The name is absent

22

where i = 0.1,..., n; D_i indicates the number of death at time t_i∙, S_i indicates the
number of survival at time t_i∕, N_i indicates the number of objects at risk at time t_i.

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 Z_i, ...,Z⅛.

A(i∣Zι,...,Z_fe) = λ_o{t)e⁰^⁺-⁺^-

= λ₀(t')exp(Z' β)∙,                       (2.16)

Partial likelihood function:

-∣-ι- λp(t)exp{Z β}

ɪl Σ Ao(i)eτp(Z'√3)

j∈H(ti)

-∩- exp(Z'β)

ɪɪ ∑ exp{Z'_jβ)

j∈B(t_i)

ɪɪ exp(Z'β) ,

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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