13_AS_3_lec_a

J zxj zyj p t zy exp z j 1 j yj j 1 is constant

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Unformatted text preview: es Relative risk The ratio of hazard rates of two diﬀerent lives x and y , p p βj zxj exp j =1 λ (t ; Zx ) = = exp βj {zxj − zyj } p λ (t ; Zy ) exp βz j =1 j yj j =1 is constant at all times, which explains the qualiﬁcation of proportional hazards model. This ratio is also called the relative risk of an individual with risk factor Zx as compared to an individual with risk factor Zy . 9/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model On the proportionality of hazard rates Advantages of proportionality Under the Cox model, diﬀerences of hazard rates of diﬀerent groups (diﬀerent covariates) are accounted for via the exponential term (linear function inside the exponential), which leads to a simple expression for the relative risk The Cox model is not the only model with proportional hazards; one can generalise Cox to λ(t ; Zi ) = λ0 (t )g (Zi ) where g (Z ) is any function of Z , but not t . If we are only interested in the diﬀerence due to covariates and NOT the baseline hazard - we can ignore λo (t ) and concentrate on the function g (Z ) only (β terms in Cox). 10/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model On the proportionality of hazard rates Example The following data for each patient have been recorded: 0 for females 1 if patient attended Hospital B Z1 = Z2 = 1 for males 0 otherwise Z3 = 1 0 if patient attended Hosp...
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This document was uploaded on 04/03/2014.

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