13_AS_3_lec_a

The numerator depends on information for the

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Unformatted text preview: j ) 16/45 This is a partial likelihood since it considers only likelihood of the deaths (censored observations contribute to the denominator) and does not depend on the times of death (just the order) (this is different to the Kaplan Meier approach). The numerator depends on information for the individual who experiences death; The denominator utilises information about all information about all lives who have not yet experienced death. ˆ β are asymptotically normal Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Estimation of the regression parameters β Example A group of seven lives was observed over a period of time as part of a mortality investigation. Each of the lives was under observation at all ages from age 45 until death or policy expiry: Life 1 2 3 4 5 6 7 Sex F M F M M M F Age at Exit 47 50 52 55 64 65 65 Reason L D D L D L L where “L” means “Lapse” and “D” denotes “Death”. 17/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Estimation of the regression parameters β The following proportional hazards model has been proposed: λ(t ; Z ) = λ0 (t ) e β Z where Z = 1 for males and 0 for females. Write down the partial likelihood. 18/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model...
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