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Unformatted text preview: k factors) by a
1 × p vector
Zi = (zi 1 , zi 2 , . . . , zip )
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
In this formulation only λo (t ) depends on time but is
independent of the covariates
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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- Three '14