Unformatted text preview: 12/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model
Estimation of the regression parameters β Partial likelihood estimation of β
To estimate β = (β1 , β2 , . . . βp ), we will select the ones that
maximize the partial likelihood under the following assumptions:
lives are independent
Ordered times of observed death are t1 < t2 < · · · < tk
dj : number of deaths occuring at time tj (1 ≤ j ≤ k )
We will label all the lives as 1, · · · , n.
R (tj ) is the set of the label of all lives who are still under
study at a time just prior to tj .
Use (j ) to denote the label of the life who dies at tj
13/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model
Estimation of the regression parameters β Two cases We will distinguish two cases:
1 assume that only one death occurs at each tj
(dj = 1 for 1 ≤ j ≤ k ) 2 Relax that assumption.
In practice there might be ties in the data, that is
2 some dj > 1; or
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This document was uploaded on 04/03/2014.
- Three '14