13_AS_3_lec_a

031 2 0025 and 3 0011 compare the force of mortality

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Unformatted text preview: ital C 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: Semi-parametric 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: Semi-parametric 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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