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Unformatted text preview: Estimation of the regression parameters β Case 2: partial likelihood in present of ties in the data
We will consider Breslow’s approximation:
exp β sjT k L (β ) =
j =1 dj
exp β ZiT i R (tj ) where sj is the sum of the covariate vectors Z of the dj lives
observed to die at time tj .
This approximation works well when the number of ties are
There are other methods (see K&M, Section 8.4) Breslow is the standard approximation in SAS
19/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model
Estimation of the regression parameters β Example
An investigation was carried out into the survival times (measured
in months) of patients in hospital following liver transplants. For
patient i , the covariates are zi 1 = 0 for placebo, 1 for treatment X,
and zi 2 = weight of the patient (measured in kg).
The observed lifetimes (with weights in brackets) were as follows:
Placebo Treatment X
14 (75) 14 (68)
16 (86) 14∗ (49)
Observations with an...
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This document was uploaded on 04/03/2014.
- Three '14