Proportional Hazard Model:

Proportional hazard model is a generic term for models (particularly survival models in medicine) that have the form

where L is the hazard function or hazard rate, {x_i} are covariates, {b_i} are coefficients of the model - effects of the corresponding covariates, and h(t) gives the effect of duration on the hazard rate.

In a proportional hazard model, the effect of an independent variable on the hazard rate is assumed to be multiplicative. For example, the variable "smoking" in a model might have the effect of increasing the hazard rate 30%.

Examples of proportional hazard model are exponential, Weibull, and Gompertz models given respectively by

Cox proposed an ingenious principle for estimating all proportional hazard models without knowing the function h(t) or even the base hazard rate h₀(t). Using this principle one estimates the effects {b_i} of the covariates {x_i}, but not the effect of duration h(t).

This is known as the Cox Proportional Hazard Model.