Survival Analysis Using SAS®: A Practical Guide

Partial Likelihood

What’s remarkable about partial likelihood is that you can estimate the β coefficients of the proportional hazards model without having to specify the baseline hazard function λ₀(t). In this section, we will

• consider some general properties of partial likelihood

• look at two simple examples using PROC PHREG

• examine the mathematics of the method in some detail.

The likelihood function for the proportional hazards model of equation (5.1) can be factored into two parts:

• one part depends on both λ₀(t) and β (the vector of coefficients)

• the other part depends on β alone.

What partial likelihood does, in effect, is discard the first part and treat the second part—the partial likelihood function—as though it were an ordinary likelihood ...