13_AS_3_lec_a

If the model is correct and the b s mles are close to

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Unformatted text preview: s 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 35/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Diagnostics for the Cox regression model Diagnostics for the Cox model We will discuss two types of diagnostics: 1 goodness-of-fit via Cox-Snell residuals 2 appropriateness of the proportionality assumption via graphica techniques Notation: Cj : right censoring time δj = 0 means censoring, that is, Xj = 36/45 Cj Tj if δj = 0 . if δj = 1 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Diagnostics for the Cox regression model Cox-Snell residuals The Cox-Snell residuals are defined as p ˆ ˆ ej = − log(S (Xj ; zj )) = Λ0 (Xj ) exp( T bk zjk ) k =1 where b is the MLE of β , and ˆ Λ0 (t ) is Breslow’s estimator of the cumulative baseline hazard rate. If the model is correct and the b ’s (MLEs) are close to the true values of β , then the Cox-Snell residuals ej ’s behave as a...
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