Survival Analysis Using SAS®: A Practical Guide

Unobserved Heterogeneity

An implicit assumption of all the hazard models we have considered so far is that if two individuals have identical values on the covariates, they also have identical hazard functions. If there are no covariates in the model, then the entire sample is presumed to have a single hazard function. Obviously, this is an unrealistic assumption. Individuals and their environments differ in so many respects that no set of measured covariates can possibly capture all the variation among them. In an ordinary linear regression model, this residual or unobserved heterogeneity is explicitly represented by a random disturbance term, for example,

y = βx + ε

where ε represents all unmeasured sources of variation in y. But in a Cox regression ...