13_AS_3_lec_a

zip example consider the covariate vector zi sex

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Unformatted text preview: k factors) by a 1 × p vector Zi = (zi 1 , zi 2 , . . . , zip ) Example: Consider the covariate vector Zi = (sex, age, weight, symptoms). If the 3rd life is a 68 year old male, weighing 74kg, with mild symptoms of the condition under investigation (graded as 1 on a scale of 0 to 5), then we have Z3 = (0, 68, 74, 1). 5/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Main assumptions 1 Introduction 2 Main assumptions 3 On the proportionality of hazard rates 4 Estimation of the regression parameters β 5 Hypothesis tests on the β ’s 6 Estimation of the full survival function 7 Diagnostics for the Cox regression model 5/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Main assumptions Let the hazard function for the i th life with covariates Zi be p λ (t ; Zi ) = λo (t ) exp β ZiT = λo (t ) exp βj zij j =1 where: λo (t ) is the baseline hazard β1 , β2 , . . . βp are the regression parameters zi 1 , zi 2 , . . . zip are the covariates for the i th subject Note: In this formulation only λo (t ) depends on time but is independent of the covariates p conversely, exp j =1 βj zij is independent of t but dependent on the covariates 6/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Main assumptions Interpretation - sign of β If βj is positive, the hazard rate increases with the j th covariate, ie there is a positive correlation between hazard rate and the j th cov...
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