13_AS_3_lec_a

# Note this approximation works well when the number of

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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 . Note: This approximation works well when the number of ties are relatively small 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 3 (83) 6∗ (58) 9 (68) 11 (73) 14 (75) 14 (68) 16 (86) 14∗ (49) Observations with an...
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## This document was uploaded on 04/03/2014.

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