Proportional Hazards Models - Relationship To Poisson Models

Relationship To Poisson Models

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. This was more important in the days of slower computers but can still be useful for particularly large data sets or complex problems. Authors giving the mathematical details include Laird and Olivier (1981), who remark

"Note that we do not assume is true, but simply use it as a device for deriving the likelihood."

The book on generalized linear models by McCullagh and Nelder has a chapter on converting proportional hazards models to generalized linear models.