There is a relationship between proportional hazards models and Poisson regression models which is sometimes used to fit approximate proportional hazards models in software for Poisson regression. The usual reason for doing this is that calculation is much quicker.
There is a correlation between proportional hazards models and Poisson regression models, which can be exploited to approximate proportional hazards models in software optimized for Poisson regression. The rationale for adopting this method is that it accelerates computational processes.