13_AS_3_lec_a

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online