Healthcare Data Analytics

A Review of Clinical Prediction Models 363

it do es not specify th e form of λ

0

(t); in fact, the hazard ratio does not depend on the baseline hazard

function; for two ind ividuals, th e hazard ratio is

λ(t, X

1

)

λ(t, X

2

)

=

λ

0

(t)exp(X

1

β)

λ

0

(t)exp(X

2

β)

= exp[(X

1

−X

2

)β]. (10.42)

Since the hazard ratio is a constant, and all the subjects share the same baseline hazard function , the

Cox model is a propor tional hazards model. Based on this Cox assumption the survival function is

given by

S(t) = exp(−Λ

0

(t)exp(Xβ)) = S

0

(t)

exp(X β)

(10.43)

where Λ

0

(t) is the c umulative baseline hazard function , and S

0

(t) = exp(−Λ

0

(t)) is the baseline

survival fu nction.

10.4.3.2