22
where i = 0.1,..., n; Di indicates the number of death at time ti∙, Si indicates the
number of survival at time ti∕, Ni indicates the number of objects at risk at time ti.
The survival function calculated by the K-M estimator is a step function. The
K-M estimator is popular due to the simplicity of its calculation and its ease of
interpretation.
2.3.4 Cox regression model
Cox regression model is also called the Relative Risk model. It is a hazard function
including covariates, denoted as Zi, ...,Z⅛.
A(i∣Zι,...,Zfe) = λo{t)e0^+-+^-
= λ0(t')exp(Z' β)∙, (2.16)
Partial likelihood function:
-∣-ι- λp(t)exp{Z β}
L(∕3) =
ɪl Σ Ao(i)eτp(Z'√3)
j∈H(ti)
-∩- exp(Z'β)
ɪɪ ∑ exp{Z'jβ)
j∈B(ti)
ɪɪ exp(Z'β) ,
(2.17)
i=ι [∑e.τp(Z^)]'5fc
fc=l
where δ⅛ is an indicator function. It indicates the number of failures at time к (with
ties).
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