS: $$\log(h(t,z)/h_0(t))$$

This would be beneficial for a proof I am working on. In the case this works, I would be interested in what $$h_0(t)$$ is. Can we estimate the $$h_0(t)$$ for human beings?

First, there is no single "$$h_0(t)$$ for human beings" that applies in all situations. This page shows a plot of hazard of death as a function of age from birth to age 100 for the US in 2003. But this hazard necessarily represents an average over the population, which would be hard to translate to a hazard function representing the baseline covariate values for your study. Furthermore, many applications of survival analysis don't cover the entire lifespan. For example, survival studies of adult cancer patients would be restricted to the latter parts of the age range. You want to have a baseline $$h_0(t)$$ that is as specific as possible to the population of interest, estimated from your sample of the population. For example, comparing different cancer treatments would use hazard functions for patients with that particular type of cancer, not hazards for the general population.
Second, the hazard function $$h(t)$$ is the instantaneous hazard: the risk of an event given that you haven't yet had an event. So at any time $$T$$ you have to consider the entire history of $$h(t)$$ up to that time, the cumulative hazard, to get the probability of having already survived that long. So the simple OLS approach you seem to be proposing wouldn't work.