Nonparametric Methods in Statistics with SAS Applications

COX PROPORTIONAL HAZARDS MODEL 129

where S

0

(t) = exp



−



t

0

h

0

(u)du



is the baseline survival function, and r =

exp



β

1

x

1

+ ···+

β

m

x

m



is the relative risk of an individual. Note that analogous

to the baseline hazard function, the baseline survival function corresponds to an in-

dividual for whom all predictors have zero values.

6.3.2 Estimation of Regression Coefficients and Baseline Survival Function

The regression coefficients

β

1

,...,

β

m

are estimated by the method of partial like-

lihood estimation, where the portion of the likelihood function that has no time-

dependent multiplicative factors is maximized. Suppose distinct ordered event times

are t

1

< ··· <