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otherwise
T Suppose the force of mortality at time t is modelled by λ0 (t )e β Z
ˆ
and the parameter values have been estimated to be β1 = 0.031,
ˆ2 = −0.025 and β3 = 0.011.
ˆ
β
Compare the force of mortality for a female patient who attended
Hospital A with that of:
1
2
11/45 a female patient who attended Hospital B
a male patient who attended Hospital C Actuarial Statistics – Module 3: Semiparametric methods: Cox Regression Model
On the proportionality of hazard rates Solution
1 The hazard rate at time t for a female who attended Hospital
A is
λfemale ,A (t ) = λ0 (t )
and the hazard rate at time t for a female who attended
Hospital B is
λfemale ,B (t ) = λ0 (t )e −0.025
The ratio is
λfemale ,A (t )
= e 0.025 = 1.0253
λfemale ,B (t ) 12/45 2 So we estimate that the hazard rate for a female who
attended Hospital A is 2.53% higher than that of a female
who attended Hospital B.
ratio: e −0.042 = 0.9589 Actuarial Statistics – Module 3: Semiparametric methods: Cox Regression Model
Estimation of the regression parameters β 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...
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This document was uploaded on 04/03/2014.
 Three '14

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